NAME

       BN_mod_mul_reciprocal,  BN_div_recp, BN_RECP_CTX_new, BN_RECP_CTX_init, BN_RECP_CTX_free,
       BN_RECP_CTX_set - modular multiplication using reciprocal

SYNOPSIS

        #include <openssl/bn.h>

        BN_RECP_CTX *BN_RECP_CTX_new(void);
        void BN_RECP_CTX_init(BN_RECP_CTX *recp);
        void BN_RECP_CTX_free(BN_RECP_CTX *recp);

        int BN_RECP_CTX_set(BN_RECP_CTX *recp, const BIGNUM *m, BN_CTX *ctx);

        int BN_div_recp(BIGNUM *dv, BIGNUM *rem, BIGNUM *a, BN_RECP_CTX *recp,
               BN_CTX *ctx);

        int BN_mod_mul_reciprocal(BIGNUM *r, BIGNUM *a, BIGNUM *b,
               BN_RECP_CTX *recp, BN_CTX *ctx);

DESCRIPTION

       BN_mod_mul_reciprocal() can be used to perform an efficient BN_mod_mul(3) operation when
       the operation will be performed repeatedly with the same modulus. It computes r=(a*b)%m
       using recp=1/m, which is set as described below.  ctx is a previously allocated BN_CTX
       used for temporary variables.

       BN_RECP_CTX_new() allocates and initializes a BN_RECP structure.  BN_RECP_CTX_init()
       initializes an existing uninitialized BN_RECP.

       BN_RECP_CTX_free() frees the components of the BN_RECP, and, if it was created by
       BN_RECP_CTX_new(), also the structure itself.

       BN_RECP_CTX_set() stores m in recp and sets it up for computing 1/m and shifting it left
       by BN_num_bits(m)+1 to make it an integer. The result and the number of bits it was
       shifted left will later be stored in recp.

       BN_div_recp() divides a by m using recp. It places the quotient in dv and the remainder in
       rem.

       The BN_RECP_CTX structure is defined as follows:

        typedef struct bn_recp_ctx_st
               {
               BIGNUM N;       /* the divisor */
               BIGNUM Nr;      /* the reciprocal */
               int num_bits;
               int shift;
               int flags;
               } BN_RECP_CTX;

       It cannot be shared between threads.

RETURN VALUES

       BN_RECP_CTX_new() returns the newly allocated BN_RECP_CTX, and NULL on error.

       BN_RECP_CTX_init() and BN_RECP_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).

SEE ALSO

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

HISTORY

       BN_RECP_CTX was added in SSLeay 0.9.0. Before that, the function BN_reciprocal() was used
       instead, and the BN_mod_mul_reciprocal() arguments were different.