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Title "BN_mod_mul_montgomery 3" For nroff, turn off justification. Always turn off hyphenation; it makes
way too many mistakes in technical documents.
BN_mod_mul_montgomery, BN_MONT_CTX_new, BN_MONT_CTX_init, BN_MONT_CTX_free, BN_MONT_CTX_set, BN_MONT_CTX_copy, BN_from_montgomery, BN_to_montgomery - Montgomery multiplication Header "SYNOPSIS" .Vb 1 #include <openssl/bn.h> \& BN_MONT_CTX *BN_MONT_CTX_new(void); void BN_MONT_CTX_init(BN_MONT_CTX *ctx); void BN_MONT_CTX_free(BN_MONT_CTX *mont); \& int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *m, BN_CTX *ctx); BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from); \& int BN_mod_mul_montgomery(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_MONT_CTX *mont, BN_CTX *ctx); \& int BN_from_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont, BN_CTX *ctx); \& int BN_to_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont, BN_CTX *ctx); .Ve Header "DESCRIPTION" These functions implement Montgomery multiplication. They are used automatically when BN_mod_exp\|(3) is called with suitable input, but they may be useful when several operations are to be performed using the same modulus.

\fIBN_MONT_CTX_new() allocates and initializes a \s-1BN_MONT_CTX\s0 structure. \fIBN_MONT_CTX_init() initializes an existing uninitialized \s-1BN_MONT_CTX\s0.

\fIBN_MONT_CTX_set() sets up the mont structure from the modulus m by precomputing its inverse and a value R.

\fIBN_MONT_CTX_copy() copies the \s-1BN_MONT_CTX\s0 from to to.

\fIBN_MONT_CTX_free() frees the components of the \s-1BN_MONT_CTX\s0, and, if it was created by BN_MONT_CTX_new(), also the structure itself.

\fIBN_mod_mul_montgomery() computes Mont(a,b):=a*b*R^-1 and places the result in r.

\fIBN_from_montgomery() performs the Montgomery reduction r = a*R^-1.

\fIBN_to_montgomery() computes Mont(a,R^2), i.e. a*R. Note that a must be non-negative and smaller than the modulus.

For all functions, ctx is a previously allocated \s-1BN_CTX\s0 used for temporary variables.

The \s-1BN_MONT_CTX\s0 structure is defined as follows:

.Vb 10 typedef struct bn_mont_ctx_st { int ri; /* number of bits in R */ BIGNUM RR; /* R^2 (used to convert to Montgomery form) */ BIGNUM N; /* The modulus */ BIGNUM Ni; /* R*(1/R mod N) - N*Ni = 1 * (Ni is only stored for bignum algorithm) */ BN_ULONG n0; /* least significant word of Ni */ int flags; } BN_MONT_CTX; .Ve

\fIBN_to_montgomery() is a macro.

Header "RETURN VALUES" \fIBN_MONT_CTX_new() returns the newly allocated \s-1BN_MONT_CTX\s0, and \s-1NULL\s0 on error.

\fIBN_MONT_CTX_init() and BN_MONT_CTX_free() have no return values.

For the other functions, 1 is returned for success, 0 on error. The error codes can be obtained by ERR_get_error\|(3).

Header "WARNING" The inputs must be reduced modulo m, otherwise the result will be outside the expected range. Header "SEE ALSO" \fIbn\|(3), ERR_get_error\|(3), BN_add\|(3), \fIBN_CTX_new\|(3) Header "HISTORY" \fIBN_MONT_CTX_new(), BN_MONT_CTX_free(), BN_MONT_CTX_set(), \fIBN_mod_mul_montgomery(), BN_from_montgomery() and BN_to_montgomery() are available in all versions of SSLeay and OpenSSL.

\fIBN_MONT_CTX_init() and BN_MONT_CTX_copy() were added in SSLeay 0.9.1b.