Added RSA key generation code (i15, i31, i62).
This commit is contained in:
Thomas Pornin
parent
a0054ad821
commit
491a45337d
15 changed files with 2865 additions and 13 deletions
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@ -84,7 +84,7 @@ extern "C" {
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* random masking, but "true" constant-time code.
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*
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* - They support only private keys with two prime factors. RSA private
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* key with three or more prime factors are nominally supported, but
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* keys with three or more prime factors are nominally supported, but
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* rarely used; they may offer faster operations, at the expense of
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* more code and potentially a reduction in security if there are
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* "too many" prime factors.
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@ -92,7 +92,7 @@ extern "C" {
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* - The public exponent may have arbitrary length. Of course, it is
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* a good idea to keep public exponents small, so that public key
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* operations are fast; but, contrary to some widely deployed
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* implementations, BearSSL has no problem with public exponent
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* implementations, BearSSL has no problem with public exponents
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* longer than 32 bits.
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*
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* - The two prime factors of the modulus need not have the same length
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@ -170,7 +170,7 @@ typedef struct {
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/**
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* \brief RSA private key.
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*
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* The structure references the primvate factors, reduced private
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* The structure references the private factors, reduced private
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* exponents, and CRT coefficient. It also contains the bit length of
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* the modulus. The big integers use unsigned big-endian representation;
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* extra leading bytes of value 0 are allowed. However, the modulus bit
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@ -1032,6 +1032,158 @@ uint32_t br_rsa_i62_oaep_decrypt(
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const br_hash_class *dig, const void *label, size_t label_len,
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const br_rsa_private_key *sk, void *data, size_t *len);
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/**
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* \brief Get buffer size to hold RSA private key elements.
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*
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* This macro returns the length (in bytes) of the buffer needed to
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* receive the elements of a RSA private key, as generated by one of
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* the `br_rsa_*_keygen()` functions. If the provided size is a constant
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* expression, then the whole macro evaluates to a constant expression.
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*
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* \param size target key size (modulus size, in bits)
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* \return the length of the private key buffer, in bytes.
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*/
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#define BR_RSA_KBUF_PRIV_SIZE(size) (5 * (((size) + 15) >> 4))
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/**
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* \brief Get buffer size to hold RSA public key elements.
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*
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* This macro returns the length (in bytes) of the buffer needed to
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* receive the elements of a RSA public key, as generated by one of
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* the `br_rsa_*_keygen()` functions. If the provided size is a constant
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* expression, then the whole macro evaluates to a constant expression.
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*
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* \param size target key size (modulus size, in bits)
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* \return the length of the public key buffer, in bytes.
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*/
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#define BR_RSA_KBUF_PUB_SIZE(size) (4 + (((size) + 7) >> 3))
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/**
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* \brief Type for RSA key pair generator implementation.
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*
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* This function generates a new RSA key pair whose modulus has bit
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* length `size` bits. The private key elements are written in the
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* `kbuf_priv` buffer, and pointer values and length fields to these
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* elements are populated in the provided private key structure `sk`.
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* Similarly, the public key elements are written in `kbuf_pub`, with
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* pointers and lengths set in `pk`.
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*
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* If `sk` is `NULL`, then `kbuf_pub` may be `NULL`, and only the
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* private key is set.
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*
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* If `pubexp` is not zero, then its value will be used as public
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* exponent. Valid RSA public exponent values are odd integers
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* greater than 1. If `pubexp` is zero, then the public exponent will
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* have value 3.
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*
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* The provided PRNG (`rng_ctx`) must have already been initialized
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* and seeded.
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*
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* Returned value is 1 on success, 0 on error. An error is reported
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* if the requested range is outside of the supported key sizes, or
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* if an invalid non-zero public exponent value is provided. Supported
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* range starts at 512 bits, and up to an implementation-defined
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* maximum (by default 4096 bits). Note that key sizes up to 768 bits
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* have been broken in practice, and sizes lower than 2048 bits are
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* usually considered to be weak and should not be used.
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*
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* \param rng_ctx source PRNG context (already initialized)
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* \param sk RSA private key structure (destination)
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* \param kbuf_priv buffer for private key elements
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* \param pk RSA public key structure (destination), or `NULL`
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* \param kbuf_pub buffer for public key elements, or `NULL`
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* \param size target RSA modulus size (in bits)
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* \param pubexp public exponent to use, or zero
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* \return 1 on success, 0 on error (invalid parameters)
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*/
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typedef uint32_t (*br_rsa_keygen)(
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const br_prng_class **rng_ctx,
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br_rsa_private_key *sk, unsigned char *kbuf_priv,
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br_rsa_public_key *pk, unsigned char *kbuf_pub,
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unsigned size, uint32_t pubexp);
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/**
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* \brief RSA key pair generation with the "i15" engine.
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*
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* \see br_rsa_keygen
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*
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* \param rng_ctx source PRNG context (already initialized)
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* \param sk RSA private key structure (destination)
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* \param kbuf_priv buffer for private key elements
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* \param pk RSA public key structure (destination), or `NULL`
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* \param kbuf_pub buffer for public key elements, or `NULL`
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* \param size target RSA modulus size (in bits)
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* \param pubexp public exponent to use, or zero
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* \return 1 on success, 0 on error (invalid parameters)
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*/
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uint32_t br_rsa_i15_keygen(
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const br_prng_class **rng_ctx,
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br_rsa_private_key *sk, unsigned char *kbuf_priv,
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br_rsa_public_key *pk, unsigned char *kbuf_pub,
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unsigned size, uint32_t pubexp);
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/**
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* \brief RSA key pair generation with the "i31" engine.
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*
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* \see br_rsa_keygen
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*
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* \param rng_ctx source PRNG context (already initialized)
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* \param sk RSA private key structure (destination)
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* \param kbuf_priv buffer for private key elements
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* \param pk RSA public key structure (destination), or `NULL`
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* \param kbuf_pub buffer for public key elements, or `NULL`
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* \param size target RSA modulus size (in bits)
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* \param pubexp public exponent to use, or zero
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* \return 1 on success, 0 on error (invalid parameters)
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*/
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uint32_t br_rsa_i31_keygen(
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const br_prng_class **rng_ctx,
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br_rsa_private_key *sk, unsigned char *kbuf_priv,
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br_rsa_public_key *pk, unsigned char *kbuf_pub,
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unsigned size, uint32_t pubexp);
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/**
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* \brief RSA key pair generation with the "i62" engine.
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*
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* This function is defined only on architecture that offer a 64x64->128
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* opcode. Use `br_rsa_i62_keygen_get()` to dynamically obtain a pointer
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* to that function.
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*
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* \see br_rsa_keygen
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*
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* \param rng_ctx source PRNG context (already initialized)
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* \param sk RSA private key structure (destination)
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* \param kbuf_priv buffer for private key elements
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* \param pk RSA public key structure (destination), or `NULL`
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* \param kbuf_pub buffer for public key elements, or `NULL`
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* \param size target RSA modulus size (in bits)
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* \param pubexp public exponent to use, or zero
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* \return 1 on success, 0 on error (invalid parameters)
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*/
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uint32_t br_rsa_i62_keygen(
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const br_prng_class **rng_ctx,
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br_rsa_private_key *sk, unsigned char *kbuf_priv,
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br_rsa_public_key *pk, unsigned char *kbuf_pub,
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unsigned size, uint32_t pubexp);
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/**
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* \brief Get the RSA "i62" implementation (key pair generation),
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* if available.
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*
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* \return the implementation, or 0.
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*/
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br_rsa_keygen br_rsa_i62_keygen_get(void);
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/**
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* \brief Get "default" RSA implementation (key pair generation).
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*
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* This returns the preferred implementation of RSA (key pair generation)
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* on the current system.
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*
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* \return the default implementation.
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*/
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br_rsa_keygen br_rsa_keygen_get_default(void);
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#ifdef __cplusplus
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}
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#endif
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28
mk/Rules.mk
28
mk/Rules.mk
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@ -72,6 +72,7 @@ OBJ = \
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$(OBJDIR)$Pi15_encode$O \
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$(OBJDIR)$Pi15_fmont$O \
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$(OBJDIR)$Pi15_iszero$O \
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$(OBJDIR)$Pi15_moddiv$O \
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$(OBJDIR)$Pi15_modpow$O \
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$(OBJDIR)$Pi15_modpow2$O \
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$(OBJDIR)$Pi15_montmul$O \
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@ -90,6 +91,7 @@ OBJ = \
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$(OBJDIR)$Pi31_encode$O \
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$(OBJDIR)$Pi31_fmont$O \
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$(OBJDIR)$Pi31_iszero$O \
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$(OBJDIR)$Pi31_moddiv$O \
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$(OBJDIR)$Pi31_modpow$O \
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$(OBJDIR)$Pi31_modpow2$O \
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$(OBJDIR)$Pi31_montmul$O \
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@ -122,18 +124,22 @@ OBJ = \
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$(OBJDIR)$Phmac_ct$O \
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$(OBJDIR)$Phmac_drbg$O \
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$(OBJDIR)$Psysrng$O \
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$(OBJDIR)$Prsa_default_keygen$O \
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$(OBJDIR)$Prsa_default_oaep_decrypt$O \
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$(OBJDIR)$Prsa_default_oaep_encrypt$O \
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$(OBJDIR)$Prsa_default_pkcs1_sign$O \
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$(OBJDIR)$Prsa_default_pkcs1_vrfy$O \
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$(OBJDIR)$Prsa_default_priv$O \
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$(OBJDIR)$Prsa_default_pub$O \
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$(OBJDIR)$Prsa_i15_keygen$O \
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$(OBJDIR)$Prsa_i15_oaep_decrypt$O \
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$(OBJDIR)$Prsa_i15_oaep_encrypt$O \
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$(OBJDIR)$Prsa_i15_pkcs1_sign$O \
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$(OBJDIR)$Prsa_i15_pkcs1_vrfy$O \
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$(OBJDIR)$Prsa_i15_priv$O \
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$(OBJDIR)$Prsa_i15_pub$O \
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$(OBJDIR)$Prsa_i31_keygen$O \
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$(OBJDIR)$Prsa_i31_keygen_inner$O \
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$(OBJDIR)$Prsa_i31_oaep_decrypt$O \
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$(OBJDIR)$Prsa_i31_oaep_encrypt$O \
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$(OBJDIR)$Prsa_i31_pkcs1_sign$O \
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@ -146,6 +152,7 @@ OBJ = \
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$(OBJDIR)$Prsa_i32_pkcs1_vrfy$O \
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$(OBJDIR)$Prsa_i32_priv$O \
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$(OBJDIR)$Prsa_i32_pub$O \
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$(OBJDIR)$Prsa_i62_keygen$O \
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$(OBJDIR)$Prsa_i62_oaep_decrypt$O \
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$(OBJDIR)$Prsa_i62_oaep_encrypt$O \
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$(OBJDIR)$Prsa_i62_pkcs1_sign$O \
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@ -544,6 +551,9 @@ $(OBJDIR)$Pi15_fmont$O: src$Pint$Pi15_fmont.c $(HEADERSPRIV)
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$(OBJDIR)$Pi15_iszero$O: src$Pint$Pi15_iszero.c $(HEADERSPRIV)
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$(CC) $(CFLAGS) $(INCFLAGS) $(CCOUT)$(OBJDIR)$Pi15_iszero$O src$Pint$Pi15_iszero.c
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$(OBJDIR)$Pi15_moddiv$O: src$Pint$Pi15_moddiv.c $(HEADERSPRIV)
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$(CC) $(CFLAGS) $(INCFLAGS) $(CCOUT)$(OBJDIR)$Pi15_moddiv$O src$Pint$Pi15_moddiv.c
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$(OBJDIR)$Pi15_modpow$O: src$Pint$Pi15_modpow.c $(HEADERSPRIV)
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$(CC) $(CFLAGS) $(INCFLAGS) $(CCOUT)$(OBJDIR)$Pi15_modpow$O src$Pint$Pi15_modpow.c
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@ -598,6 +608,9 @@ $(OBJDIR)$Pi31_fmont$O: src$Pint$Pi31_fmont.c $(HEADERSPRIV)
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$(OBJDIR)$Pi31_iszero$O: src$Pint$Pi31_iszero.c $(HEADERSPRIV)
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$(CC) $(CFLAGS) $(INCFLAGS) $(CCOUT)$(OBJDIR)$Pi31_iszero$O src$Pint$Pi31_iszero.c
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$(OBJDIR)$Pi31_moddiv$O: src$Pint$Pi31_moddiv.c $(HEADERSPRIV)
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$(CC) $(CFLAGS) $(INCFLAGS) $(CCOUT)$(OBJDIR)$Pi31_moddiv$O src$Pint$Pi31_moddiv.c
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$(OBJDIR)$Pi31_modpow$O: src$Pint$Pi31_modpow.c $(HEADERSPRIV)
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$(CC) $(CFLAGS) $(INCFLAGS) $(CCOUT)$(OBJDIR)$Pi31_modpow$O src$Pint$Pi31_modpow.c
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@ -694,6 +707,9 @@ $(OBJDIR)$Phmac_drbg$O: src$Prand$Phmac_drbg.c $(HEADERSPRIV)
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$(OBJDIR)$Psysrng$O: src$Prand$Psysrng.c $(HEADERSPRIV)
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$(CC) $(CFLAGS) $(INCFLAGS) $(CCOUT)$(OBJDIR)$Psysrng$O src$Prand$Psysrng.c
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$(OBJDIR)$Prsa_default_keygen$O: src$Prsa$Prsa_default_keygen.c $(HEADERSPRIV)
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$(CC) $(CFLAGS) $(INCFLAGS) $(CCOUT)$(OBJDIR)$Prsa_default_keygen$O src$Prsa$Prsa_default_keygen.c
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$(OBJDIR)$Prsa_default_oaep_decrypt$O: src$Prsa$Prsa_default_oaep_decrypt.c $(HEADERSPRIV)
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$(CC) $(CFLAGS) $(INCFLAGS) $(CCOUT)$(OBJDIR)$Prsa_default_oaep_decrypt$O src$Prsa$Prsa_default_oaep_decrypt.c
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@ -712,6 +728,9 @@ $(OBJDIR)$Prsa_default_priv$O: src$Prsa$Prsa_default_priv.c $(HEADERSPRIV)
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$(OBJDIR)$Prsa_default_pub$O: src$Prsa$Prsa_default_pub.c $(HEADERSPRIV)
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$(CC) $(CFLAGS) $(INCFLAGS) $(CCOUT)$(OBJDIR)$Prsa_default_pub$O src$Prsa$Prsa_default_pub.c
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$(OBJDIR)$Prsa_i15_keygen$O: src$Prsa$Prsa_i15_keygen.c $(HEADERSPRIV)
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$(CC) $(CFLAGS) $(INCFLAGS) $(CCOUT)$(OBJDIR)$Prsa_i15_keygen$O src$Prsa$Prsa_i15_keygen.c
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$(OBJDIR)$Prsa_i15_oaep_decrypt$O: src$Prsa$Prsa_i15_oaep_decrypt.c $(HEADERSPRIV)
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$(CC) $(CFLAGS) $(INCFLAGS) $(CCOUT)$(OBJDIR)$Prsa_i15_oaep_decrypt$O src$Prsa$Prsa_i15_oaep_decrypt.c
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@ -730,6 +749,12 @@ $(OBJDIR)$Prsa_i15_priv$O: src$Prsa$Prsa_i15_priv.c $(HEADERSPRIV)
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$(OBJDIR)$Prsa_i15_pub$O: src$Prsa$Prsa_i15_pub.c $(HEADERSPRIV)
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$(CC) $(CFLAGS) $(INCFLAGS) $(CCOUT)$(OBJDIR)$Prsa_i15_pub$O src$Prsa$Prsa_i15_pub.c
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$(OBJDIR)$Prsa_i31_keygen$O: src$Prsa$Prsa_i31_keygen.c $(HEADERSPRIV)
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$(CC) $(CFLAGS) $(INCFLAGS) $(CCOUT)$(OBJDIR)$Prsa_i31_keygen$O src$Prsa$Prsa_i31_keygen.c
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$(OBJDIR)$Prsa_i31_keygen_inner$O: src$Prsa$Prsa_i31_keygen_inner.c $(HEADERSPRIV)
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$(CC) $(CFLAGS) $(INCFLAGS) $(CCOUT)$(OBJDIR)$Prsa_i31_keygen_inner$O src$Prsa$Prsa_i31_keygen_inner.c
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$(OBJDIR)$Prsa_i31_oaep_decrypt$O: src$Prsa$Prsa_i31_oaep_decrypt.c $(HEADERSPRIV)
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$(CC) $(CFLAGS) $(INCFLAGS) $(CCOUT)$(OBJDIR)$Prsa_i31_oaep_decrypt$O src$Prsa$Prsa_i31_oaep_decrypt.c
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@ -766,6 +791,9 @@ $(OBJDIR)$Prsa_i32_priv$O: src$Prsa$Prsa_i32_priv.c $(HEADERSPRIV)
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$(OBJDIR)$Prsa_i32_pub$O: src$Prsa$Prsa_i32_pub.c $(HEADERSPRIV)
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$(CC) $(CFLAGS) $(INCFLAGS) $(CCOUT)$(OBJDIR)$Prsa_i32_pub$O src$Prsa$Prsa_i32_pub.c
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$(OBJDIR)$Prsa_i62_keygen$O: src$Prsa$Prsa_i62_keygen.c $(HEADERSPRIV)
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$(CC) $(CFLAGS) $(INCFLAGS) $(CCOUT)$(OBJDIR)$Prsa_i62_keygen$O src$Prsa$Prsa_i62_keygen.c
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$(OBJDIR)$Prsa_i62_oaep_decrypt$O: src$Prsa$Prsa_i62_oaep_decrypt.c $(HEADERSPRIV)
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$(CC) $(CFLAGS) $(INCFLAGS) $(CCOUT)$(OBJDIR)$Prsa_i62_oaep_decrypt$O src$Prsa$Prsa_i62_oaep_decrypt.c
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@ -120,6 +120,7 @@ coresrc=" \
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src/int/i15_encode.c \
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src/int/i15_fmont.c \
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src/int/i15_iszero.c \
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src/int/i15_moddiv.c \
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src/int/i15_modpow.c \
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src/int/i15_modpow2.c \
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src/int/i15_montmul.c \
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@ -138,6 +139,7 @@ coresrc=" \
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src/int/i31_encode.c \
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src/int/i31_fmont.c \
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src/int/i31_iszero.c \
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src/int/i31_moddiv.c \
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src/int/i31_modpow.c \
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src/int/i31_modpow2.c \
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src/int/i31_montmul.c \
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@ -170,18 +172,22 @@ coresrc=" \
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src/mac/hmac_ct.c \
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src/rand/hmac_drbg.c \
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src/rand/sysrng.c \
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src/rsa/rsa_default_keygen.c \
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src/rsa/rsa_default_oaep_decrypt.c \
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src/rsa/rsa_default_oaep_encrypt.c \
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src/rsa/rsa_default_pkcs1_sign.c \
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src/rsa/rsa_default_pkcs1_vrfy.c \
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src/rsa/rsa_default_priv.c \
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src/rsa/rsa_default_pub.c \
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src/rsa/rsa_i15_keygen.c \
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src/rsa/rsa_i15_oaep_decrypt.c \
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src/rsa/rsa_i15_oaep_encrypt.c \
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src/rsa/rsa_i15_pkcs1_sign.c \
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src/rsa/rsa_i15_pkcs1_vrfy.c \
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src/rsa/rsa_i15_priv.c \
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src/rsa/rsa_i15_pub.c \
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src/rsa/rsa_i31_keygen.c \
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src/rsa/rsa_i31_keygen_inner.c \
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src/rsa/rsa_i31_oaep_decrypt.c \
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src/rsa/rsa_i31_oaep_encrypt.c \
|
||||
src/rsa/rsa_i31_pkcs1_sign.c \
|
||||
|
|
@ -194,6 +200,7 @@ coresrc=" \
|
|||
src/rsa/rsa_i32_pkcs1_vrfy.c \
|
||||
src/rsa/rsa_i32_priv.c \
|
||||
src/rsa/rsa_i32_pub.c \
|
||||
src/rsa/rsa_i62_keygen.c \
|
||||
src/rsa/rsa_i62_oaep_decrypt.c \
|
||||
src/rsa/rsa_i62_oaep_encrypt.c \
|
||||
src/rsa/rsa_i62_pkcs1_sign.c \
|
||||
|
|
|
|||
67
src/inner.h
67
src/inner.h
|
|
@ -48,10 +48,22 @@
|
|||
* already set their root keys to RSA-4096, so we should be able to
|
||||
* process such keys.
|
||||
*
|
||||
* This value MUST be a multiple of 64.
|
||||
* This value MUST be a multiple of 64. This value MUST NOT exceed 47666
|
||||
* (some computations in RSA key generation rely on the factor size being
|
||||
* no more than 23833 bits). RSA key sizes beyond 3072 bits don't make a
|
||||
* lot of sense anyway.
|
||||
*/
|
||||
#define BR_MAX_RSA_SIZE 4096
|
||||
|
||||
/*
|
||||
* Minimum size for a RSA modulus (in bits); this value is used only to
|
||||
* filter out invalid parameters for key pair generation. Normally,
|
||||
* applications should not use RSA keys smaller than 2048 bits; but some
|
||||
* specific cases might need shorter keys, for legacy or research
|
||||
* purposes.
|
||||
*/
|
||||
#define BR_MIN_RSA_SIZE 512
|
||||
|
||||
/*
|
||||
* Maximum size for a RSA factor (in bits). This is for RSA private-key
|
||||
* operations. Default is to support factors up to a bit more than half
|
||||
|
|
@ -1474,6 +1486,23 @@ uint32_t br_i31_modpow_opt(uint32_t *x, const unsigned char *e, size_t elen,
|
|||
*/
|
||||
void br_i31_mulacc(uint32_t *d, const uint32_t *a, const uint32_t *b);
|
||||
|
||||
/*
|
||||
* Compute x/y mod m, result in x. Values x and y must be between 0 and
|
||||
* m-1, and have the same announced bit length as m. Modulus m must be
|
||||
* odd. The "m0i" parameter is equal to -1/m mod 2^31. The array 't'
|
||||
* must point to a temporary area that can hold at least three integers
|
||||
* of the size of m.
|
||||
*
|
||||
* m may not overlap x and y. x and y may overlap each other (this can
|
||||
* be useful to test whether a value is invertible modulo m). t must be
|
||||
* disjoint from all other arrays.
|
||||
*
|
||||
* Returned value is 1 on success, 0 otherwise. Success is attained if
|
||||
* y is invertible modulo m.
|
||||
*/
|
||||
uint32_t br_i31_moddiv(uint32_t *x, const uint32_t *y,
|
||||
const uint32_t *m, uint32_t m0i, uint32_t *t);
|
||||
|
||||
/* ==================================================================== */
|
||||
|
||||
/*
|
||||
|
|
@ -1528,9 +1557,36 @@ void br_i15_reduce(uint16_t *x, const uint16_t *a, const uint16_t *m);
|
|||
|
||||
void br_i15_mulacc(uint16_t *d, const uint16_t *a, const uint16_t *b);
|
||||
|
||||
uint32_t br_i15_moddiv(uint16_t *x, const uint16_t *y,
|
||||
const uint16_t *m, uint16_t m0i, uint16_t *t);
|
||||
|
||||
/*
|
||||
* Variant of br_i31_modpow_opt() that internally uses 64x64->128
|
||||
* multiplications. It expects the same parameters as br_i31_modpow_opt(),
|
||||
* except that the temporaries should be 64-bit integers, not 32-bit
|
||||
* integers.
|
||||
*/
|
||||
uint32_t br_i62_modpow_opt(uint32_t *x31, const unsigned char *e, size_t elen,
|
||||
const uint32_t *m31, uint32_t m0i31, uint64_t *tmp, size_t twlen);
|
||||
|
||||
/*
|
||||
* Type for a function with the same API as br_i31_modpow_opt() (some
|
||||
* implementations of this type may have stricter alignment requirements
|
||||
* on the temporaries).
|
||||
*/
|
||||
typedef uint32_t (*br_i31_modpow_opt_type)(uint32_t *x,
|
||||
const unsigned char *e, size_t elen,
|
||||
const uint32_t *m, uint32_t m0i, uint32_t *tmp, size_t twlen);
|
||||
|
||||
/*
|
||||
* Wrapper for br_i62_modpow_opt() that uses the same type as
|
||||
* br_i31_modpow_opt(); however, it requires its 'tmp' argument to the
|
||||
* 64-bit aligned.
|
||||
*/
|
||||
uint32_t br_i62_modpow_opt_as_i31(uint32_t *x,
|
||||
const unsigned char *e, size_t elen,
|
||||
const uint32_t *m, uint32_t m0i, uint32_t *tmp, size_t twlen);
|
||||
|
||||
/* ==================================================================== */
|
||||
|
||||
static inline size_t
|
||||
|
|
@ -1912,6 +1968,15 @@ uint32_t br_rsa_oaep_unpad(const br_hash_class *dig,
|
|||
void br_mgf1_xor(void *data, size_t len,
|
||||
const br_hash_class *dig, const void *seed, size_t seed_len);
|
||||
|
||||
/*
|
||||
* Inner function for RSA key generation; used by the "i31" and "i62"
|
||||
* implementations.
|
||||
*/
|
||||
uint32_t br_rsa_i31_keygen_inner(const br_prng_class **rng,
|
||||
br_rsa_private_key *sk, unsigned char *kbuf_priv,
|
||||
br_rsa_public_key *pk, unsigned char *kbuf_pub,
|
||||
unsigned size, uint32_t pubexp, br_i31_modpow_opt_type mp31);
|
||||
|
||||
/* ==================================================================== */
|
||||
/*
|
||||
* Elliptic curves.
|
||||
|
|
|
|||
465
src/int/i15_moddiv.c
Normal file
465
src/int/i15_moddiv.c
Normal file
|
|
@ -0,0 +1,465 @@
|
|||
/*
|
||||
* Copyright (c) 2018 Thomas Pornin <pornin@bolet.org>
|
||||
*
|
||||
* Permission is hereby granted, free of charge, to any person obtaining
|
||||
* a copy of this software and associated documentation files (the
|
||||
* "Software"), to deal in the Software without restriction, including
|
||||
* without limitation the rights to use, copy, modify, merge, publish,
|
||||
* distribute, sublicense, and/or sell copies of the Software, and to
|
||||
* permit persons to whom the Software is furnished to do so, subject to
|
||||
* the following conditions:
|
||||
*
|
||||
* The above copyright notice and this permission notice shall be
|
||||
* included in all copies or substantial portions of the Software.
|
||||
*
|
||||
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
|
||||
* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
|
||||
* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
|
||||
* NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
|
||||
* BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
|
||||
* ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
|
||||
* CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
|
||||
* SOFTWARE.
|
||||
*/
|
||||
|
||||
#include "inner.h"
|
||||
|
||||
/*
|
||||
* In this file, we handle big integers with a custom format, i.e.
|
||||
* without the usual one-word header. Value is split into 15-bit words,
|
||||
* each stored in a 16-bit slot (top bit is zero) in little-endian
|
||||
* order. The length (in words) is provided explicitly. In some cases,
|
||||
* the value can be negative (using two's complement representation). In
|
||||
* some cases, the top word is allowed to have a 16th bit.
|
||||
*/
|
||||
|
||||
/*
|
||||
* Negate big integer conditionally. The value consists of 'len' words,
|
||||
* with 15 bits in each word (the top bit of each word should be 0,
|
||||
* except possibly for the last word). If 'ctl' is 1, the negation is
|
||||
* computed; otherwise, if 'ctl' is 0, then the value is unchanged.
|
||||
*/
|
||||
static void
|
||||
cond_negate(uint16_t *a, size_t len, uint32_t ctl)
|
||||
{
|
||||
size_t k;
|
||||
uint32_t cc, xm;
|
||||
|
||||
cc = ctl;
|
||||
xm = 0x7FFF & -ctl;
|
||||
for (k = 0; k < len; k ++) {
|
||||
uint32_t aw;
|
||||
|
||||
aw = a[k];
|
||||
aw = (aw ^ xm) + cc;
|
||||
a[k] = aw & 0x7FFF;
|
||||
cc = (aw >> 15) & 1;
|
||||
}
|
||||
}
|
||||
|
||||
/*
|
||||
* Finish modular reduction. Rules on input parameters:
|
||||
*
|
||||
* if neg = 1, then -m <= a < 0
|
||||
* if neg = 0, then 0 <= a < 2*m
|
||||
*
|
||||
* If neg = 0, then the top word of a[] may use 16 bits.
|
||||
*
|
||||
* Also, modulus m must be odd.
|
||||
*/
|
||||
static void
|
||||
finish_mod(uint16_t *a, size_t len, const uint16_t *m, uint32_t neg)
|
||||
{
|
||||
size_t k;
|
||||
uint32_t cc, xm, ym;
|
||||
|
||||
/*
|
||||
* First pass: compare a (assumed nonnegative) with m.
|
||||
*/
|
||||
cc = 0;
|
||||
for (k = 0; k < len; k ++) {
|
||||
uint32_t aw, mw;
|
||||
|
||||
aw = a[k];
|
||||
mw = m[k];
|
||||
cc = (aw - mw - cc) >> 31;
|
||||
}
|
||||
|
||||
/*
|
||||
* At this point:
|
||||
* if neg = 1, then we must add m (regardless of cc)
|
||||
* if neg = 0 and cc = 0, then we must subtract m
|
||||
* if neg = 0 and cc = 1, then we must do nothing
|
||||
*/
|
||||
xm = 0x7FFF & -neg;
|
||||
ym = -(neg | (1 - cc));
|
||||
cc = neg;
|
||||
for (k = 0; k < len; k ++) {
|
||||
uint32_t aw, mw;
|
||||
|
||||
aw = a[k];
|
||||
mw = (m[k] ^ xm) & ym;
|
||||
aw = aw - mw - cc;
|
||||
a[k] = aw & 0x7FFF;
|
||||
cc = aw >> 31;
|
||||
}
|
||||
}
|
||||
|
||||
/*
|
||||
* Compute:
|
||||
* a <- (a*pa+b*pb)/(2^15)
|
||||
* b <- (a*qa+b*qb)/(2^15)
|
||||
* The division is assumed to be exact (i.e. the low word is dropped).
|
||||
* If the final a is negative, then it is negated. Similarly for b.
|
||||
* Returned value is the combination of two bits:
|
||||
* bit 0: 1 if a had to be negated, 0 otherwise
|
||||
* bit 1: 1 if b had to be negated, 0 otherwise
|
||||
*
|
||||
* Factors pa, pb, qa and qb must be at most 2^15 in absolute value.
|
||||
* Source integers a and b must be nonnegative; top word is not allowed
|
||||
* to contain an extra 16th bit.
|
||||
*/
|
||||
static uint32_t
|
||||
co_reduce(uint16_t *a, uint16_t *b, size_t len,
|
||||
int32_t pa, int32_t pb, int32_t qa, int32_t qb)
|
||||
{
|
||||
size_t k;
|
||||
int32_t cca, ccb;
|
||||
uint32_t nega, negb;
|
||||
|
||||
cca = 0;
|
||||
ccb = 0;
|
||||
for (k = 0; k < len; k ++) {
|
||||
uint32_t wa, wb, za, zb;
|
||||
uint16_t tta, ttb;
|
||||
|
||||
/*
|
||||
* Since:
|
||||
* |pa| <= 2^15
|
||||
* |pb| <= 2^15
|
||||
* 0 <= wa <= 2^15 - 1
|
||||
* 0 <= wb <= 2^15 - 1
|
||||
* |cca| <= 2^16 - 1
|
||||
* Then:
|
||||
* |za| <= (2^15-1)*(2^16) + (2^16-1) = 2^31 - 1
|
||||
*
|
||||
* Thus, the new value of cca is such that |cca| <= 2^16 - 1.
|
||||
* The same applies to ccb.
|
||||
*/
|
||||
wa = a[k];
|
||||
wb = b[k];
|
||||
za = wa * (uint32_t)pa + wb * (uint32_t)pb + (uint32_t)cca;
|
||||
zb = wa * (uint32_t)qa + wb * (uint32_t)qb + (uint32_t)ccb;
|
||||
if (k > 0) {
|
||||
a[k - 1] = za & 0x7FFF;
|
||||
b[k - 1] = zb & 0x7FFF;
|
||||
}
|
||||
tta = za >> 15;
|
||||
ttb = zb >> 15;
|
||||
cca = *(int16_t *)&tta;
|
||||
ccb = *(int16_t *)&ttb;
|
||||
}
|
||||
a[len - 1] = (uint16_t)cca;
|
||||
b[len - 1] = (uint16_t)ccb;
|
||||
nega = (uint32_t)cca >> 31;
|
||||
negb = (uint32_t)ccb >> 31;
|
||||
cond_negate(a, len, nega);
|
||||
cond_negate(b, len, negb);
|
||||
return nega | (negb << 1);
|
||||
}
|
||||
|
||||
/*
|
||||
* Compute:
|
||||
* a <- (a*pa+b*pb)/(2^15) mod m
|
||||
* b <- (a*qa+b*qb)/(2^15) mod m
|
||||
*
|
||||
* m0i is equal to -1/m[0] mod 2^15.
|
||||
*
|
||||
* Factors pa, pb, qa and qb must be at most 2^15 in absolute value.
|
||||
* Source integers a and b must be nonnegative; top word is not allowed
|
||||
* to contain an extra 16th bit.
|
||||
*/
|
||||
static void
|
||||
co_reduce_mod(uint16_t *a, uint16_t *b, size_t len,
|
||||
int32_t pa, int32_t pb, int32_t qa, int32_t qb,
|
||||
const uint16_t *m, uint16_t m0i)
|
||||
{
|
||||
size_t k;
|
||||
int32_t cca, ccb, fa, fb;
|
||||
|
||||
cca = 0;
|
||||
ccb = 0;
|
||||
fa = ((a[0] * (uint32_t)pa + b[0] * (uint32_t)pb) * m0i) & 0x7FFF;
|
||||
fb = ((a[0] * (uint32_t)qa + b[0] * (uint32_t)qb) * m0i) & 0x7FFF;
|
||||
for (k = 0; k < len; k ++) {
|
||||
uint32_t wa, wb, za, zb;
|
||||
uint32_t tta, ttb;
|
||||
|
||||
/*
|
||||
* In this loop, carries 'cca' and 'ccb' always fit on
|
||||
* 17 bits (in absolute value).
|
||||
*/
|
||||
wa = a[k];
|
||||
wb = b[k];
|
||||
za = wa * (uint32_t)pa + wb * (uint32_t)pb
|
||||
+ m[k] * (uint32_t)fa + (uint32_t)cca;
|
||||
zb = wa * (uint32_t)qa + wb * (uint32_t)qb
|
||||
+ m[k] * (uint32_t)fb + (uint32_t)ccb;
|
||||
if (k > 0) {
|
||||
a[k - 1] = za & 0x7FFF;
|
||||
b[k - 1] = zb & 0x7FFF;
|
||||
}
|
||||
|
||||
/*
|
||||
* The XOR-and-sub construction below does an arithmetic
|
||||
* right shift in a portable way (technically, right-shifting
|
||||
* a negative signed value is implementation-defined in C).
|
||||
*/
|
||||
#define M ((uint32_t)1 << 16)
|
||||
tta = za >> 15;
|
||||
ttb = zb >> 15;
|
||||
tta = (tta ^ M) - M;
|
||||
ttb = (ttb ^ M) - M;
|
||||
cca = *(int32_t *)&tta;
|
||||
ccb = *(int32_t *)&ttb;
|
||||
#undef M
|
||||
}
|
||||
a[len - 1] = (uint32_t)cca;
|
||||
b[len - 1] = (uint32_t)ccb;
|
||||
|
||||
/*
|
||||
* At this point:
|
||||
* -m <= a < 2*m
|
||||
* -m <= b < 2*m
|
||||
* (this is a case of Montgomery reduction)
|
||||
* The top word of 'a' and 'b' may have a 16-th bit set.
|
||||
* We may have to add or subtract the modulus.
|
||||
*/
|
||||
finish_mod(a, len, m, (uint32_t)cca >> 31);
|
||||
finish_mod(b, len, m, (uint32_t)ccb >> 31);
|
||||
}
|
||||
|
||||
/* see inner.h */
|
||||
uint32_t
|
||||
br_i15_moddiv(uint16_t *x, const uint16_t *y, const uint16_t *m, uint16_t m0i,
|
||||
uint16_t *t)
|
||||
{
|
||||
/*
|
||||
* Algorithm is an extended binary GCD. We maintain four values
|
||||
* a, b, u and v, with the following invariants:
|
||||
*
|
||||
* a * x = y * u mod m
|
||||
* b * x = y * v mod m
|
||||
*
|
||||
* Starting values are:
|
||||
*
|
||||
* a = y
|
||||
* b = m
|
||||
* u = x
|
||||
* v = 0
|
||||
*
|
||||
* The formal definition of the algorithm is a sequence of steps:
|
||||
*
|
||||
* - If a is even, then a <- a/2 and u <- u/2 mod m.
|
||||
* - Otherwise, if b is even, then b <- b/2 and v <- v/2 mod m.
|
||||
* - Otherwise, if a > b, then a <- (a-b)/2 and u <- (u-v)/2 mod m.
|
||||
* - Otherwise, b <- (b-a)/2 and v <- (v-u)/2 mod m.
|
||||
*
|
||||
* Algorithm stops when a = b. At that point, they both are equal
|
||||
* to GCD(y,m); the modular division succeeds if that value is 1.
|
||||
* The result of the modular division is then u (or v: both are
|
||||
* equal at that point).
|
||||
*
|
||||
* Each step makes either a or b shrink by at least one bit; hence,
|
||||
* if m has bit length k bits, then 2k-2 steps are sufficient.
|
||||
*
|
||||
*
|
||||
* Though complexity is quadratic in the size of m, the bit-by-bit
|
||||
* processing is not very efficient. We can speed up processing by
|
||||
* remarking that the decisions are taken based only on observation
|
||||
* of the top and low bits of a and b.
|
||||
*
|
||||
* In the loop below, at each iteration, we use the two top words
|
||||
* of a and b, and the low words of a and b, to compute reduction
|
||||
* parameters pa, pb, qa and qb such that the new values for a
|
||||
* and b are:
|
||||
*
|
||||
* a' = (a*pa + b*pb) / (2^15)
|
||||
* b' = (a*qa + b*qb) / (2^15)
|
||||
*
|
||||
* the division being exact.
|
||||
*
|
||||
* Since the choices are based on the top words, they may be slightly
|
||||
* off, requiring an optional correction: if a' < 0, then we replace
|
||||
* pa with -pa, and pb with -pb. The total length of a and b is
|
||||
* thus reduced by at least 14 bits at each iteration.
|
||||
*
|
||||
* The stopping conditions are still the same, though: when a
|
||||
* and b become equal, they must be both odd (since m is odd,
|
||||
* the GCD cannot be even), therefore the next operation is a
|
||||
* subtraction, and one of the values becomes 0. At that point,
|
||||
* nothing else happens, i.e. one value is stuck at 0, and the
|
||||
* other one is the GCD.
|
||||
*/
|
||||
size_t len, k;
|
||||
uint16_t *a, *b, *u, *v;
|
||||
uint32_t num, r;
|
||||
|
||||
len = (m[0] + 15) >> 4;
|
||||
a = t;
|
||||
b = a + len;
|
||||
u = x + 1;
|
||||
v = b + len;
|
||||
memcpy(a, y + 1, len * sizeof *y);
|
||||
memcpy(b, m + 1, len * sizeof *m);
|
||||
memset(v, 0, len * sizeof *v);
|
||||
|
||||
/*
|
||||
* Loop below ensures that a and b are reduced by some bits each,
|
||||
* for a total of at least 14 bits.
|
||||
*/
|
||||
for (num = ((m[0] - (m[0] >> 4)) << 1) + 14; num >= 14; num -= 14) {
|
||||
size_t j;
|
||||
uint32_t c0, c1;
|
||||
uint32_t a0, a1, b0, b1;
|
||||
uint32_t a_hi, b_hi, a_lo, b_lo;
|
||||
int32_t pa, pb, qa, qb;
|
||||
int i;
|
||||
|
||||
/*
|
||||
* Extract top words of a and b. If j is the highest
|
||||
* index >= 1 such that a[j] != 0 or b[j] != 0, then we want
|
||||
* (a[j] << 15) + a[j - 1], and (b[j] << 15) + b[j - 1].
|
||||
* If a and b are down to one word each, then we use a[0]
|
||||
* and b[0].
|
||||
*/
|
||||
c0 = (uint32_t)-1;
|
||||
c1 = (uint32_t)-1;
|
||||
a0 = 0;
|
||||
a1 = 0;
|
||||
b0 = 0;
|
||||
b1 = 0;
|
||||
j = len;
|
||||
while (j -- > 0) {
|
||||
uint32_t aw, bw;
|
||||
|
||||
aw = a[j];
|
||||
bw = b[j];
|
||||
a0 ^= (a0 ^ aw) & c0;
|
||||
a1 ^= (a1 ^ aw) & c1;
|
||||
b0 ^= (b0 ^ bw) & c0;
|
||||
b1 ^= (b1 ^ bw) & c1;
|
||||
c1 = c0;
|
||||
c0 &= (((aw | bw) + 0xFFFF) >> 16) - (uint32_t)1;
|
||||
}
|
||||
|
||||
/*
|
||||
* If c1 = 0, then we grabbed two words for a and b.
|
||||
* If c1 != 0 but c0 = 0, then we grabbed one word. It
|
||||
* is not possible that c1 != 0 and c0 != 0, because that
|
||||
* would mean that both integers are zero.
|
||||
*/
|
||||
a1 |= a0 & c1;
|
||||
a0 &= ~c1;
|
||||
b1 |= b0 & c1;
|
||||
b0 &= ~c1;
|
||||
a_hi = (a0 << 15) + a1;
|
||||
b_hi = (b0 << 15) + b1;
|
||||
a_lo = a[0];
|
||||
b_lo = b[0];
|
||||
|
||||
/*
|
||||
* Compute reduction factors:
|
||||
*
|
||||
* a' = a*pa + b*pb
|
||||
* b' = a*qa + b*qb
|
||||
*
|
||||
* such that a' and b' are both multiple of 2^15, but are
|
||||
* only marginally larger than a and b.
|
||||
*/
|
||||
pa = 1;
|
||||
pb = 0;
|
||||
qa = 0;
|
||||
qb = 1;
|
||||
for (i = 0; i < 15; i ++) {
|
||||
/*
|
||||
* At each iteration:
|
||||
*
|
||||
* a <- (a-b)/2 if: a is odd, b is odd, a_hi > b_hi
|
||||
* b <- (b-a)/2 if: a is odd, b is odd, a_hi <= b_hi
|
||||
* a <- a/2 if: a is even
|
||||
* b <- b/2 if: a is odd, b is even
|
||||
*
|
||||
* We multiply a_lo and b_lo by 2 at each
|
||||
* iteration, thus a division by 2 really is a
|
||||
* non-multiplication by 2.
|
||||
*/
|
||||
uint32_t r, oa, ob, cAB, cBA, cA;
|
||||
|
||||
/*
|
||||
* cAB = 1 if b must be subtracted from a
|
||||
* cBA = 1 if a must be subtracted from b
|
||||
* cA = 1 if a is divided by 2, 0 otherwise
|
||||
*
|
||||
* Rules:
|
||||
*
|
||||
* cAB and cBA cannot be both 1.
|
||||
* if a is not divided by 2, b is.
|
||||
*/
|
||||
r = GT(a_hi, b_hi);
|
||||
oa = (a_lo >> i) & 1;
|
||||
ob = (b_lo >> i) & 1;
|
||||
cAB = oa & ob & r;
|
||||
cBA = oa & ob & NOT(r);
|
||||
cA = cAB | NOT(oa);
|
||||
|
||||
/*
|
||||
* Conditional subtractions.
|
||||
*/
|
||||
a_lo -= b_lo & -cAB;
|
||||
a_hi -= b_hi & -cAB;
|
||||
pa -= qa & -(int32_t)cAB;
|
||||
pb -= qb & -(int32_t)cAB;
|
||||
b_lo -= a_lo & -cBA;
|
||||
b_hi -= a_hi & -cBA;
|
||||
qa -= pa & -(int32_t)cBA;
|
||||
qb -= pb & -(int32_t)cBA;
|
||||
|
||||
/*
|
||||
* Shifting.
|
||||
*/
|
||||
a_lo += a_lo & (cA - 1);
|
||||
pa += pa & ((int32_t)cA - 1);
|
||||
pb += pb & ((int32_t)cA - 1);
|
||||
a_hi ^= (a_hi ^ (a_hi >> 1)) & -cA;
|
||||
b_lo += b_lo & -cA;
|
||||
qa += qa & -(int32_t)cA;
|
||||
qb += qb & -(int32_t)cA;
|
||||
b_hi ^= (b_hi ^ (b_hi >> 1)) & (cA - 1);
|
||||
}
|
||||
|
||||
/*
|
||||
* Replace a and b with new values a' and b'.
|
||||
*/
|
||||
r = co_reduce(a, b, len, pa, pb, qa, qb);
|
||||
pa -= pa * ((r & 1) << 1);
|
||||
pb -= pb * ((r & 1) << 1);
|
||||
qa -= qa * (r & 2);
|
||||
qb -= qb * (r & 2);
|
||||
co_reduce_mod(u, v, len, pa, pb, qa, qb, m + 1, m0i);
|
||||
}
|
||||
|
||||
/*
|
||||
* Now one of the arrays should be 0, and the other contains
|
||||
* the GCD. If a is 0, then u is 0 as well, and v contains
|
||||
* the division result.
|
||||
* Result is correct if and only if GCD is 1.
|
||||
*/
|
||||
r = (a[0] | b[0]) ^ 1;
|
||||
u[0] |= v[0];
|
||||
for (k = 1; k < len; k ++) {
|
||||
r |= a[k] | b[k];
|
||||
u[k] |= v[k];
|
||||
}
|
||||
return EQ0(r);
|
||||
}
|
||||
488
src/int/i31_moddiv.c
Normal file
488
src/int/i31_moddiv.c
Normal file
|
|
@ -0,0 +1,488 @@
|
|||
/*
|
||||
* Copyright (c) 2018 Thomas Pornin <pornin@bolet.org>
|
||||
*
|
||||
* Permission is hereby granted, free of charge, to any person obtaining
|
||||
* a copy of this software and associated documentation files (the
|
||||
* "Software"), to deal in the Software without restriction, including
|
||||
* without limitation the rights to use, copy, modify, merge, publish,
|
||||
* distribute, sublicense, and/or sell copies of the Software, and to
|
||||
* permit persons to whom the Software is furnished to do so, subject to
|
||||
* the following conditions:
|
||||
*
|
||||
* The above copyright notice and this permission notice shall be
|
||||
* included in all copies or substantial portions of the Software.
|
||||
*
|
||||
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
|
||||
* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
|
||||
* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
|
||||
* NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
|
||||
* BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
|
||||
* ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
|
||||
* CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
|
||||
* SOFTWARE.
|
||||
*/
|
||||
|
||||
#include "inner.h"
|
||||
|
||||
/*
|
||||
* In this file, we handle big integers with a custom format, i.e.
|
||||
* without the usual one-word header. Value is split into 31-bit words,
|
||||
* each stored in a 32-bit slot (top bit is zero) in little-endian
|
||||
* order. The length (in words) is provided explicitly. In some cases,
|
||||
* the value can be negative (using two's complement representation). In
|
||||
* some cases, the top word is allowed to have a 32th bit.
|
||||
*/
|
||||
|
||||
/*
|
||||
* Negate big integer conditionally. The value consists of 'len' words,
|
||||
* with 31 bits in each word (the top bit of each word should be 0,
|
||||
* except possibly for the last word). If 'ctl' is 1, the negation is
|
||||
* computed; otherwise, if 'ctl' is 0, then the value is unchanged.
|
||||
*/
|
||||
static void
|
||||
cond_negate(uint32_t *a, size_t len, uint32_t ctl)
|
||||
{
|
||||
size_t k;
|
||||
uint32_t cc, xm;
|
||||
|
||||
cc = ctl;
|
||||
xm = -ctl >> 1;
|
||||
for (k = 0; k < len; k ++) {
|
||||
uint32_t aw;
|
||||
|
||||
aw = a[k];
|
||||
aw = (aw ^ xm) + cc;
|
||||
a[k] = aw & 0x7FFFFFFF;
|
||||
cc = aw >> 31;
|
||||
}
|
||||
}
|
||||
|
||||
/*
|
||||
* Finish modular reduction. Rules on input parameters:
|
||||
*
|
||||
* if neg = 1, then -m <= a < 0
|
||||
* if neg = 0, then 0 <= a < 2*m
|
||||
*
|
||||
* If neg = 0, then the top word of a[] may use 32 bits.
|
||||
*
|
||||
* Also, modulus m must be odd.
|
||||
*/
|
||||
static void
|
||||
finish_mod(uint32_t *a, size_t len, const uint32_t *m, uint32_t neg)
|
||||
{
|
||||
size_t k;
|
||||
uint32_t cc, xm, ym;
|
||||
|
||||
/*
|
||||
* First pass: compare a (assumed nonnegative) with m.
|
||||
* Note that if the final word uses the top extra bit, then
|
||||
* subtracting m must yield a value less than 2^31, since we
|
||||
* assumed that a < 2*m.
|
||||
*/
|
||||
cc = 0;
|
||||
for (k = 0; k < len; k ++) {
|
||||
uint32_t aw, mw;
|
||||
|
||||
aw = a[k];
|
||||
mw = m[k];
|
||||
cc = (aw - mw - cc) >> 31;
|
||||
}
|
||||
|
||||
/*
|
||||
* At this point:
|
||||
* if neg = 1, then we must add m (regardless of cc)
|
||||
* if neg = 0 and cc = 0, then we must subtract m
|
||||
* if neg = 0 and cc = 1, then we must do nothing
|
||||
*/
|
||||
xm = -neg >> 1;
|
||||
ym = -(neg | (1 - cc));
|
||||
cc = neg;
|
||||
for (k = 0; k < len; k ++) {
|
||||
uint32_t aw, mw;
|
||||
|
||||
aw = a[k];
|
||||
mw = (m[k] ^ xm) & ym;
|
||||
aw = aw - mw - cc;
|
||||
a[k] = aw & 0x7FFFFFFF;
|
||||
cc = aw >> 31;
|
||||
}
|
||||
}
|
||||
|
||||
/*
|
||||
* Compute:
|
||||
* a <- (a*pa+b*pb)/(2^31)
|
||||
* b <- (a*qa+b*qb)/(2^31)
|
||||
* The division is assumed to be exact (i.e. the low word is dropped).
|
||||
* If the final a is negative, then it is negated. Similarly for b.
|
||||
* Returned value is the combination of two bits:
|
||||
* bit 0: 1 if a had to be negated, 0 otherwise
|
||||
* bit 1: 1 if b had to be negated, 0 otherwise
|
||||
*
|
||||
* Factors pa, pb, qa and qb must be at most 2^31 in absolute value.
|
||||
* Source integers a and b must be nonnegative; top word is not allowed
|
||||
* to contain an extra 32th bit.
|
||||
*/
|
||||
static uint32_t
|
||||
co_reduce(uint32_t *a, uint32_t *b, size_t len,
|
||||
int64_t pa, int64_t pb, int64_t qa, int64_t qb)
|
||||
{
|
||||
size_t k;
|
||||
int64_t cca, ccb;
|
||||
uint32_t nega, negb;
|
||||
|
||||
cca = 0;
|
||||
ccb = 0;
|
||||
for (k = 0; k < len; k ++) {
|
||||
uint32_t wa, wb;
|
||||
uint64_t za, zb;
|
||||
uint64_t tta, ttb;
|
||||
|
||||
/*
|
||||
* Since:
|
||||
* |pa| <= 2^31
|
||||
* |pb| <= 2^31
|
||||
* 0 <= wa <= 2^31 - 1
|
||||
* 0 <= wb <= 2^31 - 1
|
||||
* |cca| <= 2^32 - 1
|
||||
* Then:
|
||||
* |za| <= (2^31-1)*(2^32) + (2^32-1) = 2^63 - 1
|
||||
*
|
||||
* Thus, the new value of cca is such that |cca| <= 2^32 - 1.
|
||||
* The same applies to ccb.
|
||||
*/
|
||||
wa = a[k];
|
||||
wb = b[k];
|
||||
za = wa * (uint64_t)pa + wb * (uint64_t)pb + (uint64_t)cca;
|
||||
zb = wa * (uint64_t)qa + wb * (uint64_t)qb + (uint64_t)ccb;
|
||||
if (k > 0) {
|
||||
a[k - 1] = za & 0x7FFFFFFF;
|
||||
b[k - 1] = zb & 0x7FFFFFFF;
|
||||
}
|
||||
|
||||
/*
|
||||
* For the new values of cca and ccb, we need a signed
|
||||
* right-shift; since, in C, right-shifting a signed
|
||||
* negative value is implementation-defined, we use a
|
||||
* custom portable sign extension expression.
|
||||
*/
|
||||
#define M ((uint64_t)1 << 32)
|
||||
tta = za >> 31;
|
||||
ttb = zb >> 31;
|
||||
tta = (tta ^ M) - M;
|
||||
ttb = (ttb ^ M) - M;
|
||||
cca = *(int64_t *)&tta;
|
||||
ccb = *(int64_t *)&ttb;
|
||||
#undef M
|
||||
}
|
||||
a[len - 1] = (uint32_t)cca;
|
||||
b[len - 1] = (uint32_t)ccb;
|
||||
|
||||
nega = (uint32_t)((uint64_t)cca >> 63);
|
||||
negb = (uint32_t)((uint64_t)ccb >> 63);
|
||||
cond_negate(a, len, nega);
|
||||
cond_negate(b, len, negb);
|
||||
return nega | (negb << 1);
|
||||
}
|
||||
|
||||
/*
|
||||
* Compute:
|
||||
* a <- (a*pa+b*pb)/(2^31) mod m
|
||||
* b <- (a*qa+b*qb)/(2^31) mod m
|
||||
*
|
||||
* m0i is equal to -1/m[0] mod 2^31.
|
||||
*
|
||||
* Factors pa, pb, qa and qb must be at most 2^31 in absolute value.
|
||||
* Source integers a and b must be nonnegative; top word is not allowed
|
||||
* to contain an extra 32th bit.
|
||||
*/
|
||||
static void
|
||||
co_reduce_mod(uint32_t *a, uint32_t *b, size_t len,
|
||||
int64_t pa, int64_t pb, int64_t qa, int64_t qb,
|
||||
const uint32_t *m, uint32_t m0i)
|
||||
{
|
||||
size_t k;
|
||||
int64_t cca, ccb;
|
||||
uint32_t fa, fb;
|
||||
|
||||
cca = 0;
|
||||
ccb = 0;
|
||||
fa = ((a[0] * (uint32_t)pa + b[0] * (uint32_t)pb) * m0i) & 0x7FFFFFFF;
|
||||
fb = ((a[0] * (uint32_t)qa + b[0] * (uint32_t)qb) * m0i) & 0x7FFFFFFF;
|
||||
for (k = 0; k < len; k ++) {
|
||||
uint32_t wa, wb;
|
||||
uint64_t za, zb;
|
||||
uint64_t tta, ttb;
|
||||
|
||||
/*
|
||||
* In this loop, carries 'cca' and 'ccb' always fit on
|
||||
* 33 bits (in absolute value).
|
||||
*/
|
||||
wa = a[k];
|
||||
wb = b[k];
|
||||
za = wa * (uint64_t)pa + wb * (uint64_t)pb
|
||||
+ m[k] * (uint64_t)fa + (uint64_t)cca;
|
||||
zb = wa * (uint64_t)qa + wb * (uint64_t)qb
|
||||
+ m[k] * (uint64_t)fb + (uint64_t)ccb;
|
||||
if (k > 0) {
|
||||
a[k - 1] = (uint32_t)za & 0x7FFFFFFF;
|
||||
b[k - 1] = (uint32_t)zb & 0x7FFFFFFF;
|
||||
}
|
||||
|
||||
#define M ((uint64_t)1 << 32)
|
||||
tta = za >> 31;
|
||||
ttb = zb >> 31;
|
||||
tta = (tta ^ M) - M;
|
||||
ttb = (ttb ^ M) - M;
|
||||
cca = *(int64_t *)&tta;
|
||||
ccb = *(int64_t *)&ttb;
|
||||
#undef M
|
||||
}
|
||||
a[len - 1] = (uint32_t)cca;
|
||||
b[len - 1] = (uint32_t)ccb;
|
||||
|
||||
/*
|
||||
* At this point:
|
||||
* -m <= a < 2*m
|
||||
* -m <= b < 2*m
|
||||
* (this is a case of Montgomery reduction)
|
||||
* The top word of 'a' and 'b' may have a 32-th bit set.
|
||||
* We may have to add or subtract the modulus.
|
||||
*/
|
||||
finish_mod(a, len, m, (uint32_t)((uint64_t)cca >> 63));
|
||||
finish_mod(b, len, m, (uint32_t)((uint64_t)ccb >> 63));
|
||||
}
|
||||
|
||||
/* see inner.h */
|
||||
uint32_t
|
||||
br_i31_moddiv(uint32_t *x, const uint32_t *y, const uint32_t *m, uint32_t m0i,
|
||||
uint32_t *t)
|
||||
{
|
||||
/*
|
||||
* Algorithm is an extended binary GCD. We maintain four values
|
||||
* a, b, u and v, with the following invariants:
|
||||
*
|
||||
* a * x = y * u mod m
|
||||
* b * x = y * v mod m
|
||||
*
|
||||
* Starting values are:
|
||||
*
|
||||
* a = y
|
||||
* b = m
|
||||
* u = x
|
||||
* v = 0
|
||||
*
|
||||
* The formal definition of the algorithm is a sequence of steps:
|
||||
*
|
||||
* - If a is even, then a <- a/2 and u <- u/2 mod m.
|
||||
* - Otherwise, if b is even, then b <- b/2 and v <- v/2 mod m.
|
||||
* - Otherwise, if a > b, then a <- (a-b)/2 and u <- (u-v)/2 mod m.
|
||||
* - Otherwise, b <- (b-a)/2 and v <- (v-u)/2 mod m.
|
||||
*
|
||||
* Algorithm stops when a = b. At that point, they both are equal
|
||||
* to GCD(y,m); the modular division succeeds if that value is 1.
|
||||
* The result of the modular division is then u (or v: both are
|
||||
* equal at that point).
|
||||
*
|
||||
* Each step makes either a or b shrink by at least one bit; hence,
|
||||
* if m has bit length k bits, then 2k-2 steps are sufficient.
|
||||
*
|
||||
*
|
||||
* Though complexity is quadratic in the size of m, the bit-by-bit
|
||||
* processing is not very efficient. We can speed up processing by
|
||||
* remarking that the decisions are taken based only on observation
|
||||
* of the top and low bits of a and b.
|
||||
*
|
||||
* In the loop below, at each iteration, we use the two top words
|
||||
* of a and b, and the low words of a and b, to compute reduction
|
||||
* parameters pa, pb, qa and qb such that the new values for a
|
||||
* and b are:
|
||||
*
|
||||
* a' = (a*pa + b*pb) / (2^31)
|
||||
* b' = (a*qa + b*qb) / (2^31)
|
||||
*
|
||||
* the division being exact.
|
||||
*
|
||||
* Since the choices are based on the top words, they may be slightly
|
||||
* off, requiring an optional correction: if a' < 0, then we replace
|
||||
* pa with -pa, and pb with -pb. The total length of a and b is
|
||||
* thus reduced by at least 30 bits at each iteration.
|
||||
*
|
||||
* The stopping conditions are still the same, though: when a
|
||||
* and b become equal, they must be both odd (since m is odd,
|
||||
* the GCD cannot be even), therefore the next operation is a
|
||||
* subtraction, and one of the values becomes 0. At that point,
|
||||
* nothing else happens, i.e. one value is stuck at 0, and the
|
||||
* other one is the GCD.
|
||||
*/
|
||||
size_t len, k;
|
||||
uint32_t *a, *b, *u, *v;
|
||||
uint32_t num, r;
|
||||
|
||||
len = (m[0] + 31) >> 5;
|
||||
a = t;
|
||||
b = a + len;
|
||||
u = x + 1;
|
||||
v = b + len;
|
||||
memcpy(a, y + 1, len * sizeof *y);
|
||||
memcpy(b, m + 1, len * sizeof *m);
|
||||
memset(v, 0, len * sizeof *v);
|
||||
|
||||
/*
|
||||
* Loop below ensures that a and b are reduced by some bits each,
|
||||
* for a total of at least 30 bits.
|
||||
*/
|
||||
for (num = ((m[0] - (m[0] >> 5)) << 1) + 30; num >= 30; num -= 30) {
|
||||
size_t j;
|
||||
uint32_t c0, c1;
|
||||
uint32_t a0, a1, b0, b1;
|
||||
uint64_t a_hi, b_hi;
|
||||
uint32_t a_lo, b_lo;
|
||||
int64_t pa, pb, qa, qb;
|
||||
int i;
|
||||
|
||||
/*
|
||||
* Extract top words of a and b. If j is the highest
|
||||
* index >= 1 such that a[j] != 0 or b[j] != 0, then we want
|
||||
* (a[j] << 31) + a[j - 1], and (b[j] << 31) + b[j - 1].
|
||||
* If a and b are down to one word each, then we use a[0]
|
||||
* and b[0].
|
||||
*/
|
||||
c0 = (uint32_t)-1;
|
||||
c1 = (uint32_t)-1;
|
||||
a0 = 0;
|
||||
a1 = 0;
|
||||
b0 = 0;
|
||||
b1 = 0;
|
||||
j = len;
|
||||
while (j -- > 0) {
|
||||
uint32_t aw, bw;
|
||||
|
||||
aw = a[j];
|
||||
bw = b[j];
|
||||
a0 ^= (a0 ^ aw) & c0;
|
||||
a1 ^= (a1 ^ aw) & c1;
|
||||
b0 ^= (b0 ^ bw) & c0;
|
||||
b1 ^= (b1 ^ bw) & c1;
|
||||
c1 = c0;
|
||||
c0 &= (((aw | bw) + 0x7FFFFFFF) >> 31) - (uint32_t)1;
|
||||
}
|
||||
|
||||
/*
|
||||
* If c1 = 0, then we grabbed two words for a and b.
|
||||
* If c1 != 0 but c0 = 0, then we grabbed one word. It
|
||||
* is not possible that c1 != 0 and c0 != 0, because that
|
||||
* would mean that both integers are zero.
|
||||
*/
|
||||
a1 |= a0 & c1;
|
||||
a0 &= ~c1;
|
||||
b1 |= b0 & c1;
|
||||
b0 &= ~c1;
|
||||
a_hi = ((uint64_t)a0 << 31) + a1;
|
||||
b_hi = ((uint64_t)b0 << 31) + b1;
|
||||
a_lo = a[0];
|
||||
b_lo = b[0];
|
||||
|
||||
/*
|
||||
* Compute reduction factors:
|
||||
*
|
||||
* a' = a*pa + b*pb
|
||||
* b' = a*qa + b*qb
|
||||
*
|
||||
* such that a' and b' are both multiple of 2^31, but are
|
||||
* only marginally larger than a and b.
|
||||
*/
|
||||
pa = 1;
|
||||
pb = 0;
|
||||
qa = 0;
|
||||
qb = 1;
|
||||
for (i = 0; i < 31; i ++) {
|
||||
/*
|
||||
* At each iteration:
|
||||
*
|
||||
* a <- (a-b)/2 if: a is odd, b is odd, a_hi > b_hi
|
||||
* b <- (b-a)/2 if: a is odd, b is odd, a_hi <= b_hi
|
||||
* a <- a/2 if: a is even
|
||||
* b <- b/2 if: a is odd, b is even
|
||||
*
|
||||
* We multiply a_lo and b_lo by 2 at each
|
||||
* iteration, thus a division by 2 really is a
|
||||
* non-multiplication by 2.
|
||||
*/
|
||||
uint32_t r, oa, ob, cAB, cBA, cA;
|
||||
uint64_t rz;
|
||||
|
||||
/*
|
||||
* r = GT(a_hi, b_hi)
|
||||
* But the GT() function works on uint32_t operands,
|
||||
* so we inline a 64-bit version here.
|
||||
*/
|
||||
rz = b_hi - a_hi;
|
||||
r = (uint32_t)((rz ^ ((a_hi ^ b_hi)
|
||||
& (a_hi ^ rz))) >> 63);
|
||||
|
||||
/*
|
||||
* cAB = 1 if b must be subtracted from a
|
||||
* cBA = 1 if a must be subtracted from b
|
||||
* cA = 1 if a is divided by 2, 0 otherwise
|
||||
*
|
||||
* Rules:
|
||||
*
|
||||
* cAB and cBA cannot be both 1.
|
||||
* if a is not divided by 2, b is.
|
||||
*/
|
||||
oa = (a_lo >> i) & 1;
|
||||
ob = (b_lo >> i) & 1;
|
||||
cAB = oa & ob & r;
|
||||
cBA = oa & ob & NOT(r);
|
||||
cA = cAB | NOT(oa);
|
||||
|
||||
/*
|
||||
* Conditional subtractions.
|
||||
*/
|
||||
a_lo -= b_lo & -cAB;
|
||||
a_hi -= b_hi & -(uint64_t)cAB;
|
||||
pa -= qa & -(int64_t)cAB;
|
||||
pb -= qb & -(int64_t)cAB;
|
||||
b_lo -= a_lo & -cBA;
|
||||
b_hi -= a_hi & -(uint64_t)cBA;
|
||||
qa -= pa & -(int64_t)cBA;
|
||||
qb -= pb & -(int64_t)cBA;
|
||||
|
||||
/*
|
||||
* Shifting.
|
||||
*/
|
||||
a_lo += a_lo & (cA - 1);
|
||||
pa += pa & ((int64_t)cA - 1);
|
||||
pb += pb & ((int64_t)cA - 1);
|
||||
a_hi ^= (a_hi ^ (a_hi >> 1)) & -(uint64_t)cA;
|
||||
b_lo += b_lo & -cA;
|
||||
qa += qa & -(int64_t)cA;
|
||||
qb += qb & -(int64_t)cA;
|
||||
b_hi ^= (b_hi ^ (b_hi >> 1)) & ((uint64_t)cA - 1);
|
||||
}
|
||||
|
||||
/*
|
||||
* Replace a and b with new values a' and b'.
|
||||
*/
|
||||
r = co_reduce(a, b, len, pa, pb, qa, qb);
|
||||
pa -= pa * ((r & 1) << 1);
|
||||
pb -= pb * ((r & 1) << 1);
|
||||
qa -= qa * (r & 2);
|
||||
qb -= qb * (r & 2);
|
||||
co_reduce_mod(u, v, len, pa, pb, qa, qb, m + 1, m0i);
|
||||
}
|
||||
|
||||
/*
|
||||
* Now one of the arrays should be 0, and the other contains
|
||||
* the GCD. If a is 0, then u is 0 as well, and v contains
|
||||
* the division result.
|
||||
* Result is correct if and only if GCD is 1.
|
||||
*/
|
||||
r = (a[0] | b[0]) ^ 1;
|
||||
u[0] |= v[0];
|
||||
for (k = 1; k < len; k ++) {
|
||||
r |= a[k] | b[k];
|
||||
u[k] |= v[k];
|
||||
}
|
||||
return EQ0(r);
|
||||
}
|
||||
|
|
@ -244,7 +244,7 @@ br_i62_modpow_opt(uint32_t *x31, const unsigned char *e, size_t elen,
|
|||
mw62num = (mw31num + 1) >> 1;
|
||||
|
||||
/*
|
||||
* In order to apply this function, we must have enough room tp
|
||||
* In order to apply this function, we must have enough room to
|
||||
* copy the operand and modulus into the temporary array, along
|
||||
* with at least two temporaries. If there is not enough room,
|
||||
* switch to br_i31_modpow(). We also use br_i31_modpow() if the
|
||||
|
|
@ -477,3 +477,17 @@ br_i62_modpow_opt(uint32_t *x31, const unsigned char *e, size_t elen,
|
|||
}
|
||||
|
||||
#endif
|
||||
|
||||
/* see inner.h */
|
||||
uint32_t
|
||||
br_i62_modpow_opt_as_i31(uint32_t *x31, const unsigned char *e, size_t elen,
|
||||
const uint32_t *m31, uint32_t m0i31, uint32_t *tmp, size_t twlen)
|
||||
{
|
||||
/*
|
||||
* As documented, this function expects the 'tmp' argument to be
|
||||
* 64-bit aligned. This is OK since this function is internal (it
|
||||
* is not part of BearSSL's public API).
|
||||
*/
|
||||
return br_i62_modpow_opt(x31, e, elen, m31, m0i31,
|
||||
(uint64_t *)tmp, twlen >> 1);
|
||||
}
|
||||
|
|
|
|||
38
src/rsa/rsa_default_keygen.c
Normal file
38
src/rsa/rsa_default_keygen.c
Normal file
|
|
@ -0,0 +1,38 @@
|
|||
/*
|
||||
* Copyright (c) 2018 Thomas Pornin <pornin@bolet.org>
|
||||
*
|
||||
* Permission is hereby granted, free of charge, to any person obtaining
|
||||
* a copy of this software and associated documentation files (the
|
||||
* "Software"), to deal in the Software without restriction, including
|
||||
* without limitation the rights to use, copy, modify, merge, publish,
|
||||
* distribute, sublicense, and/or sell copies of the Software, and to
|
||||
* permit persons to whom the Software is furnished to do so, subject to
|
||||
* the following conditions:
|
||||
*
|
||||
* The above copyright notice and this permission notice shall be
|
||||
* included in all copies or substantial portions of the Software.
|
||||
*
|
||||
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
|
||||
* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
|
||||
* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
|
||||
* NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
|
||||
* BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
|
||||
* ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
|
||||
* CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
|
||||
* SOFTWARE.
|
||||
*/
|
||||
|
||||
#include "inner.h"
|
||||
|
||||
/* see bearssl_rsa.h */
|
||||
br_rsa_keygen
|
||||
br_rsa_keygen_get_default(void)
|
||||
{
|
||||
#if BR_INT128 || BR_UMUL128
|
||||
return &br_rsa_i62_keygen;
|
||||
#elif BR_LOMUL
|
||||
return &br_rsa_i15_keygen;
|
||||
#else
|
||||
return &br_rsa_i31_keygen;
|
||||
#endif
|
||||
}
|
||||
583
src/rsa/rsa_i15_keygen.c
Normal file
583
src/rsa/rsa_i15_keygen.c
Normal file
|
|
@ -0,0 +1,583 @@
|
|||
/*
|
||||
* Copyright (c) 2018 Thomas Pornin <pornin@bolet.org>
|
||||
*
|
||||
* Permission is hereby granted, free of charge, to any person obtaining
|
||||
* a copy of this software and associated documentation files (the
|
||||
* "Software"), to deal in the Software without restriction, including
|
||||
* without limitation the rights to use, copy, modify, merge, publish,
|
||||
* distribute, sublicense, and/or sell copies of the Software, and to
|
||||
* permit persons to whom the Software is furnished to do so, subject to
|
||||
* the following conditions:
|
||||
*
|
||||
* The above copyright notice and this permission notice shall be
|
||||
* included in all copies or substantial portions of the Software.
|
||||
*
|
||||
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
|
||||
* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
|
||||
* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
|
||||
* NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
|
||||
* BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
|
||||
* ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
|
||||
* CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
|
||||
* SOFTWARE.
|
||||
*/
|
||||
|
||||
#include "inner.h"
|
||||
|
||||
/*
|
||||
* Make a random integer of the provided size. The size is encoded.
|
||||
* The header word is untouched.
|
||||
*/
|
||||
static void
|
||||
mkrand(const br_prng_class **rng, uint16_t *x, uint32_t esize)
|
||||
{
|
||||
size_t u, len;
|
||||
unsigned m;
|
||||
|
||||
len = (esize + 15) >> 4;
|
||||
(*rng)->generate(rng, x + 1, len * sizeof(uint16_t));
|
||||
for (u = 1; u < len; u ++) {
|
||||
x[u] &= 0x7FFF;
|
||||
}
|
||||
m = esize & 15;
|
||||
if (m == 0) {
|
||||
x[len] &= 0x7FFF;
|
||||
} else {
|
||||
x[len] &= 0x7FFF >> (15 - m);
|
||||
}
|
||||
}
|
||||
|
||||
/*
|
||||
* This is the big-endian unsigned representation of the product of
|
||||
* all small primes from 13 to 1481.
|
||||
*/
|
||||
static const unsigned char SMALL_PRIMES[] = {
|
||||
0x2E, 0xAB, 0x92, 0xD1, 0x8B, 0x12, 0x47, 0x31, 0x54, 0x0A,
|
||||
0x99, 0x5D, 0x25, 0x5E, 0xE2, 0x14, 0x96, 0x29, 0x1E, 0xB7,
|
||||
0x78, 0x70, 0xCC, 0x1F, 0xA5, 0xAB, 0x8D, 0x72, 0x11, 0x37,
|
||||
0xFB, 0xD8, 0x1E, 0x3F, 0x5B, 0x34, 0x30, 0x17, 0x8B, 0xE5,
|
||||
0x26, 0x28, 0x23, 0xA1, 0x8A, 0xA4, 0x29, 0xEA, 0xFD, 0x9E,
|
||||
0x39, 0x60, 0x8A, 0xF3, 0xB5, 0xA6, 0xEB, 0x3F, 0x02, 0xB6,
|
||||
0x16, 0xC3, 0x96, 0x9D, 0x38, 0xB0, 0x7D, 0x82, 0x87, 0x0C,
|
||||
0xF7, 0xBE, 0x24, 0xE5, 0x5F, 0x41, 0x04, 0x79, 0x76, 0x40,
|
||||
0xE7, 0x00, 0x22, 0x7E, 0xB5, 0x85, 0x7F, 0x8D, 0x01, 0x50,
|
||||
0xE9, 0xD3, 0x29, 0x42, 0x08, 0xB3, 0x51, 0x40, 0x7B, 0xD7,
|
||||
0x8D, 0xCC, 0x10, 0x01, 0x64, 0x59, 0x28, 0xB6, 0x53, 0xF3,
|
||||
0x50, 0x4E, 0xB1, 0xF2, 0x58, 0xCD, 0x6E, 0xF5, 0x56, 0x3E,
|
||||
0x66, 0x2F, 0xD7, 0x07, 0x7F, 0x52, 0x4C, 0x13, 0x24, 0xDC,
|
||||
0x8E, 0x8D, 0xCC, 0xED, 0x77, 0xC4, 0x21, 0xD2, 0xFD, 0x08,
|
||||
0xEA, 0xD7, 0xC0, 0x5C, 0x13, 0x82, 0x81, 0x31, 0x2F, 0x2B,
|
||||
0x08, 0xE4, 0x80, 0x04, 0x7A, 0x0C, 0x8A, 0x3C, 0xDC, 0x22,
|
||||
0xE4, 0x5A, 0x7A, 0xB0, 0x12, 0x5E, 0x4A, 0x76, 0x94, 0x77,
|
||||
0xC2, 0x0E, 0x92, 0xBA, 0x8A, 0xA0, 0x1F, 0x14, 0x51, 0x1E,
|
||||
0x66, 0x6C, 0x38, 0x03, 0x6C, 0xC7, 0x4A, 0x4B, 0x70, 0x80,
|
||||
0xAF, 0xCA, 0x84, 0x51, 0xD8, 0xD2, 0x26, 0x49, 0xF5, 0xA8,
|
||||
0x5E, 0x35, 0x4B, 0xAC, 0xCE, 0x29, 0x92, 0x33, 0xB7, 0xA2,
|
||||
0x69, 0x7D, 0x0C, 0xE0, 0x9C, 0xDB, 0x04, 0xD6, 0xB4, 0xBC,
|
||||
0x39, 0xD7, 0x7F, 0x9E, 0x9D, 0x78, 0x38, 0x7F, 0x51, 0x54,
|
||||
0x50, 0x8B, 0x9E, 0x9C, 0x03, 0x6C, 0xF5, 0x9D, 0x2C, 0x74,
|
||||
0x57, 0xF0, 0x27, 0x2A, 0xC3, 0x47, 0xCA, 0xB9, 0xD7, 0x5C,
|
||||
0xFF, 0xC2, 0xAC, 0x65, 0x4E, 0xBD
|
||||
};
|
||||
|
||||
/*
|
||||
* We need temporary values for at least 7 integers of the same size
|
||||
* as a factor (including header word); more space helps with performance
|
||||
* (in modular exponentiations), but we much prefer to remain under
|
||||
* 2 kilobytes in total, to save stack space. The macro TEMPS below
|
||||
* exceeds 1024 (which is a count in 16-bit words) when BR_MAX_RSA_SIZE
|
||||
* is greater than 4350 (default value is 4096, so the 2-kB limit is
|
||||
* maintained unless BR_MAX_RSA_SIZE was modified).
|
||||
*/
|
||||
#define MAX(x, y) ((x) > (y) ? (x) : (y))
|
||||
#define TEMPS MAX(1024, 7 * ((((BR_MAX_RSA_SIZE + 1) >> 1) + 29) / 15))
|
||||
|
||||
/*
|
||||
* Perform trial division on a candidate prime. This computes
|
||||
* y = SMALL_PRIMES mod x, then tries to compute y/y mod x. The
|
||||
* br_i15_moddiv() function will report an error if y is not invertible
|
||||
* modulo x. Returned value is 1 on success (none of the small primes
|
||||
* divides x), 0 on error (a non-trivial GCD is obtained).
|
||||
*
|
||||
* This function assumes that x is odd.
|
||||
*/
|
||||
static uint32_t
|
||||
trial_divisions(const uint16_t *x, uint16_t *t)
|
||||
{
|
||||
uint16_t *y;
|
||||
uint16_t x0i;
|
||||
|
||||
y = t;
|
||||
t += 1 + ((x[0] + 15) >> 4);
|
||||
x0i = br_i15_ninv15(x[1]);
|
||||
br_i15_decode_reduce(y, SMALL_PRIMES, sizeof SMALL_PRIMES, x);
|
||||
return br_i15_moddiv(y, y, x, x0i, t);
|
||||
}
|
||||
|
||||
/*
|
||||
* Perform n rounds of Miller-Rabin on the candidate prime x. This
|
||||
* function assumes that x = 3 mod 4.
|
||||
*
|
||||
* Returned value is 1 on success (all rounds completed successfully),
|
||||
* 0 otherwise.
|
||||
*/
|
||||
static uint32_t
|
||||
miller_rabin(const br_prng_class **rng, const uint16_t *x, int n,
|
||||
uint16_t *t, size_t tlen)
|
||||
{
|
||||
/*
|
||||
* Since x = 3 mod 4, the Miller-Rabin test is simple:
|
||||
* - get a random base a (such that 1 < a < x-1)
|
||||
* - compute z = a^((x-1)/2) mod x
|
||||
* - if z != 1 and z != x-1, the number x is composite
|
||||
*
|
||||
* We generate bases 'a' randomly with a size which is
|
||||
* one bit less than x, which ensures that a < x-1. It
|
||||
* is not useful to verify that a > 1 because the probability
|
||||
* that we get a value a equal to 0 or 1 is much smaller
|
||||
* than the probability of our Miller-Rabin tests not to
|
||||
* detect a composite, which is already quite smaller than the
|
||||
* probability of the hardware misbehaving and return a
|
||||
* composite integer because of some glitch (e.g. bad RAM
|
||||
* or ill-timed cosmic ray).
|
||||
*/
|
||||
unsigned char *xm1d2;
|
||||
size_t xlen, xm1d2_len, xm1d2_len_u16, u;
|
||||
uint32_t asize;
|
||||
unsigned cc;
|
||||
uint16_t x0i;
|
||||
|
||||
/*
|
||||
* Compute (x-1)/2 (encoded).
|
||||
*/
|
||||
xm1d2 = (unsigned char *)t;
|
||||
xm1d2_len = ((x[0] - (x[0] >> 4)) + 7) >> 3;
|
||||
br_i15_encode(xm1d2, xm1d2_len, x);
|
||||
cc = 0;
|
||||
for (u = 0; u < xm1d2_len; u ++) {
|
||||
unsigned w;
|
||||
|
||||
w = xm1d2[u];
|
||||
xm1d2[u] = (unsigned char)((w >> 1) | cc);
|
||||
cc = w << 7;
|
||||
}
|
||||
|
||||
/*
|
||||
* We used some words of the provided buffer for (x-1)/2.
|
||||
*/
|
||||
xm1d2_len_u16 = (xm1d2_len + 1) >> 1;
|
||||
t += xm1d2_len_u16;
|
||||
tlen -= xm1d2_len_u16;
|
||||
|
||||
xlen = (x[0] + 15) >> 4;
|
||||
asize = x[0] - 1 - EQ0(x[0] & 15);
|
||||
x0i = br_i15_ninv15(x[1]);
|
||||
while (n -- > 0) {
|
||||
uint16_t *a;
|
||||
uint32_t eq1, eqm1;
|
||||
|
||||
/*
|
||||
* Generate a random base. We don't need the base to be
|
||||
* really uniform modulo x, so we just get a random
|
||||
* number which is one bit shorter than x.
|
||||
*/
|
||||
a = t;
|
||||
a[0] = x[0];
|
||||
a[xlen] = 0;
|
||||
mkrand(rng, a, asize);
|
||||
|
||||
/*
|
||||
* Compute a^((x-1)/2) mod x. We assume here that the
|
||||
* function will not fail (the temporary array is large
|
||||
* enough).
|
||||
*/
|
||||
br_i15_modpow_opt(a, xm1d2, xm1d2_len,
|
||||
x, x0i, t + 1 + xlen, tlen - 1 - xlen);
|
||||
|
||||
/*
|
||||
* We must obtain either 1 or x-1. Note that x is odd,
|
||||
* hence x-1 differs from x only in its low word (no
|
||||
* carry).
|
||||
*/
|
||||
eq1 = a[1] ^ 1;
|
||||
eqm1 = a[1] ^ (x[1] - 1);
|
||||
for (u = 2; u <= xlen; u ++) {
|
||||
eq1 |= a[u];
|
||||
eqm1 |= a[u] ^ x[u];
|
||||
}
|
||||
|
||||
if ((EQ0(eq1) | EQ0(eqm1)) == 0) {
|
||||
return 0;
|
||||
}
|
||||
}
|
||||
return 1;
|
||||
}
|
||||
|
||||
/*
|
||||
* Create a random prime of the provided size. 'size' is the _encoded_
|
||||
* bit length. The two top bits and the two bottom bits are set to 1.
|
||||
*/
|
||||
static void
|
||||
mkprime(const br_prng_class **rng, uint16_t *x, uint32_t esize,
|
||||
uint32_t pubexp, uint16_t *t, size_t tlen)
|
||||
{
|
||||
size_t len;
|
||||
|
||||
x[0] = esize;
|
||||
len = (esize + 15) >> 4;
|
||||
for (;;) {
|
||||
size_t u;
|
||||
uint32_t m3, m5, m7, m11;
|
||||
int rounds;
|
||||
|
||||
/*
|
||||
* Generate random bits. We force the two top bits and the
|
||||
* two bottom bits to 1.
|
||||
*/
|
||||
mkrand(rng, x, esize);
|
||||
if ((esize & 15) == 0) {
|
||||
x[len] |= 0x6000;
|
||||
} else if ((esize & 15) == 1) {
|
||||
x[len] |= 0x0001;
|
||||
x[len - 1] |= 0x4000;
|
||||
} else {
|
||||
x[len] |= 0x0003 << ((esize & 15) - 2);
|
||||
}
|
||||
x[1] |= 0x0003;
|
||||
|
||||
/*
|
||||
* Trial division with low primes (3, 5, 7 and 11). We
|
||||
* use the following properties:
|
||||
*
|
||||
* 2^2 = 1 mod 3
|
||||
* 2^4 = 1 mod 5
|
||||
* 2^3 = 1 mod 7
|
||||
* 2^10 = 1 mod 11
|
||||
*/
|
||||
m3 = 0;
|
||||
m5 = 0;
|
||||
m7 = 0;
|
||||
m11 = 0;
|
||||
for (u = 0; u < len; u ++) {
|
||||
uint32_t w;
|
||||
|
||||
w = x[1 + u];
|
||||
m3 += w << (u & 1);
|
||||
m3 = (m3 & 0xFF) + (m3 >> 8);
|
||||
m5 += w << ((4 - u) & 3);
|
||||
m5 = (m5 & 0xFF) + (m5 >> 8);
|
||||
m7 += w;
|
||||
m7 = (m7 & 0x1FF) + (m7 >> 9);
|
||||
m11 += w << (5 & -(u & 1));
|
||||
m11 = (m11 & 0x3FF) + (m11 >> 10);
|
||||
}
|
||||
|
||||
/*
|
||||
* Maximum values of m* at this point:
|
||||
* m3: 511
|
||||
* m5: 2310
|
||||
* m7: 510
|
||||
* m11: 2047
|
||||
* We use the same properties to make further reductions.
|
||||
*/
|
||||
|
||||
m3 = (m3 & 0x0F) + (m3 >> 4); /* max: 46 */
|
||||
m3 = (m3 & 0x0F) + (m3 >> 4); /* max: 16 */
|
||||
m3 = ((m3 * 43) >> 5) & 3;
|
||||
|
||||
m5 = (m5 & 0xFF) + (m5 >> 8); /* max: 263 */
|
||||
m5 = (m5 & 0x0F) + (m5 >> 4); /* max: 30 */
|
||||
m5 = (m5 & 0x0F) + (m5 >> 4); /* max: 15 */
|
||||
m5 -= 10 & -GT(m5, 9);
|
||||
m5 -= 5 & -GT(m5, 4);
|
||||
|
||||
m7 = (m7 & 0x3F) + (m7 >> 6); /* max: 69 */
|
||||
m7 = (m7 & 7) + (m7 >> 3); /* max: 14 */
|
||||
m7 = ((m7 * 147) >> 7) & 7;
|
||||
|
||||
/*
|
||||
* 2^5 = 32 = -1 mod 11.
|
||||
*/
|
||||
m11 = (m11 & 0x1F) + 66 - (m11 >> 5); /* max: 97 */
|
||||
m11 -= 88 & -GT(m11, 87);
|
||||
m11 -= 44 & -GT(m11, 43);
|
||||
m11 -= 22 & -GT(m11, 21);
|
||||
m11 -= 11 & -GT(m11, 10);
|
||||
|
||||
/*
|
||||
* If any of these modulo is 0, then the candidate is
|
||||
* not prime. Also, if pubexp is 3, 5, 7 or 11, and the
|
||||
* corresponding modulus is 1, then the candidate must
|
||||
* be rejected, because we need e to be invertible
|
||||
* modulo p-1. We can use simple comparisons here
|
||||
* because they won't leak information on a candidate
|
||||
* that we keep, only on one that we reject (and is thus
|
||||
* not secret).
|
||||
*/
|
||||
if (m3 == 0 || m5 == 0 || m7 == 0 || m11 == 0) {
|
||||
continue;
|
||||
}
|
||||
if ((pubexp == 3 && m3 == 1)
|
||||
|| (pubexp == 5 && m5 == 5)
|
||||
|| (pubexp == 7 && m5 == 7)
|
||||
|| (pubexp == 11 && m5 == 11))
|
||||
{
|
||||
continue;
|
||||
}
|
||||
|
||||
/*
|
||||
* More trial divisions.
|
||||
*/
|
||||
if (!trial_divisions(x, t)) {
|
||||
continue;
|
||||
}
|
||||
|
||||
/*
|
||||
* Miller-Rabin algorithm. Since we selected a random
|
||||
* integer, not a maliciously crafted integer, we can use
|
||||
* relatively few rounds to lower the risk of a false
|
||||
* positive (i.e. declaring prime a non-prime) under
|
||||
* 2^(-80). It is not useful to lower the probability much
|
||||
* below that, since that would be substantially below
|
||||
* the probability of the hardware misbehaving. Sufficient
|
||||
* numbers of rounds are extracted from the Handbook of
|
||||
* Applied Cryptography, note 4.49 (page 149).
|
||||
*
|
||||
* Since we work on the encoded size (esize), we need to
|
||||
* compare with encoded thresholds.
|
||||
*/
|
||||
if (esize < 320) {
|
||||
rounds = 12;
|
||||
} else if (esize < 480) {
|
||||
rounds = 9;
|
||||
} else if (esize < 693) {
|
||||
rounds = 6;
|
||||
} else if (esize < 906) {
|
||||
rounds = 4;
|
||||
} else if (esize < 1386) {
|
||||
rounds = 3;
|
||||
} else {
|
||||
rounds = 2;
|
||||
}
|
||||
|
||||
if (miller_rabin(rng, x, rounds, t, tlen)) {
|
||||
return;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
/*
|
||||
* Let p be a prime (p > 2^33, p = 3 mod 4). Let m = (p-1)/2, provided
|
||||
* as parameter (with announced bit length equal to that of p). This
|
||||
* function computes d = 1/e mod p-1 (for an odd integer e). Returned
|
||||
* value is 1 on success, 0 on error (an error is reported if e is not
|
||||
* invertible modulo p-1).
|
||||
*
|
||||
* The temporary buffer (t) must have room for at least 4 integers of
|
||||
* the size of p.
|
||||
*/
|
||||
static uint32_t
|
||||
invert_pubexp(uint16_t *d, const uint16_t *m, uint32_t e, uint16_t *t)
|
||||
{
|
||||
uint16_t *f;
|
||||
uint32_t r;
|
||||
|
||||
f = t;
|
||||
t += 1 + ((m[0] + 15) >> 4);
|
||||
|
||||
/*
|
||||
* Compute d = 1/e mod m. Since p = 3 mod 4, m is odd.
|
||||
*/
|
||||
br_i15_zero(d, m[0]);
|
||||
d[1] = 1;
|
||||
br_i15_zero(f, m[0]);
|
||||
f[1] = e & 0x7FFF;
|
||||
f[2] = (e >> 15) & 0x7FFF;
|
||||
f[3] = e >> 30;
|
||||
r = br_i15_moddiv(d, f, m, br_i15_ninv15(m[1]), t);
|
||||
|
||||
/*
|
||||
* We really want d = 1/e mod p-1, with p = 2m. By the CRT,
|
||||
* the result is either the d we got, or d + m.
|
||||
*
|
||||
* Let's write e*d = 1 + k*m, for some integer k. Integers e
|
||||
* and m are odd. If d is odd, then e*d is odd, which implies
|
||||
* that k must be even; in that case, e*d = 1 + (k/2)*2m, and
|
||||
* thus d is already fine. Conversely, if d is even, then k
|
||||
* is odd, and we must add m to d in order to get the correct
|
||||
* result.
|
||||
*/
|
||||
br_i15_add(d, m, (uint32_t)(1 - (d[1] & 1)));
|
||||
|
||||
return r;
|
||||
}
|
||||
|
||||
/*
|
||||
* Swap two buffers in RAM. They must be disjoint.
|
||||
*/
|
||||
static void
|
||||
bufswap(void *b1, void *b2, size_t len)
|
||||
{
|
||||
size_t u;
|
||||
unsigned char *buf1, *buf2;
|
||||
|
||||
buf1 = b1;
|
||||
buf2 = b2;
|
||||
for (u = 0; u < len; u ++) {
|
||||
unsigned w;
|
||||
|
||||
w = buf1[u];
|
||||
buf1[u] = buf2[u];
|
||||
buf2[u] = w;
|
||||
}
|
||||
}
|
||||
|
||||
/* see bearssl_rsa.h */
|
||||
uint32_t
|
||||
br_rsa_i15_keygen(const br_prng_class **rng,
|
||||
br_rsa_private_key *sk, unsigned char *kbuf_priv,
|
||||
br_rsa_public_key *pk, unsigned char *kbuf_pub,
|
||||
unsigned size, uint32_t pubexp)
|
||||
{
|
||||
uint32_t esize_p, esize_q;
|
||||
size_t plen, qlen, tlen;
|
||||
uint16_t *p, *q, *t;
|
||||
uint16_t tmp[TEMPS];
|
||||
uint32_t r;
|
||||
|
||||
if (size < BR_MIN_RSA_SIZE || size > BR_MAX_RSA_SIZE) {
|
||||
return 0;
|
||||
}
|
||||
if (pubexp == 0) {
|
||||
pubexp = 3;
|
||||
} else if (pubexp == 1 || (pubexp & 1) == 0) {
|
||||
return 0;
|
||||
}
|
||||
|
||||
esize_p = (size + 1) >> 1;
|
||||
esize_q = size - esize_p;
|
||||
sk->n_bitlen = size;
|
||||
sk->p = kbuf_priv;
|
||||
sk->plen = (esize_p + 7) >> 3;
|
||||
sk->q = sk->p + sk->plen;
|
||||
sk->qlen = (esize_q + 7) >> 3;
|
||||
sk->dp = sk->q + sk->qlen;
|
||||
sk->dplen = sk->plen;
|
||||
sk->dq = sk->dp + sk->dplen;
|
||||
sk->dqlen = sk->qlen;
|
||||
sk->iq = sk->dq + sk->dqlen;
|
||||
sk->iqlen = sk->plen;
|
||||
|
||||
if (pk != NULL) {
|
||||
pk->n = kbuf_pub;
|
||||
pk->nlen = (size + 7) >> 3;
|
||||
pk->e = pk->n + pk->nlen;
|
||||
pk->elen = 4;
|
||||
br_enc32be(pk->e, pubexp);
|
||||
while (*pk->e == 0) {
|
||||
pk->e ++;
|
||||
pk->elen --;
|
||||
}
|
||||
}
|
||||
|
||||
/*
|
||||
* We now switch to encoded sizes.
|
||||
*
|
||||
* floor((x * 17477) / (2^18)) is equal to floor(x/15) for all
|
||||
* integers x from 0 to 23833.
|
||||
*/
|
||||
esize_p += MUL15(esize_p, 17477) >> 18;
|
||||
esize_q += MUL15(esize_q, 17477) >> 18;
|
||||
plen = (esize_p + 15) >> 4;
|
||||
qlen = (esize_q + 15) >> 4;
|
||||
p = tmp;
|
||||
q = p + 1 + plen;
|
||||
t = q + 1 + qlen;
|
||||
tlen = ((sizeof tmp) / sizeof(uint16_t)) - (2 + plen + qlen);
|
||||
|
||||
/*
|
||||
* When looking for primes p and q, we temporarily divide
|
||||
* candidates by 2, in order to compute the inverse of the
|
||||
* public exponent.
|
||||
*/
|
||||
|
||||
for (;;) {
|
||||
mkprime(rng, p, esize_p, pubexp, t, tlen);
|
||||
br_i15_rshift(p, 1);
|
||||
if (invert_pubexp(t, p, pubexp, t + 1 + plen)) {
|
||||
br_i15_add(p, p, 1);
|
||||
p[1] |= 1;
|
||||
br_i15_encode(sk->p, sk->plen, p);
|
||||
br_i15_encode(sk->dp, sk->dplen, t);
|
||||
break;
|
||||
}
|
||||
}
|
||||
|
||||
for (;;) {
|
||||
mkprime(rng, q, esize_q, pubexp, t, tlen);
|
||||
br_i15_rshift(q, 1);
|
||||
if (invert_pubexp(t, q, pubexp, t + 1 + qlen)) {
|
||||
br_i15_add(q, q, 1);
|
||||
q[1] |= 1;
|
||||
br_i15_encode(sk->q, sk->qlen, q);
|
||||
br_i15_encode(sk->dq, sk->dqlen, t);
|
||||
break;
|
||||
}
|
||||
}
|
||||
|
||||
/*
|
||||
* If p and q have the same size, then it is possible that q > p
|
||||
* (when the target modulus size is odd, we generate p with a
|
||||
* greater bit length than q). If q > p, we want to swap p and q
|
||||
* (and also dp and dq) for two reasons:
|
||||
* - The final step below (inversion of q modulo p) is easier if
|
||||
* p > q.
|
||||
* - While BearSSL's RSA code is perfectly happy with RSA keys such
|
||||
* that p < q, some other implementations have restrictions and
|
||||
* require p > q.
|
||||
*
|
||||
* Note that we can do a simple non-constant-time swap here,
|
||||
* because the only information we leak here is that we insist on
|
||||
* returning p and q such that p > q, which is not a secret.
|
||||
*/
|
||||
if (esize_p == esize_q && br_i15_sub(p, q, 0) == 1) {
|
||||
bufswap(p, q, (1 + plen) * sizeof *p);
|
||||
bufswap(sk->p, sk->q, sk->plen);
|
||||
bufswap(sk->dp, sk->dq, sk->dplen);
|
||||
}
|
||||
|
||||
/*
|
||||
* We have produced p, q, dp and dq. We can now compute iq = 1/d mod p.
|
||||
*
|
||||
* We ensured that p >= q, so this is just a matter of updating the
|
||||
* header word for q (and possibly adding an extra word).
|
||||
*
|
||||
* Theoretically, the call below may fail, in case we were
|
||||
* extraordinarily unlucky, and p = q. Another failure case is if
|
||||
* Miller-Rabin failed us _twice_, and p and q are non-prime and
|
||||
* have a factor is common. We report the error mostly because it
|
||||
* is cheap and we can, but in practice this never happens (or, at
|
||||
* least, it happens way less often than hardware glitches).
|
||||
*/
|
||||
q[0] = p[0];
|
||||
if (plen > qlen) {
|
||||
q[plen] = 0;
|
||||
t ++;
|
||||
tlen --;
|
||||
}
|
||||
br_i15_zero(t, p[0]);
|
||||
t[1] = 1;
|
||||
r = br_i15_moddiv(t, q, p, br_i15_ninv15(p[1]), t + 1 + plen);
|
||||
br_i15_encode(sk->iq, sk->iqlen, t);
|
||||
|
||||
/*
|
||||
* Compute the public modulus too, if required.
|
||||
*/
|
||||
if (pk != NULL) {
|
||||
br_i15_zero(t, p[0]);
|
||||
br_i15_mulacc(t, p, q);
|
||||
br_i15_encode(pk->n, pk->nlen, t);
|
||||
}
|
||||
|
||||
return r;
|
||||
}
|
||||
37
src/rsa/rsa_i31_keygen.c
Normal file
37
src/rsa/rsa_i31_keygen.c
Normal file
|
|
@ -0,0 +1,37 @@
|
|||
/*
|
||||
* Copyright (c) 2018 Thomas Pornin <pornin@bolet.org>
|
||||
*
|
||||
* Permission is hereby granted, free of charge, to any person obtaining
|
||||
* a copy of this software and associated documentation files (the
|
||||
* "Software"), to deal in the Software without restriction, including
|
||||
* without limitation the rights to use, copy, modify, merge, publish,
|
||||
* distribute, sublicense, and/or sell copies of the Software, and to
|
||||
* permit persons to whom the Software is furnished to do so, subject to
|
||||
* the following conditions:
|
||||
*
|
||||
* The above copyright notice and this permission notice shall be
|
||||
* included in all copies or substantial portions of the Software.
|
||||
*
|
||||
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
|
||||
* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
|
||||
* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
|
||||
* NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
|
||||
* BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
|
||||
* ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
|
||||
* CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
|
||||
* SOFTWARE.
|
||||
*/
|
||||
|
||||
#include "inner.h"
|
||||
|
||||
/* see bearssl_rsa.h */
|
||||
uint32_t
|
||||
br_rsa_i31_keygen(const br_prng_class **rng,
|
||||
br_rsa_private_key *sk, unsigned char *kbuf_priv,
|
||||
br_rsa_public_key *pk, unsigned char *kbuf_pub,
|
||||
unsigned size, uint32_t pubexp)
|
||||
{
|
||||
return br_rsa_i31_keygen_inner(rng,
|
||||
sk, kbuf_priv, pk, kbuf_pub, size, pubexp,
|
||||
&br_i31_modpow_opt);
|
||||
}
|
||||
608
src/rsa/rsa_i31_keygen_inner.c
Normal file
608
src/rsa/rsa_i31_keygen_inner.c
Normal file
|
|
@ -0,0 +1,608 @@
|
|||
/*
|
||||
* Copyright (c) 2018 Thomas Pornin <pornin@bolet.org>
|
||||
*
|
||||
* Permission is hereby granted, free of charge, to any person obtaining
|
||||
* a copy of this software and associated documentation files (the
|
||||
* "Software"), to deal in the Software without restriction, including
|
||||
* without limitation the rights to use, copy, modify, merge, publish,
|
||||
* distribute, sublicense, and/or sell copies of the Software, and to
|
||||
* permit persons to whom the Software is furnished to do so, subject to
|
||||
* the following conditions:
|
||||
*
|
||||
* The above copyright notice and this permission notice shall be
|
||||
* included in all copies or substantial portions of the Software.
|
||||
*
|
||||
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
|
||||
* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
|
||||
* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
|
||||
* NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
|
||||
* BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
|
||||
* ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
|
||||
* CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
|
||||
* SOFTWARE.
|
||||
*/
|
||||
|
||||
#include "inner.h"
|
||||
|
||||
/*
|
||||
* Make a random integer of the provided size. The size is encoded.
|
||||
* The header word is untouched.
|
||||
*/
|
||||
static void
|
||||
mkrand(const br_prng_class **rng, uint32_t *x, uint32_t esize)
|
||||
{
|
||||
size_t u, len;
|
||||
unsigned m;
|
||||
|
||||
len = (esize + 31) >> 5;
|
||||
(*rng)->generate(rng, x + 1, len * sizeof(uint32_t));
|
||||
for (u = 1; u < len; u ++) {
|
||||
x[u] &= 0x7FFFFFFF;
|
||||
}
|
||||
m = esize & 31;
|
||||
if (m == 0) {
|
||||
x[len] &= 0x7FFFFFFF;
|
||||
} else {
|
||||
x[len] &= 0x7FFFFFFF >> (31 - m);
|
||||
}
|
||||
}
|
||||
|
||||
/*
|
||||
* This is the big-endian unsigned representation of the product of
|
||||
* all small primes from 13 to 1481.
|
||||
*/
|
||||
static const unsigned char SMALL_PRIMES[] = {
|
||||
0x2E, 0xAB, 0x92, 0xD1, 0x8B, 0x12, 0x47, 0x31, 0x54, 0x0A,
|
||||
0x99, 0x5D, 0x25, 0x5E, 0xE2, 0x14, 0x96, 0x29, 0x1E, 0xB7,
|
||||
0x78, 0x70, 0xCC, 0x1F, 0xA5, 0xAB, 0x8D, 0x72, 0x11, 0x37,
|
||||
0xFB, 0xD8, 0x1E, 0x3F, 0x5B, 0x34, 0x30, 0x17, 0x8B, 0xE5,
|
||||
0x26, 0x28, 0x23, 0xA1, 0x8A, 0xA4, 0x29, 0xEA, 0xFD, 0x9E,
|
||||
0x39, 0x60, 0x8A, 0xF3, 0xB5, 0xA6, 0xEB, 0x3F, 0x02, 0xB6,
|
||||
0x16, 0xC3, 0x96, 0x9D, 0x38, 0xB0, 0x7D, 0x82, 0x87, 0x0C,
|
||||
0xF7, 0xBE, 0x24, 0xE5, 0x5F, 0x41, 0x04, 0x79, 0x76, 0x40,
|
||||
0xE7, 0x00, 0x22, 0x7E, 0xB5, 0x85, 0x7F, 0x8D, 0x01, 0x50,
|
||||
0xE9, 0xD3, 0x29, 0x42, 0x08, 0xB3, 0x51, 0x40, 0x7B, 0xD7,
|
||||
0x8D, 0xCC, 0x10, 0x01, 0x64, 0x59, 0x28, 0xB6, 0x53, 0xF3,
|
||||
0x50, 0x4E, 0xB1, 0xF2, 0x58, 0xCD, 0x6E, 0xF5, 0x56, 0x3E,
|
||||
0x66, 0x2F, 0xD7, 0x07, 0x7F, 0x52, 0x4C, 0x13, 0x24, 0xDC,
|
||||
0x8E, 0x8D, 0xCC, 0xED, 0x77, 0xC4, 0x21, 0xD2, 0xFD, 0x08,
|
||||
0xEA, 0xD7, 0xC0, 0x5C, 0x13, 0x82, 0x81, 0x31, 0x2F, 0x2B,
|
||||
0x08, 0xE4, 0x80, 0x04, 0x7A, 0x0C, 0x8A, 0x3C, 0xDC, 0x22,
|
||||
0xE4, 0x5A, 0x7A, 0xB0, 0x12, 0x5E, 0x4A, 0x76, 0x94, 0x77,
|
||||
0xC2, 0x0E, 0x92, 0xBA, 0x8A, 0xA0, 0x1F, 0x14, 0x51, 0x1E,
|
||||
0x66, 0x6C, 0x38, 0x03, 0x6C, 0xC7, 0x4A, 0x4B, 0x70, 0x80,
|
||||
0xAF, 0xCA, 0x84, 0x51, 0xD8, 0xD2, 0x26, 0x49, 0xF5, 0xA8,
|
||||
0x5E, 0x35, 0x4B, 0xAC, 0xCE, 0x29, 0x92, 0x33, 0xB7, 0xA2,
|
||||
0x69, 0x7D, 0x0C, 0xE0, 0x9C, 0xDB, 0x04, 0xD6, 0xB4, 0xBC,
|
||||
0x39, 0xD7, 0x7F, 0x9E, 0x9D, 0x78, 0x38, 0x7F, 0x51, 0x54,
|
||||
0x50, 0x8B, 0x9E, 0x9C, 0x03, 0x6C, 0xF5, 0x9D, 0x2C, 0x74,
|
||||
0x57, 0xF0, 0x27, 0x2A, 0xC3, 0x47, 0xCA, 0xB9, 0xD7, 0x5C,
|
||||
0xFF, 0xC2, 0xAC, 0x65, 0x4E, 0xBD
|
||||
};
|
||||
|
||||
/*
|
||||
* We need temporary values for at least 7 integers of the same size
|
||||
* as a factor (including header word); more space helps with performance
|
||||
* (in modular exponentiations), but we much prefer to remain under
|
||||
* 2 kilobytes in total, to save stack space. The macro TEMPS below
|
||||
* exceeds 512 (which is a count in 32-bit words) when BR_MAX_RSA_SIZE
|
||||
* is greater than 4464 (default value is 4096, so the 2-kB limit is
|
||||
* maintained unless BR_MAX_RSA_SIZE was modified).
|
||||
*/
|
||||
#define MAX(x, y) ((x) > (y) ? (x) : (y))
|
||||
#define ROUND2(x) ((((x) + 1) >> 1) << 1)
|
||||
|
||||
#define TEMPS MAX(512, ROUND2(7 * ((((BR_MAX_RSA_SIZE + 1) >> 1) + 61) / 31)))
|
||||
|
||||
/*
|
||||
* Perform trial division on a candidate prime. This computes
|
||||
* y = SMALL_PRIMES mod x, then tries to compute y/y mod x. The
|
||||
* br_i31_moddiv() function will report an error if y is not invertible
|
||||
* modulo x. Returned value is 1 on success (none of the small primes
|
||||
* divides x), 0 on error (a non-trivial GCD is obtained).
|
||||
*
|
||||
* This function assumes that x is odd.
|
||||
*/
|
||||
static uint32_t
|
||||
trial_divisions(const uint32_t *x, uint32_t *t)
|
||||
{
|
||||
uint32_t *y;
|
||||
uint32_t x0i;
|
||||
|
||||
y = t;
|
||||
t += 1 + ((x[0] + 31) >> 5);
|
||||
x0i = br_i31_ninv31(x[1]);
|
||||
br_i31_decode_reduce(y, SMALL_PRIMES, sizeof SMALL_PRIMES, x);
|
||||
return br_i31_moddiv(y, y, x, x0i, t);
|
||||
}
|
||||
|
||||
/*
|
||||
* Perform n rounds of Miller-Rabin on the candidate prime x. This
|
||||
* function assumes that x = 3 mod 4.
|
||||
*
|
||||
* Returned value is 1 on success (all rounds completed successfully),
|
||||
* 0 otherwise.
|
||||
*/
|
||||
static uint32_t
|
||||
miller_rabin(const br_prng_class **rng, const uint32_t *x, int n,
|
||||
uint32_t *t, size_t tlen, br_i31_modpow_opt_type mp31)
|
||||
{
|
||||
/*
|
||||
* Since x = 3 mod 4, the Miller-Rabin test is simple:
|
||||
* - get a random base a (such that 1 < a < x-1)
|
||||
* - compute z = a^((x-1)/2) mod x
|
||||
* - if z != 1 and z != x-1, the number x is composite
|
||||
*
|
||||
* We generate bases 'a' randomly with a size which is
|
||||
* one bit less than x, which ensures that a < x-1. It
|
||||
* is not useful to verify that a > 1 because the probability
|
||||
* that we get a value a equal to 0 or 1 is much smaller
|
||||
* than the probability of our Miller-Rabin tests not to
|
||||
* detect a composite, which is already quite smaller than the
|
||||
* probability of the hardware misbehaving and return a
|
||||
* composite integer because of some glitch (e.g. bad RAM
|
||||
* or ill-timed cosmic ray).
|
||||
*/
|
||||
unsigned char *xm1d2;
|
||||
size_t xlen, xm1d2_len, xm1d2_len_u32, u;
|
||||
uint32_t asize;
|
||||
unsigned cc;
|
||||
uint32_t x0i;
|
||||
|
||||
/*
|
||||
* Compute (x-1)/2 (encoded).
|
||||
*/
|
||||
xm1d2 = (unsigned char *)t;
|
||||
xm1d2_len = ((x[0] - (x[0] >> 5)) + 7) >> 3;
|
||||
br_i31_encode(xm1d2, xm1d2_len, x);
|
||||
cc = 0;
|
||||
for (u = 0; u < xm1d2_len; u ++) {
|
||||
unsigned w;
|
||||
|
||||
w = xm1d2[u];
|
||||
xm1d2[u] = (unsigned char)((w >> 1) | cc);
|
||||
cc = w << 7;
|
||||
}
|
||||
|
||||
/*
|
||||
* We used some words of the provided buffer for (x-1)/2.
|
||||
*/
|
||||
xm1d2_len_u32 = (xm1d2_len + 3) >> 2;
|
||||
t += xm1d2_len_u32;
|
||||
tlen -= xm1d2_len_u32;
|
||||
|
||||
xlen = (x[0] + 31) >> 5;
|
||||
asize = x[0] - 1 - EQ0(x[0] & 31);
|
||||
x0i = br_i31_ninv31(x[1]);
|
||||
while (n -- > 0) {
|
||||
uint32_t *a, *t2;
|
||||
uint32_t eq1, eqm1;
|
||||
size_t t2len;
|
||||
|
||||
/*
|
||||
* Generate a random base. We don't need the base to be
|
||||
* really uniform modulo x, so we just get a random
|
||||
* number which is one bit shorter than x.
|
||||
*/
|
||||
a = t;
|
||||
a[0] = x[0];
|
||||
a[xlen] = 0;
|
||||
mkrand(rng, a, asize);
|
||||
|
||||
/*
|
||||
* Compute a^((x-1)/2) mod x. We assume here that the
|
||||
* function will not fail (the temporary array is large
|
||||
* enough).
|
||||
*/
|
||||
t2 = t + 1 + xlen;
|
||||
t2len = tlen - 1 - xlen;
|
||||
if ((t2len & 1) != 0) {
|
||||
/*
|
||||
* Since the source array is 64-bit aligned and
|
||||
* has an even number of elements (TEMPS), we
|
||||
* can use the parity of the remaining length to
|
||||
* detect and adjust alignment.
|
||||
*/
|
||||
t2 ++;
|
||||
t2len --;
|
||||
}
|
||||
mp31(a, xm1d2, xm1d2_len, x, x0i, t2, t2len);
|
||||
|
||||
/*
|
||||
* We must obtain either 1 or x-1. Note that x is odd,
|
||||
* hence x-1 differs from x only in its low word (no
|
||||
* carry).
|
||||
*/
|
||||
eq1 = a[1] ^ 1;
|
||||
eqm1 = a[1] ^ (x[1] - 1);
|
||||
for (u = 2; u <= xlen; u ++) {
|
||||
eq1 |= a[u];
|
||||
eqm1 |= a[u] ^ x[u];
|
||||
}
|
||||
|
||||
if ((EQ0(eq1) | EQ0(eqm1)) == 0) {
|
||||
return 0;
|
||||
}
|
||||
}
|
||||
return 1;
|
||||
}
|
||||
|
||||
/*
|
||||
* Create a random prime of the provided size. 'size' is the _encoded_
|
||||
* bit length. The two top bits and the two bottom bits are set to 1.
|
||||
*/
|
||||
static void
|
||||
mkprime(const br_prng_class **rng, uint32_t *x, uint32_t esize,
|
||||
uint32_t pubexp, uint32_t *t, size_t tlen, br_i31_modpow_opt_type mp31)
|
||||
{
|
||||
size_t len;
|
||||
|
||||
x[0] = esize;
|
||||
len = (esize + 31) >> 5;
|
||||
for (;;) {
|
||||
size_t u;
|
||||
uint32_t m3, m5, m7, m11;
|
||||
int rounds, s7, s11;
|
||||
|
||||
/*
|
||||
* Generate random bits. We force the two top bits and the
|
||||
* two bottom bits to 1.
|
||||
*/
|
||||
mkrand(rng, x, esize);
|
||||
if ((esize & 31) == 0) {
|
||||
x[len] |= 0x60000000;
|
||||
} else if ((esize & 31) == 1) {
|
||||
x[len] |= 0x00000001;
|
||||
x[len - 1] |= 0x40000000;
|
||||
} else {
|
||||
x[len] |= 0x00000003 << ((esize & 31) - 2);
|
||||
}
|
||||
x[1] |= 0x00000003;
|
||||
|
||||
/*
|
||||
* Trial division with low primes (3, 5, 7 and 11). We
|
||||
* use the following properties:
|
||||
*
|
||||
* 2^2 = 1 mod 3
|
||||
* 2^4 = 1 mod 5
|
||||
* 2^3 = 1 mod 7
|
||||
* 2^10 = 1 mod 11
|
||||
*/
|
||||
m3 = 0;
|
||||
m5 = 0;
|
||||
m7 = 0;
|
||||
m11 = 0;
|
||||
s7 = 0;
|
||||
s11 = 0;
|
||||
for (u = 0; u < len; u ++) {
|
||||
uint32_t w, w3, w5, w7, w11;
|
||||
|
||||
w = x[1 + u];
|
||||
w3 = (w & 0xFFFF) + (w >> 16); /* max: 98302 */
|
||||
w5 = (w & 0xFFFF) + (w >> 16); /* max: 98302 */
|
||||
w7 = (w & 0x7FFF) + (w >> 15); /* max: 98302 */
|
||||
w11 = (w & 0xFFFFF) + (w >> 20); /* max: 1050622 */
|
||||
|
||||
m3 += w3 << (u & 1);
|
||||
m3 = (m3 & 0xFF) + (m3 >> 8); /* max: 1025 */
|
||||
|
||||
m5 += w5 << ((4 - u) & 3);
|
||||
m5 = (m5 & 0xFFF) + (m5 >> 12); /* max: 4479 */
|
||||
|
||||
m7 += w7 << s7;
|
||||
m7 = (m7 & 0x1FF) + (m7 >> 9); /* max: 1280 */
|
||||
if (++ s7 == 3) {
|
||||
s7 = 0;
|
||||
}
|
||||
|
||||
m11 += w11 << s11;
|
||||
if (++ s11 == 10) {
|
||||
s11 = 0;
|
||||
}
|
||||
m11 = (m11 & 0x3FF) + (m11 >> 10); /* max: 526847 */
|
||||
}
|
||||
|
||||
m3 = (m3 & 0x3F) + (m3 >> 6); /* max: 78 */
|
||||
m3 = (m3 & 0x0F) + (m3 >> 4); /* max: 18 */
|
||||
m3 = ((m3 * 43) >> 5) & 3;
|
||||
|
||||
m5 = (m5 & 0xFF) + (m5 >> 8); /* max: 271 */
|
||||
m5 = (m5 & 0x0F) + (m5 >> 4); /* max: 31 */
|
||||
m5 -= 20 & -GT(m5, 19);
|
||||
m5 -= 10 & -GT(m5, 9);
|
||||
m5 -= 5 & -GT(m5, 4);
|
||||
|
||||
m7 = (m7 & 0x3F) + (m7 >> 6); /* max: 82 */
|
||||
m7 = (m7 & 0x07) + (m7 >> 3); /* max: 16 */
|
||||
m7 = ((m7 * 147) >> 7) & 7;
|
||||
|
||||
/*
|
||||
* 2^5 = 32 = -1 mod 11.
|
||||
*/
|
||||
m11 = (m11 & 0x3FF) + (m11 >> 10); /* max: 1536 */
|
||||
m11 = (m11 & 0x3FF) + (m11 >> 10); /* max: 1023 */
|
||||
m11 = (m11 & 0x1F) + 33 - (m11 >> 5); /* max: 64 */
|
||||
m11 -= 44 & -GT(m11, 43);
|
||||
m11 -= 22 & -GT(m11, 21);
|
||||
m11 -= 11 & -GT(m11, 10);
|
||||
|
||||
/*
|
||||
* If any of these modulo is 0, then the candidate is
|
||||
* not prime. Also, if pubexp is 3, 5, 7 or 11, and the
|
||||
* corresponding modulus is 1, then the candidate must
|
||||
* be rejected, because we need e to be invertible
|
||||
* modulo p-1. We can use simple comparisons here
|
||||
* because they won't leak information on a candidate
|
||||
* that we keep, only on one that we reject (and is thus
|
||||
* not secret).
|
||||
*/
|
||||
if (m3 == 0 || m5 == 0 || m7 == 0 || m11 == 0) {
|
||||
continue;
|
||||
}
|
||||
if ((pubexp == 3 && m3 == 1)
|
||||
|| (pubexp == 5 && m5 == 5)
|
||||
|| (pubexp == 7 && m5 == 7)
|
||||
|| (pubexp == 11 && m5 == 11))
|
||||
{
|
||||
continue;
|
||||
}
|
||||
|
||||
/*
|
||||
* More trial divisions.
|
||||
*/
|
||||
if (!trial_divisions(x, t)) {
|
||||
continue;
|
||||
}
|
||||
|
||||
/*
|
||||
* Miller-Rabin algorithm. Since we selected a random
|
||||
* integer, not a maliciously crafted integer, we can use
|
||||
* relatively few rounds to lower the risk of a false
|
||||
* positive (i.e. declaring prime a non-prime) under
|
||||
* 2^(-80). It is not useful to lower the probability much
|
||||
* below that, since that would be substantially below
|
||||
* the probability of the hardware misbehaving. Sufficient
|
||||
* numbers of rounds are extracted from the Handbook of
|
||||
* Applied Cryptography, note 4.49 (page 149).
|
||||
*
|
||||
* Since we work on the encoded size (esize), we need to
|
||||
* compare with encoded thresholds.
|
||||
*/
|
||||
if (esize < 309) {
|
||||
rounds = 12;
|
||||
} else if (esize < 464) {
|
||||
rounds = 9;
|
||||
} else if (esize < 670) {
|
||||
rounds = 6;
|
||||
} else if (esize < 877) {
|
||||
rounds = 4;
|
||||
} else if (esize < 1341) {
|
||||
rounds = 3;
|
||||
} else {
|
||||
rounds = 2;
|
||||
}
|
||||
|
||||
if (miller_rabin(rng, x, rounds, t, tlen, mp31)) {
|
||||
return;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
/*
|
||||
* Let p be a prime (p > 2^33, p = 3 mod 4). Let m = (p-1)/2, provided
|
||||
* as parameter (with announced bit length equal to that of p). This
|
||||
* function computes d = 1/e mod p-1 (for an odd integer e). Returned
|
||||
* value is 1 on success, 0 on error (an error is reported if e is not
|
||||
* invertible modulo p-1).
|
||||
*
|
||||
* The temporary buffer (t) must have room for at least 4 integers of
|
||||
* the size of p.
|
||||
*/
|
||||
static uint32_t
|
||||
invert_pubexp(uint32_t *d, const uint32_t *m, uint32_t e, uint32_t *t)
|
||||
{
|
||||
uint32_t *f;
|
||||
uint32_t r;
|
||||
|
||||
f = t;
|
||||
t += 1 + ((m[0] + 31) >> 5);
|
||||
|
||||
/*
|
||||
* Compute d = 1/e mod m. Since p = 3 mod 4, m is odd.
|
||||
*/
|
||||
br_i31_zero(d, m[0]);
|
||||
d[1] = 1;
|
||||
br_i31_zero(f, m[0]);
|
||||
f[1] = e & 0x7FFFFFFF;
|
||||
f[2] = e >> 31;
|
||||
r = br_i31_moddiv(d, f, m, br_i31_ninv31(m[1]), t);
|
||||
|
||||
/*
|
||||
* We really want d = 1/e mod p-1, with p = 2m. By the CRT,
|
||||
* the result is either the d we got, or d + m.
|
||||
*
|
||||
* Let's write e*d = 1 + k*m, for some integer k. Integers e
|
||||
* and m are odd. If d is odd, then e*d is odd, which implies
|
||||
* that k must be even; in that case, e*d = 1 + (k/2)*2m, and
|
||||
* thus d is already fine. Conversely, if d is even, then k
|
||||
* is odd, and we must add m to d in order to get the correct
|
||||
* result.
|
||||
*/
|
||||
br_i31_add(d, m, (uint32_t)(1 - (d[1] & 1)));
|
||||
|
||||
return r;
|
||||
}
|
||||
|
||||
/*
|
||||
* Swap two buffers in RAM. They must be disjoint.
|
||||
*/
|
||||
static void
|
||||
bufswap(void *b1, void *b2, size_t len)
|
||||
{
|
||||
size_t u;
|
||||
unsigned char *buf1, *buf2;
|
||||
|
||||
buf1 = b1;
|
||||
buf2 = b2;
|
||||
for (u = 0; u < len; u ++) {
|
||||
unsigned w;
|
||||
|
||||
w = buf1[u];
|
||||
buf1[u] = buf2[u];
|
||||
buf2[u] = w;
|
||||
}
|
||||
}
|
||||
|
||||
/* see inner.h */
|
||||
uint32_t
|
||||
br_rsa_i31_keygen_inner(const br_prng_class **rng,
|
||||
br_rsa_private_key *sk, unsigned char *kbuf_priv,
|
||||
br_rsa_public_key *pk, unsigned char *kbuf_pub,
|
||||
unsigned size, uint32_t pubexp, br_i31_modpow_opt_type mp31)
|
||||
{
|
||||
uint32_t esize_p, esize_q;
|
||||
size_t plen, qlen, tlen;
|
||||
uint32_t *p, *q, *t;
|
||||
union {
|
||||
uint32_t t32[TEMPS];
|
||||
uint64_t t64[TEMPS >> 1]; /* for 64-bit alignment */
|
||||
} tmp;
|
||||
uint32_t r;
|
||||
|
||||
if (size < BR_MIN_RSA_SIZE || size > BR_MAX_RSA_SIZE) {
|
||||
return 0;
|
||||
}
|
||||
if (pubexp == 0) {
|
||||
pubexp = 3;
|
||||
} else if (pubexp == 1 || (pubexp & 1) == 0) {
|
||||
return 0;
|
||||
}
|
||||
|
||||
esize_p = (size + 1) >> 1;
|
||||
esize_q = size - esize_p;
|
||||
sk->n_bitlen = size;
|
||||
sk->p = kbuf_priv;
|
||||
sk->plen = (esize_p + 7) >> 3;
|
||||
sk->q = sk->p + sk->plen;
|
||||
sk->qlen = (esize_q + 7) >> 3;
|
||||
sk->dp = sk->q + sk->qlen;
|
||||
sk->dplen = sk->plen;
|
||||
sk->dq = sk->dp + sk->dplen;
|
||||
sk->dqlen = sk->qlen;
|
||||
sk->iq = sk->dq + sk->dqlen;
|
||||
sk->iqlen = sk->plen;
|
||||
|
||||
if (pk != NULL) {
|
||||
pk->n = kbuf_pub;
|
||||
pk->nlen = (size + 7) >> 3;
|
||||
pk->e = pk->n + pk->nlen;
|
||||
pk->elen = 4;
|
||||
br_enc32be(pk->e, pubexp);
|
||||
while (*pk->e == 0) {
|
||||
pk->e ++;
|
||||
pk->elen --;
|
||||
}
|
||||
}
|
||||
|
||||
/*
|
||||
* We now switch to encoded sizes.
|
||||
*
|
||||
* floor((x * 16913) / (2^19)) is equal to floor(x/31) for all
|
||||
* integers x from 0 to 34966; the intermediate product fits on
|
||||
* 30 bits, thus we can use MUL31().
|
||||
*/
|
||||
esize_p += MUL31(esize_p, 16913) >> 19;
|
||||
esize_q += MUL31(esize_q, 16913) >> 19;
|
||||
plen = (esize_p + 31) >> 5;
|
||||
qlen = (esize_q + 31) >> 5;
|
||||
p = tmp.t32;
|
||||
q = p + 1 + plen;
|
||||
t = q + 1 + qlen;
|
||||
tlen = ((sizeof tmp.t32) / sizeof(uint32_t)) - (2 + plen + qlen);
|
||||
|
||||
/*
|
||||
* When looking for primes p and q, we temporarily divide
|
||||
* candidates by 2, in order to compute the inverse of the
|
||||
* public exponent.
|
||||
*/
|
||||
|
||||
for (;;) {
|
||||
mkprime(rng, p, esize_p, pubexp, t, tlen, mp31);
|
||||
br_i31_rshift(p, 1);
|
||||
if (invert_pubexp(t, p, pubexp, t + 1 + plen)) {
|
||||
br_i31_add(p, p, 1);
|
||||
p[1] |= 1;
|
||||
br_i31_encode(sk->p, sk->plen, p);
|
||||
br_i31_encode(sk->dp, sk->dplen, t);
|
||||
break;
|
||||
}
|
||||
}
|
||||
|
||||
for (;;) {
|
||||
mkprime(rng, q, esize_q, pubexp, t, tlen, mp31);
|
||||
br_i31_rshift(q, 1);
|
||||
if (invert_pubexp(t, q, pubexp, t + 1 + qlen)) {
|
||||
br_i31_add(q, q, 1);
|
||||
q[1] |= 1;
|
||||
br_i31_encode(sk->q, sk->qlen, q);
|
||||
br_i31_encode(sk->dq, sk->dqlen, t);
|
||||
break;
|
||||
}
|
||||
}
|
||||
|
||||
/*
|
||||
* If p and q have the same size, then it is possible that q > p
|
||||
* (when the target modulus size is odd, we generate p with a
|
||||
* greater bit length than q). If q > p, we want to swap p and q
|
||||
* (and also dp and dq) for two reasons:
|
||||
* - The final step below (inversion of q modulo p) is easier if
|
||||
* p > q.
|
||||
* - While BearSSL's RSA code is perfectly happy with RSA keys such
|
||||
* that p < q, some other implementations have restrictions and
|
||||
* require p > q.
|
||||
*
|
||||
* Note that we can do a simple non-constant-time swap here,
|
||||
* because the only information we leak here is that we insist on
|
||||
* returning p and q such that p > q, which is not a secret.
|
||||
*/
|
||||
if (esize_p == esize_q && br_i31_sub(p, q, 0) == 1) {
|
||||
bufswap(p, q, (1 + plen) * sizeof *p);
|
||||
bufswap(sk->p, sk->q, sk->plen);
|
||||
bufswap(sk->dp, sk->dq, sk->dplen);
|
||||
}
|
||||
|
||||
/*
|
||||
* We have produced p, q, dp and dq. We can now compute iq = 1/d mod p.
|
||||
*
|
||||
* We ensured that p >= q, so this is just a matter of updating the
|
||||
* header word for q (and possibly adding an extra word).
|
||||
*
|
||||
* Theoretically, the call below may fail, in case we were
|
||||
* extraordinarily unlucky, and p = q. Another failure case is if
|
||||
* Miller-Rabin failed us _twice_, and p and q are non-prime and
|
||||
* have a factor is common. We report the error mostly because it
|
||||
* is cheap and we can, but in practice this never happens (or, at
|
||||
* least, it happens way less often than hardware glitches).
|
||||
*/
|
||||
q[0] = p[0];
|
||||
if (plen > qlen) {
|
||||
q[plen] = 0;
|
||||
t ++;
|
||||
tlen --;
|
||||
}
|
||||
br_i31_zero(t, p[0]);
|
||||
t[1] = 1;
|
||||
r = br_i31_moddiv(t, q, p, br_i31_ninv31(p[1]), t + 1 + plen);
|
||||
br_i31_encode(sk->iq, sk->iqlen, t);
|
||||
|
||||
/*
|
||||
* Compute the public modulus too, if required.
|
||||
*/
|
||||
if (pk != NULL) {
|
||||
br_i31_zero(t, p[0]);
|
||||
br_i31_mulacc(t, p, q);
|
||||
br_i31_encode(pk->n, pk->nlen, t);
|
||||
}
|
||||
|
||||
return r;
|
||||
}
|
||||
57
src/rsa/rsa_i62_keygen.c
Normal file
57
src/rsa/rsa_i62_keygen.c
Normal file
|
|
@ -0,0 +1,57 @@
|
|||
/*
|
||||
* Copyright (c) 2018 Thomas Pornin <pornin@bolet.org>
|
||||
*
|
||||
* Permission is hereby granted, free of charge, to any person obtaining
|
||||
* a copy of this software and associated documentation files (the
|
||||
* "Software"), to deal in the Software without restriction, including
|
||||
* without limitation the rights to use, copy, modify, merge, publish,
|
||||
* distribute, sublicense, and/or sell copies of the Software, and to
|
||||
* permit persons to whom the Software is furnished to do so, subject to
|
||||
* the following conditions:
|
||||
*
|
||||
* The above copyright notice and this permission notice shall be
|
||||
* included in all copies or substantial portions of the Software.
|
||||
*
|
||||
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
|
||||
* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
|
||||
* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
|
||||
* NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
|
||||
* BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
|
||||
* ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
|
||||
* CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
|
||||
* SOFTWARE.
|
||||
*/
|
||||
|
||||
#include "inner.h"
|
||||
|
||||
#if BR_INT128 || BR_UMUL128
|
||||
|
||||
/* see bearssl_rsa.h */
|
||||
uint32_t
|
||||
br_rsa_i62_keygen(const br_prng_class **rng,
|
||||
br_rsa_private_key *sk, unsigned char *kbuf_priv,
|
||||
br_rsa_public_key *pk, unsigned char *kbuf_pub,
|
||||
unsigned size, uint32_t pubexp)
|
||||
{
|
||||
return br_rsa_i31_keygen_inner(rng,
|
||||
sk, kbuf_priv, pk, kbuf_pub, size, pubexp,
|
||||
&br_i62_modpow_opt_as_i31);
|
||||
}
|
||||
|
||||
/* see bearssl_rsa.h */
|
||||
br_rsa_keygen
|
||||
br_rsa_i62_keygen_get()
|
||||
{
|
||||
return &br_rsa_i62_keygen;
|
||||
}
|
||||
|
||||
#else
|
||||
|
||||
/* see bearssl_rsa.h */
|
||||
br_rsa_keygen
|
||||
br_rsa_i62_keygen_get()
|
||||
{
|
||||
return 0;
|
||||
}
|
||||
|
||||
#endif
|
||||
|
|
@ -5685,6 +5685,122 @@ test_RSA_OAEP(const char *name,
|
|||
fflush(stdout);
|
||||
}
|
||||
|
||||
static void
|
||||
test_RSA_keygen(const char *name, br_rsa_keygen kg,
|
||||
br_rsa_pkcs1_sign sign, br_rsa_pkcs1_vrfy vrfy)
|
||||
{
|
||||
br_hmac_drbg_context rng;
|
||||
int i;
|
||||
|
||||
printf("Test %s: ", name);
|
||||
fflush(stdout);
|
||||
|
||||
br_hmac_drbg_init(&rng, &br_sha256_vtable, "seed for RSA keygen", 19);
|
||||
|
||||
for (i = 0; i < 40; i ++) {
|
||||
unsigned size;
|
||||
uint32_t pubexp;
|
||||
br_rsa_private_key sk;
|
||||
br_rsa_public_key pk;
|
||||
unsigned char kbuf_priv[BR_RSA_KBUF_PRIV_SIZE(2048)];
|
||||
unsigned char kbuf_pub[BR_RSA_KBUF_PUB_SIZE(2048)];
|
||||
uint32_t mod[256];
|
||||
uint32_t cc;
|
||||
size_t u, v;
|
||||
unsigned char sig[257], hv[32], hv2[sizeof hv];
|
||||
unsigned mask1, mask2;
|
||||
|
||||
if (i <= 35) {
|
||||
size = 1024 + i;
|
||||
pubexp = 17;
|
||||
} else {
|
||||
size = 2048;
|
||||
pubexp = (i << 1) - 69;
|
||||
}
|
||||
|
||||
if (!kg(&rng.vtable,
|
||||
&sk, kbuf_priv, &pk, kbuf_pub, size, pubexp))
|
||||
{
|
||||
fprintf(stderr, "RSA key pair generation failure\n");
|
||||
exit(EXIT_FAILURE);
|
||||
}
|
||||
|
||||
for (u = pk.elen; u > 0; u --) {
|
||||
if (pk.e[u - 1] != (pubexp & 0xFF)) {
|
||||
fprintf(stderr, "wrong public exponent\n");
|
||||
exit(EXIT_FAILURE);
|
||||
}
|
||||
pubexp >>= 8;
|
||||
}
|
||||
if (pubexp != 0) {
|
||||
fprintf(stderr, "truncated public exponent\n");
|
||||
exit(EXIT_FAILURE);
|
||||
}
|
||||
|
||||
memset(mod, 0, sizeof mod);
|
||||
for (u = 0; u < sk.plen; u ++) {
|
||||
for (v = 0; v < sk.qlen; v ++) {
|
||||
mod[u + v] += (uint32_t)sk.p[sk.plen - 1 - u]
|
||||
* (uint32_t)sk.q[sk.qlen - 1 - v];
|
||||
}
|
||||
}
|
||||
cc = 0;
|
||||
for (u = 0; u < sk.plen + sk.qlen; u ++) {
|
||||
mod[u] += cc;
|
||||
cc = mod[u] >> 8;
|
||||
mod[u] &= 0xFF;
|
||||
}
|
||||
for (u = 0; u < pk.nlen; u ++) {
|
||||
if (mod[pk.nlen - 1 - u] != pk.n[u]) {
|
||||
fprintf(stderr, "wrong modulus\n");
|
||||
exit(EXIT_FAILURE);
|
||||
}
|
||||
}
|
||||
if (sk.n_bitlen != size) {
|
||||
fprintf(stderr, "wrong key size\n");
|
||||
exit(EXIT_FAILURE);
|
||||
}
|
||||
if (pk.nlen != (size + 7) >> 3) {
|
||||
fprintf(stderr, "wrong modulus size (bytes)\n");
|
||||
exit(EXIT_FAILURE);
|
||||
}
|
||||
mask1 = 0x01 << ((size + 7) & 7);
|
||||
mask2 = 0xFF & -mask1;
|
||||
if ((pk.n[0] & mask2) != mask1) {
|
||||
fprintf(stderr, "wrong modulus size (bits)\n");
|
||||
exit(EXIT_FAILURE);
|
||||
}
|
||||
|
||||
rng.vtable->generate(&rng.vtable, hv, sizeof hv);
|
||||
memset(sig, 0, sizeof sig);
|
||||
sig[pk.nlen] = 0x00;
|
||||
if (!sign(BR_HASH_OID_SHA256, hv, sizeof hv, &sk, sig)) {
|
||||
fprintf(stderr, "signature error\n");
|
||||
exit(EXIT_FAILURE);
|
||||
}
|
||||
if (sig[pk.nlen] != 0x00) {
|
||||
fprintf(stderr, "signature length error\n");
|
||||
exit(EXIT_FAILURE);
|
||||
}
|
||||
if (!vrfy(sig, pk.nlen, BR_HASH_OID_SHA256, sizeof hv,
|
||||
&pk, hv2))
|
||||
{
|
||||
fprintf(stderr, "signature verification error (1)\n");
|
||||
exit(EXIT_FAILURE);
|
||||
}
|
||||
if (memcmp(hv, hv2, sizeof hv) != 0) {
|
||||
fprintf(stderr, "signature verification error (2)\n");
|
||||
exit(EXIT_FAILURE);
|
||||
}
|
||||
|
||||
printf(".");
|
||||
fflush(stdout);
|
||||
}
|
||||
|
||||
printf(" done.\n");
|
||||
fflush(stdout);
|
||||
}
|
||||
|
||||
static void
|
||||
test_RSA_i15(void)
|
||||
{
|
||||
|
|
@ -5693,6 +5809,8 @@ test_RSA_i15(void)
|
|||
&br_rsa_i15_pkcs1_sign, &br_rsa_i15_pkcs1_vrfy);
|
||||
test_RSA_OAEP("RSA i15 OAEP",
|
||||
&br_rsa_i15_oaep_encrypt, &br_rsa_i15_oaep_decrypt);
|
||||
test_RSA_keygen("RSA i15 keygen", &br_rsa_i15_keygen,
|
||||
&br_rsa_i15_pkcs1_sign, &br_rsa_i15_pkcs1_vrfy);
|
||||
}
|
||||
|
||||
static void
|
||||
|
|
@ -5703,6 +5821,8 @@ test_RSA_i31(void)
|
|||
&br_rsa_i31_pkcs1_sign, &br_rsa_i31_pkcs1_vrfy);
|
||||
test_RSA_OAEP("RSA i31 OAEP",
|
||||
&br_rsa_i31_oaep_encrypt, &br_rsa_i31_oaep_decrypt);
|
||||
test_RSA_keygen("RSA i31 keygen", &br_rsa_i31_keygen,
|
||||
&br_rsa_i31_pkcs1_sign, &br_rsa_i31_pkcs1_vrfy);
|
||||
}
|
||||
|
||||
static void
|
||||
|
|
@ -5724,6 +5844,7 @@ test_RSA_i62(void)
|
|||
br_rsa_pkcs1_vrfy vrfy;
|
||||
br_rsa_oaep_encrypt menc;
|
||||
br_rsa_oaep_decrypt mdec;
|
||||
br_rsa_keygen kgen;
|
||||
|
||||
pub = br_rsa_i62_public_get();
|
||||
priv = br_rsa_i62_private_get();
|
||||
|
|
@ -5731,16 +5852,18 @@ test_RSA_i62(void)
|
|||
vrfy = br_rsa_i62_pkcs1_vrfy_get();
|
||||
menc = br_rsa_i62_oaep_encrypt_get();
|
||||
mdec = br_rsa_i62_oaep_decrypt_get();
|
||||
kgen = br_rsa_i62_keygen_get();
|
||||
if (pub) {
|
||||
if (!priv || !sign || !vrfy || !menc || !mdec) {
|
||||
if (!priv || !sign || !vrfy || !menc || !mdec || !kgen) {
|
||||
fprintf(stderr, "Inconsistent i62 availability\n");
|
||||
exit(EXIT_FAILURE);
|
||||
}
|
||||
test_RSA_core("RSA i62 core", pub, priv);
|
||||
test_RSA_sign("RSA i62 sign", priv, sign, vrfy);
|
||||
test_RSA_OAEP("RSA i62 OAEP", menc, mdec);
|
||||
test_RSA_keygen("RSA i62 keygen", kgen, sign, vrfy);
|
||||
} else {
|
||||
if (priv || sign || vrfy || menc || mdec) {
|
||||
if (priv || sign || vrfy || menc || mdec || kgen) {
|
||||
fprintf(stderr, "Inconsistent i62 availability\n");
|
||||
exit(EXIT_FAILURE);
|
||||
}
|
||||
|
|
|
|||
|
|
@ -679,11 +679,12 @@ static const br_rsa_private_key RSA_SK = {
|
|||
|
||||
static void
|
||||
test_speed_rsa_inner(char *name,
|
||||
br_rsa_public fpub, br_rsa_private fpriv)
|
||||
br_rsa_public fpub, br_rsa_private fpriv, br_rsa_keygen kgen)
|
||||
{
|
||||
unsigned char tmp[sizeof RSA_N];
|
||||
int i;
|
||||
long num;
|
||||
br_hmac_drbg_context rng;
|
||||
|
||||
memset(tmp, 'R', sizeof tmp);
|
||||
tmp[0] = 0;
|
||||
|
|
@ -737,27 +738,82 @@ test_speed_rsa_inner(char *name,
|
|||
}
|
||||
num <<= 1;
|
||||
}
|
||||
|
||||
if (kgen == 0) {
|
||||
printf("%-30s KEYGEN UNAVAILABLE\n", name);
|
||||
fflush(stdout);
|
||||
return;
|
||||
}
|
||||
br_hmac_drbg_init(&rng, &br_sha256_vtable, "RSA keygen seed", 15);
|
||||
|
||||
num = 10;
|
||||
for (;;) {
|
||||
clock_t begin, end;
|
||||
double tt;
|
||||
long k;
|
||||
|
||||
begin = clock();
|
||||
for (k = num; k > 0; k --) {
|
||||
br_rsa_private_key sk;
|
||||
unsigned char kbuf[BR_RSA_KBUF_PRIV_SIZE(1024)];
|
||||
|
||||
kgen(&rng.vtable, &sk, kbuf, NULL, NULL, 1024, 0);
|
||||
}
|
||||
end = clock();
|
||||
tt = (double)(end - begin) / CLOCKS_PER_SEC;
|
||||
if (tt >= 10.0) {
|
||||
printf("%-30s %8.2f kgen[1024]/s\n", name,
|
||||
(double)num / tt);
|
||||
fflush(stdout);
|
||||
break;
|
||||
}
|
||||
num <<= 1;
|
||||
}
|
||||
|
||||
num = 10;
|
||||
for (;;) {
|
||||
clock_t begin, end;
|
||||
double tt;
|
||||
long k;
|
||||
|
||||
begin = clock();
|
||||
for (k = num; k > 0; k --) {
|
||||
br_rsa_private_key sk;
|
||||
unsigned char kbuf[BR_RSA_KBUF_PRIV_SIZE(2048)];
|
||||
|
||||
kgen(&rng.vtable, &sk, kbuf, NULL, NULL, 2048, 0);
|
||||
}
|
||||
end = clock();
|
||||
tt = (double)(end - begin) / CLOCKS_PER_SEC;
|
||||
if (tt >= 10.0) {
|
||||
printf("%-30s %8.2f kgen[2048]/s\n", name,
|
||||
(double)num / tt);
|
||||
fflush(stdout);
|
||||
break;
|
||||
}
|
||||
num <<= 1;
|
||||
}
|
||||
}
|
||||
|
||||
static void
|
||||
test_speed_rsa_i15(void)
|
||||
{
|
||||
test_speed_rsa_inner("RSA i15",
|
||||
&br_rsa_i15_public, &br_rsa_i15_private);
|
||||
&br_rsa_i15_public, &br_rsa_i15_private, &br_rsa_i15_keygen);
|
||||
}
|
||||
|
||||
static void
|
||||
test_speed_rsa_i31(void)
|
||||
{
|
||||
test_speed_rsa_inner("RSA i31",
|
||||
&br_rsa_i31_public, &br_rsa_i31_private);
|
||||
&br_rsa_i31_public, &br_rsa_i31_private, &br_rsa_i31_keygen);
|
||||
}
|
||||
|
||||
static void
|
||||
test_speed_rsa_i32(void)
|
||||
{
|
||||
test_speed_rsa_inner("RSA i32",
|
||||
&br_rsa_i32_public, &br_rsa_i32_private);
|
||||
&br_rsa_i32_public, &br_rsa_i32_private, 0);
|
||||
}
|
||||
|
||||
static void
|
||||
|
|
@ -765,11 +821,13 @@ test_speed_rsa_i62(void)
|
|||
{
|
||||
br_rsa_public pub;
|
||||
br_rsa_private priv;
|
||||
br_rsa_keygen kgen;
|
||||
|
||||
pub = br_rsa_i62_public_get();
|
||||
priv = br_rsa_i62_private_get();
|
||||
kgen = br_rsa_i62_keygen_get();
|
||||
if (pub) {
|
||||
test_speed_rsa_inner("RSA i62", pub, priv);
|
||||
test_speed_rsa_inner("RSA i62", pub, priv, kgen);
|
||||
} else {
|
||||
printf("%-30s UNAVAILABLE\n", "RSA i62");
|
||||
}
|
||||
|
|
|
|||
131
tools/skey.c
131
tools/skey.c
|
|
@ -105,6 +105,90 @@ print_ec(const br_ec_private_key *sk, int print_text, int print_C)
|
|||
}
|
||||
}
|
||||
|
||||
static int
|
||||
parse_rsa_spec(const char *kgen_spec, unsigned *size, uint32_t *pubexp)
|
||||
{
|
||||
const char *p;
|
||||
char *end;
|
||||
unsigned long ul;
|
||||
|
||||
p = kgen_spec;
|
||||
if (*p != 'r' && *p != 'R') {
|
||||
return 0;
|
||||
}
|
||||
p ++;
|
||||
if (*p != 's' && *p != 'S') {
|
||||
return 0;
|
||||
}
|
||||
p ++;
|
||||
if (*p != 'a' && *p != 'A') {
|
||||
return 0;
|
||||
}
|
||||
p ++;
|
||||
if (*p == 0) {
|
||||
*size = 2048;
|
||||
*pubexp = 3;
|
||||
return 1;
|
||||
} else if (*p != ':') {
|
||||
return 0;
|
||||
}
|
||||
p ++;
|
||||
ul = strtoul(p, &end, 10);
|
||||
if (ul < 512 || ul > 32768) {
|
||||
return 0;
|
||||
}
|
||||
*size = ul;
|
||||
p = end;
|
||||
if (*p == 0) {
|
||||
*pubexp = 3;
|
||||
return 1;
|
||||
} else if (*p != ':') {
|
||||
return 0;
|
||||
}
|
||||
p ++;
|
||||
ul = strtoul(p, &end, 10);
|
||||
if ((ul & 1) == 0 || ul == 1 || ((ul >> 30) >> 2) != 0) {
|
||||
return 0;
|
||||
}
|
||||
*pubexp = ul;
|
||||
if (*end != 0) {
|
||||
return 0;
|
||||
}
|
||||
return 1;
|
||||
}
|
||||
|
||||
static int
|
||||
keygen_rsa(unsigned size, uint32_t pubexp, int print_text, int print_C)
|
||||
{
|
||||
br_hmac_drbg_context rng;
|
||||
br_prng_seeder seeder;
|
||||
br_rsa_keygen kg;
|
||||
br_rsa_private_key sk;
|
||||
unsigned char *kbuf_priv;
|
||||
uint32_t r;
|
||||
|
||||
seeder = br_prng_seeder_system(NULL);
|
||||
if (seeder == 0) {
|
||||
fprintf(stderr, "ERROR: no system source of randomness\n");
|
||||
return 0;
|
||||
}
|
||||
br_hmac_drbg_init(&rng, &br_sha256_vtable, NULL, 0);
|
||||
if (!seeder(&rng.vtable)) {
|
||||
fprintf(stderr, "ERROR: system source of randomness failed\n");
|
||||
return 0;
|
||||
}
|
||||
kbuf_priv = xmalloc(BR_RSA_KBUF_PRIV_SIZE(size));
|
||||
kg = br_rsa_keygen_get_default();
|
||||
r = kg(&rng.vtable, &sk, kbuf_priv, NULL, NULL, size, pubexp);
|
||||
if (!r) {
|
||||
fprintf(stderr, "ERROR: RSA key pair generation failed\n");
|
||||
} else {
|
||||
print_rsa(&sk, print_text, print_C);
|
||||
}
|
||||
xfree(kbuf_priv);
|
||||
return r;
|
||||
}
|
||||
|
||||
static int
|
||||
decode_key(const unsigned char *buf, size_t len, int print_text, int print_C)
|
||||
{
|
||||
|
|
@ -165,6 +249,14 @@ usage_skey(void)
|
|||
" -text print public key details (human-readable)\n");
|
||||
fprintf(stderr,
|
||||
" -C print public key details (C code)\n");
|
||||
fprintf(stderr,
|
||||
" -gen spec generate a new key using the provided key specification\n");
|
||||
fprintf(stderr,
|
||||
"Key specification begins with a key type, followed by optional parameters\n");
|
||||
fprintf(stderr,
|
||||
"that depend on the key type, separated by colon characters:\n");
|
||||
fprintf(stderr,
|
||||
" rsa[:size[:pubexep]] RSA key (defaults: size = 2048, pubexp = 3)\n");
|
||||
}
|
||||
|
||||
/* see brssl.h */
|
||||
|
|
@ -178,6 +270,7 @@ do_skey(int argc, char *argv[])
|
|||
unsigned char *buf;
|
||||
size_t len;
|
||||
pem_object *pos;
|
||||
const char *kgen_spec;
|
||||
|
||||
retcode = 0;
|
||||
verbose = 1;
|
||||
|
|
@ -186,6 +279,7 @@ do_skey(int argc, char *argv[])
|
|||
num_files = 0;
|
||||
buf = NULL;
|
||||
pos = NULL;
|
||||
kgen_spec = NULL;
|
||||
for (i = 0; i < argc; i ++) {
|
||||
const char *arg;
|
||||
|
||||
|
|
@ -203,13 +297,48 @@ do_skey(int argc, char *argv[])
|
|||
print_text = 1;
|
||||
} else if (eqstr(arg, "-C")) {
|
||||
print_C = 1;
|
||||
} else if (eqstr(arg, "-gen")) {
|
||||
if (++ i >= argc) {
|
||||
fprintf(stderr,
|
||||
"ERROR: no argument for '-gen'\n");
|
||||
usage_skey();
|
||||
goto skey_exit_error;
|
||||
}
|
||||
if (kgen_spec != NULL) {
|
||||
fprintf(stderr,
|
||||
"ERROR: multiple '-gen' options\n");
|
||||
usage_skey();
|
||||
goto skey_exit_error;
|
||||
}
|
||||
kgen_spec = argv[i];
|
||||
argv[i] = NULL;
|
||||
} else {
|
||||
fprintf(stderr, "ERROR: unknown option: '%s'\n", arg);
|
||||
usage_skey();
|
||||
goto skey_exit_error;
|
||||
}
|
||||
}
|
||||
if (num_files == 0) {
|
||||
if (kgen_spec != NULL) {
|
||||
unsigned rsa_size;
|
||||
uint32_t rsa_pubexp;
|
||||
|
||||
if (num_files != 0) {
|
||||
fprintf(stderr,
|
||||
"ERROR: key files provided while generating\n");
|
||||
usage_skey();
|
||||
goto skey_exit_error;
|
||||
}
|
||||
|
||||
if (parse_rsa_spec(kgen_spec, &rsa_size, &rsa_pubexp)) {
|
||||
keygen_rsa(rsa_size, rsa_pubexp, print_text, print_C);
|
||||
} else {
|
||||
fprintf(stderr,
|
||||
"ERROR: unknown key specification: '%s'\n",
|
||||
kgen_spec);
|
||||
usage_skey();
|
||||
goto skey_exit_error;
|
||||
}
|
||||
} else if (num_files == 0) {
|
||||
fprintf(stderr, "ERROR: no private key provided\n");
|
||||
usage_skey();
|
||||
goto skey_exit_error;
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue