- NAME
- SYNOPSIS
- DESCRIPTION
- RETURN VALUES
- WARNING
- SEE ALSO
- HISTORY

# 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

# SYNOPSIS

     #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);

# DESCRIPTION

These functions implement Montgomery multiplication. They are used automatically when BN_mod_exp 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.

# WARNING

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

# SEE ALSO

bn, ERR_get_error, BN_add, BN_CTX_new

# 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.