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.

BN_MONT_CTX_new() allocates and initializes a BN_MONT_CTX structure. BN_MONT_CTX_init() initializes an existing uninitialized BN_MONT_CTX.

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

BN_MONT_CTX_copy() copies the BN_MONT_CTX from to to.

BN_MONT_CTX_free() frees the components of the BN_MONT_CTX, and, if it was created by BN_MONT_CTX_new(), also the structure itself.

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

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

BN_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 BN_CTX used for temporary variables.

The BN_MONT_CTX structure is defined as follows:

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;

BN_to_montgomery() is a macro.

RETURN VALUES

BN_MONT_CTX_new() returns the newly allocated BN_MONT_CTX, and NULL on error.

BN_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).

WARNING

The inputs must be reduced modulo m, otherwise the result will be outside the expected range.

SEE ALSO

bn(3), ERR_get_error(3), BN_add(3), BN_CTX_new(3)

HISTORY

BN_MONT_CTX_new(), BN_MONT_CTX_free(), BN_MONT_CTX_set(), BN_mod_mul_montgomery(), BN_from_montgomery() and BN_to_montgomery() are available in all versions of SSLeay and OpenSSL.

BN_MONT_CTX_init() and BN_MONT_CTX_copy() were added in SSLeay 0.9.1b.