From 78a0c1f18d5a1f0e51b7467ef7b153b8c29fbb03 Mon Sep 17 00:00:00 2001 From: Bodo Möller Date: Sun, 26 Nov 2000 16:42:38 +0000 Subject: modular arithmetics "make update" --- doc/crypto/BN_add.pod | 88 +++++++++++++++++++++++------------- doc/crypto/BN_mod_mul_montgomery.pod | 15 +++--- doc/crypto/bn.pod | 14 ++++-- 3 files changed, 76 insertions(+), 41 deletions(-) (limited to 'doc/crypto') diff --git a/doc/crypto/BN_add.pod b/doc/crypto/BN_add.pod index 0541d45643..4c8db25f70 100644 --- a/doc/crypto/BN_add.pod +++ b/doc/crypto/BN_add.pod @@ -2,8 +2,9 @@ =head1 NAME -BN_add, BN_sub, BN_mul, BN_div, BN_sqr, BN_mod, BN_mod_mul, BN_exp, -BN_mod_exp, BN_gcd - arithmetic operations on BIGNUMs +BN_add, BN_sub, BN_mul, BN_sqr, BN_div, BN_mod, BN_nnmod, BN_mod_add, +BN_mod_sub, BN_mod_mul, BN_mod_sqr, BN_exp, BN_mod_exp, BN_gcd - +arithmetic operations on BIGNUMs =head1 SYNOPSIS @@ -15,16 +16,26 @@ BN_mod_exp, BN_gcd - arithmetic operations on BIGNUMs int BN_mul(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_CTX *ctx); + int BN_sqr(BIGNUM *r, BIGNUM *a, BN_CTX *ctx); + int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *a, const BIGNUM *d, BN_CTX *ctx); - int BN_sqr(BIGNUM *r, BIGNUM *a, BN_CTX *ctx); - int BN_mod(BIGNUM *rem, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx); - int BN_mod_mul(BIGNUM *ret, BIGNUM *a, BIGNUM *b, const BIGNUM *m, + int BN_nnmod(BIGNUM *rem, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx); + + int BN_mod_add(BIGNUM *r, BIGNUM *a, BIGNUM *b, const BIGNUM *m, + BN_CTX *ctx); + + int BN_mod_sub(BIGNUM *r, BIGNUM *a, BIGNUM *b, const BIGNUM *m, + BN_CTX *ctx); + + int BN_mod_mul(BIGNUM *r, BIGNUM *a, BIGNUM *b, const BIGNUM *m, BN_CTX *ctx); + int BN_mod_sqr(BIGNUM *r, BIGNUM *a, const BIGNUM *m, BN_CTX *ctx); + int BN_exp(BIGNUM *r, BIGNUM *a, BIGNUM *p, BN_CTX *ctx); int BN_mod_exp(BIGNUM *r, BIGNUM *a, const BIGNUM *p, @@ -34,45 +45,58 @@ BN_mod_exp, BN_gcd - arithmetic operations on BIGNUMs =head1 DESCRIPTION -BN_add() adds B and B and places the result in B (C). -B may be the same B as B or B. +BN_add() adds I and I and places the result in I (C). +I may be the same B as I or I. -BN_sub() subtracts B from B and places the result in B (C). +BN_sub() subtracts I from I and places the result in I (C). -BN_mul() multiplies B and B and places the result in B (C). -B may be the same B as B or B. +BN_mul() multiplies I and I and places the result in I (C). +I may be the same B as I or I. For multiplication by powers of 2, use L. -BN_div() divides B by B and places the result in B and the -remainder in B (C). Either of B and B may -be NULL, in which case the respective value is not returned. +BN_sqr() takes the square of I and places the result in I +(C). I and I may be the same B. +This function is faster than BN_mul(r,a,a). + +BN_div() divides I by I and places the result in I and the +remainder in I (C). Either of I and I may +be B, in which case the respective value is not returned. +The result is rounded towards zero; thus if I is negative, the +remainder will be zero or negative. For division by powers of 2, use BN_rshift(3). -BN_sqr() takes the square of B and places the result in B -(C). B and B may be the same B. -This function is faster than BN_mul(r,a,a). +BN_mod() corresponds to BN_div() with I set to B. + +BN_nnmod() finds the non-negative remainder of I divided by I. + +BN_mod_add() adds I to I modulo I and places the non-negative +result in I. + +BN_mod_sub() substracts I from I modulo I and places the +non-negative result in I. -BN_mod() find the remainder of B divided by B and places it in -B (C). +BN_mod_mul() multiplies I by I and finds the non-negative +remainder respective to modulus I (C). I may be +the same B as I or I. For more efficient algorithms for +repeated computations using the same modulus, see +L and +L. -BN_mod_mul() multiplies B by B and finds the remainder when -divided by B (C). B may be the same B as B -or B. For a more efficient algorithm, see -L; for repeated -computations using the same modulus, see L. +BN_mod_sqr() takes the square of I modulo B and places the +result in I. -BN_exp() raises B to the B

-th power and places the result in B +BN_exp() raises I to the I

-th power and places the result in I (C). This function is faster than repeated applications of BN_mul(). -BN_mod_exp() computes B to the B

-th power modulo B (C to the I

-th power modulo I (C). This function uses less time and space than BN_exp(). -BN_gcd() computes the greatest common divisor of B and B and -places the result in B. B may be the same B as B or -B. +BN_gcd() computes the greatest common divisor of I and I and +places the result in I. I may be the same B as I or +I. -For all functions, B is a previously allocated B used for +For all functions, I is a previously allocated B used for temporary variables; see L. Unless noted otherwise, the result B must be different from @@ -91,9 +115,11 @@ L, L =head1 HISTORY -BN_add(), BN_sub(), BN_div(), BN_sqr(), BN_mod(), BN_mod_mul(), +BN_add(), BN_sub(), BN_sqr(), BN_div(), BN_mod(), BN_mod_mul(), BN_mod_exp() and BN_gcd() are available in all versions of SSLeay and -OpenSSL. The B argument to BN_mul() was added in SSLeay +OpenSSL. The I argument to BN_mul() was added in SSLeay 0.9.1b. BN_exp() appeared in SSLeay 0.9.0. +BN_nnmod(), BN_mod_add(), BN_mod_sub(), and BN_mod_sqr() were added in +OpenSSL 0.9.7. =cut diff --git a/doc/crypto/BN_mod_mul_montgomery.pod b/doc/crypto/BN_mod_mul_montgomery.pod index 0b8ab512df..6452470076 100644 --- a/doc/crypto/BN_mod_mul_montgomery.pod +++ b/doc/crypto/BN_mod_mul_montgomery.pod @@ -36,22 +36,23 @@ using the same modulus. BN_MONT_CTX_new() allocates and initializes a B structure. BN_MONT_CTX_init() initializes an existing uninitialized B. -BN_MONT_CTX_set() sets up the B structure from the modulus B +BN_MONT_CTX_set() sets up the I structure from the modulus I by precomputing its inverse and a value R. -BN_MONT_CTX_copy() copies the B B to B. +BN_MONT_CTX_copy() copies the B I to I. BN_MONT_CTX_free() frees the components of the B, and, if it was created by BN_MONT_CTX_new(), also the structure itself. -BN_mod_mul_montgomery() computes Mont(B,B):=B*B*R^-1 and places -the result in B. +BN_mod_mul_montgomery() computes Mont(I,I):=I*I*R^-1 and places +the result in I. -BN_from_montgomery() performs the Montgomery reduction B = B*R^-1. +BN_from_montgomery() performs the Montgomery reduction I = I*R^-1. -BN_to_montgomery() computes Mont(B,R^2), i.e. B*R. +BN_to_montgomery() computes Mont(I,R^2), i.e. I*R. +Note that I must be non-negative and smaller than the modulus. -For all functions, B is a previously allocated B used for +For all functions, I is a previously allocated B used for temporary variables. The B structure is defined as follows: diff --git a/doc/crypto/bn.pod b/doc/crypto/bn.pod index 1504a1c92d..224dfe166a 100644 --- a/doc/crypto/bn.pod +++ b/doc/crypto/bn.pod @@ -21,19 +21,27 @@ bn - multiprecision integer arithmetics BIGNUM *BN_copy(BIGNUM *a, const BIGNUM *b); BIGNUM *BN_dup(const BIGNUM *a); + BIGNUM *BN_swap(BIGNUM *a, BIGNUM *b); + int BN_num_bytes(const BIGNUM *a); int BN_num_bits(const BIGNUM *a); int BN_num_bits_word(BN_ULONG w); - int BN_add(BIGNUM *r, BIGNUM *a, BIGNUM *b); + int BN_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b); int BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b); int BN_mul(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_CTX *ctx); + int BN_sqr(BIGNUM *r, BIGNUM *a, BN_CTX *ctx); int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *a, const BIGNUM *d, BN_CTX *ctx); - int BN_sqr(BIGNUM *r, BIGNUM *a, BN_CTX *ctx); int BN_mod(BIGNUM *rem, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx); + int BN_nnmod(BIGNUM *rem, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx); + int BN_mod_add(BIGNUM *ret, BIGNUM *a, BIGNUM *b, const BIGNUM *m, + BN_CTX *ctx); + int BN_mod_sub(BIGNUM *ret, BIGNUM *a, BIGNUM *b, const BIGNUM *m, + BN_CTX *ctx); int BN_mod_mul(BIGNUM *ret, BIGNUM *a, BIGNUM *b, const BIGNUM *m, BN_CTX *ctx); + int BN_mod_sqr(BIGNUM *ret, BIGNUM *a, const BIGNUM *m, BN_CTX *ctx); int BN_exp(BIGNUM *r, BIGNUM *a, BIGNUM *p, BN_CTX *ctx); int BN_mod_exp(BIGNUM *r, BIGNUM *a, const BIGNUM *p, const BIGNUM *m, BN_CTX *ctx); @@ -137,7 +145,7 @@ of Bs to external formats is described in L. L, L, L, L, L, L, L, -L, L, +L, L, L, L, L, L, L, L, L, L, -- cgit v1.2.3