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

#include <openssl/bn.h>
BN_mod_mul_reciprocal(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_RECP_CTX *recp, BN_CTX *ctx);
BN_RECP_CTX_init(BN_RECP_CTX *recp);
BN_RECP_CTX_free(BN_RECP_CTX *recp);
BN_RECP_CTX_set(BN_RECP_CTX *recp, const BIGNUM *m, BN_CTX *ctx);
BN_div_recp(BIGNUM *dv, BIGNUM *rem, BIGNUM *a, BN_RECP_CTX *recp, BN_CTX *ctx);

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_CTX structure.
BN_RECP_CTX_init() initializes an existing uninitialized BN_RECP_CTX. It is deprecated and dangerous: see CAVEATS.
BN_RECP_CTX_free() frees the components of the BN_RECP_CTX, and, if it was created by BN_RECP_CTX_new(), also the structure itself. If recp is a NULL pointer, no action occurs.
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; 
It cannot be shared between threads.

BN_RECP_CTX_new() returns the newly allocated BN_RECP_CTX or NULL on error.
For the other functions, 1 is returned for success or 0 on error. The error codes can be obtained by ERR_get_error(3).

BN_add(3), BN_CTX_new(3), BN_new(3)

BN_mod_mul_reciprocal() first appeared in SSLeay 0.5.1 and has been available since OpenBSD 2.4.
BN_RECP_CTX was added in SSLeay 0.9.0. Before that, a function BN_reciprocal() was used instead, and the BN_mod_mul_reciprocal() arguments were different.
BN_RECP_CTX_new(), BN_RECP_CTX_init(), BN_RECP_CTX_free(), BN_RECP_CTX_set(), and BN_div_recp() first appeared in SSLeay 0.9.1 and have been available since OpenBSD 2.6.

BN_RECP_CTX_init() must not be called on a context that was used previously, or memory used by the embedded BIGNUM structures is leaked immediately. Besides, it must not be called on a context created with BN_RECP_CTX_new(), or the context itself will likely be leaked later. It can only be used on a static BN_RECP_CTX structure, on one located on the stack, or on one malloc(3)'ed manually, but all these options are discouraged because they will no longer work once BN_RECP_CTX is made opaque.
March 27, 2018 OpenBSD-current