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

```
#include <openssl/bn.h>
BN_RECP_CTX *BN_RECP_CTX_new(void);
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);
```

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 cannot be shared between threads.

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.

` void BN_RECP_CTX_init(BN_RECP_CTX *recp);`

BN_RECP_CTX_init() is no longer available as of OpenSSL 1.1.0. It was used to initialize an existing uninitialized **BN_RECP_CTX**. Typically this would be done as follows:

```
BN_RECP_CTX ctx;
BN_RECP_CTX_init(&ctx);
```

Applications should replace use of BN_RECP_CTX_init with BN_RECP_CTX_new instead:

```
BN_RECP_CTX *ctx;
ctx = BN_RECP_CTX_new();
if(!ctx) /* Handle error */
...
BN_RECP_CTX_free(ctx);
```

bn, ERR_get_error, BN_add, BN_CTX_new

**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. BN_RECP_CTX_init was removed in OpenSSL 1.1.0