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Alphabetical listing for B

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BN_mod_mul_montgomery(3)
NAME
  BN_mod_mul_montgomery, BN_MONT_CTX_new, BN_MONT_CTX_init, BN_MONT_CTX_free,
  BN_MONT_CTX_set, BN_MONT_CTX_copy, BN_from_montgomery, BN_to_montgomery -
  Montgomery multiplication

SYNOPSIS
  #include <openssl/bn.h>

  BN_MONT_CTX *BN_MONT_CTX_new(
	  void );

  void BN_MONT_CTX_init(
	  BN_MONT_CTX *ctx );

  void BN_MONT_CTX_free(
	  BN_MONT_CTX *mont );

  int BN_MONT_CTX_set(
	  BN_MONT_CTX *mont, const BIGNUM *m, BN_CTX *ctx );

  BN_MONT_CTX *BN_MONT_CTX_copy(
	  BN_MONT_CTX *to, BN_MONT_CTX *from );

  int BN_mod_mul_montgomery(
	  BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_MONT_CTX *mont, BN_CTX *ctx );

  int BN_from_montgomery(
	  BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont, BN_CTX *ctx );

  int BN_to_montgomery(
	  BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont, BN_CTX *ctx );

DESCRIPTION
  These functions implement Montgomery multiplication. They are used
  automatically when BN_mod_exp() is called with suitable input, but they may
  be useful when several operations are performed using the same modulus.

  The BN_MONT_CTX_new() function allocates and initializes a BN_MONT_CTX
  structure. The BN_MONT_CTX_init() function initializes an existing
  uninitialized BN_MONT_CTX.

  The BN_MONT_CTX_set() function sets up the mont structure from the modulus
  m by precomputing its inverse and a value R.

  The BN_MONT_CTX_copy() function copies the BN_MONT_CTX from to to.

  The BN_MONT_CTX_free() function frees the components of the BN_MONT_CTX,
  and, if it was created by BN_MONT_CTX_new(), also the structure itself.

  The BN_mod_mul_montgomery() function computes Mont(a,b):=a*b*R^-1 and
  places the result in r.

  The BN_from_montgomery() function performs the Montgomery reduction r =
  a*R^-1.

  The BN_to_montgomery() function computes Mont(a,R^2), i.e.  a*R.

  For all functions, ctx is a previously allocated BN_CTX used for temporary
  variables.

  The BN_MONT_CTX structure is defined as follows:

	typedef struct bn_mont_ctx_st
	       {
	       int ri;	       /* number of bits in R */
	       BIGNUM RR;      /* R^2 (used to convert to Montgomery form) */
	       BIGNUM N;       /* The modulus */
	       BIGNUM Ni;      /* R*(1/R mod N) - N*Ni = 1
				* (Ni is only stored for bignum algorithm) */
	       BN_ULONG n0;    /* least significant word of Ni */
	       int flags;
	       } BN_MONT_CTX;

  BN_to_montgomery() is a macro.

RETURN VALUES
  The BN_MONT_CTX_new() function returns the newly allocated BN_MONT_CTX, and
  NULL on error.

  The BN_MONT_CTX_init() and BN_MONT_CTX_free() functions have no return
  values.

  For the other functions, 1 is returned for success, 0 on error. The error
  codes can be obtained by using ERR_get_error().

HISTORY
  The BN_MONT_CTX_new(), BN_MONT_CTX_free(), BN_MONT_CTX_set(),
  BN_mod_mul_montgomery(), BN_from_montgomery(), and BN_to_montgomery()
  functions are available in all versions of SSLeay and OpenSSL.

  The BN_MONT_CTX_init() and BN_MONT_CTX_copy() functions were added in
  SSLeay 0.9.1b.

SEE ALSO
  Functions: bn(3), err(3), BN_add(3), BN_CTX_new(3)

Index for Section 3

Alphabetical listing for B

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