BN_mod_mul_montgomery 3 2003-07-24 0.9.9-dev OpenSSL

### NAME

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

### LIBRARY

libcrypto, -lcrypto

### SYNOPSIS

     #include

     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);

### 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

openssl_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.