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

# 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 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.

# SEE ALSO

bn, ERR_get_error, BN_add, BN_CTX_new

# 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.