# BN_mod_mul_reciprocal.3ssl man page

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

## 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.