NAME

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

SYNOPSIS

#include <openssl/bn.h> int
BN_mod_mul_reciprocal(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_RECP_CTX *recp, BN_CTX *ctx); 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, const BIGNUM *a, BN_RECP_CTX *recp, BN_CTX *ctx); int
BN_reciprocal(BIGNUM *r, const BIGNUM *m, int len, 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_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. BN_reciprocal() divides the len'th power of two by m and places the quotient in r, rounding it towards zero to the closest integer. 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 or NULL on error. BN_mod_mul_reciprocal(), BN_RECP_CTX_set(), and BN_div_recp() return 1 for success or 0 on error. BN_reciprocal() returns len for success or -1 on error. The error codes can be obtained by ERR_get_error(3).

SEE ALSO

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

HISTORY

BN_mod_mul_reciprocal() and BN_reciprocal() first appeared in SSLeay 0.5.1 and have been available since OpenBSD 2.4. BN_RECP_CTX was added in SSLeay 0.9.0. Before that, 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.

CAVEATS

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.