fsbl: weekly update 2023-03-25
1. update release func Change-Id: I221476630ce4f2f6a01e8f89fd96d9ac9701a270
This commit is contained in:
forum_service
@ -1,303 +1,303 @@
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/* spExtras.c */
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/***** BEGIN LICENSE BLOCK *****
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*
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* This Source Code Form is subject to the terms of the Mozilla Public
|
||||
* License, v. 2.0. If a copy of the MPL was not distributed with this
|
||||
* file, You can obtain one at http://mozilla.org/MPL/2.0/.
|
||||
*
|
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* Copyright (c) 2001-15 David Ireland, D.I. Management Services Pty Limited
|
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* <http://www.di-mgt.com.au/bigdigits.html>. All rights reserved.
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*
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***** END LICENSE BLOCK *****/
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/*
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* Last updated:
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* $Date: 2015-10-22 10:23:00 $
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* $Revision: 2.5.0 $
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* $Author: dai $
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*/
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#include <assert.h>
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#include "bigdigits.h"
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#include "spExtras.h"
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int spModMult(DIGIT_T *a, DIGIT_T x, DIGIT_T y, DIGIT_T m)
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{ /* Computes a = (x * y) mod m */
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/* Calc p[2] = x * y */
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DIGIT_T p[2];
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spMultiply(p, x, y);
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/* Then modulo */
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*a = mpShortMod(p, m, 2);
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return 0;
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}
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DIGIT_T spGcd_old(DIGIT_T x, DIGIT_T y)
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{ /* Returns gcd(x, y) */
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/* Ref: Schneier 2nd ed, p245 */
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DIGIT_T g;
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if (x + y == 0)
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return 0; /* Error */
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g = y;
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while (x > 0)
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{
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g = x;
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x = y % x;
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y = g;
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}
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return g;
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}
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DIGIT_T spGcd(DIGIT_T a, DIGIT_T b)
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{ /* Returns gcd(a, b) */
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/* Ref: Cohen, Algorithm 1.3.5 (Binary GCD)
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and Menezes, Algorithm 14.54 */
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DIGIT_T r, t;
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unsigned int k;
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/* 1. [Reduce size once] */
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if (a < b)
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{ /* exchange a and b */
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t = a;
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a = b;
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b = t;
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}
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if (0 == b)
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{
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return a;
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}
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r = a % b;
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a = b;
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b = r;
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if (0 == b)
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{
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return a;
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}
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/* 2. [Compute power of 2] */
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k = 0;
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while (ISEVEN(a) && ISEVEN(b))
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{
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a >>= 1; /* a <-- a/2 */
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b >>= 1; /* b <-- b/2 */
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k++; /* g <-- 2g */
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}
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while (a != 0)
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{
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while (ISEVEN(a))
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{
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a >>= 1; /* a <-- a/2 until a is odd */
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}
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while (ISEVEN(b))
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{
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b >>= 1; /* b <-- a/2 until b is odd */
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}
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/* t <-- |a-b|/2 */
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if (b > a)
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t = (b - a) >> 1;
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else
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t = (a - b) >> 1;
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/* If a >= b then a = t, otherwise b = t */
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if (a >= b)
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a = t;
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else
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b = t;
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}
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/* Output (2^k.b) */
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return (b << k);
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}
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/* spIsPrime */
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static DIGIT_T SMALL_PRIMES[] = { 2, 3, 5, 7, 11, 13, 17, 19 };
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#define N_SMALL_PRIMES sizeof(SMALL_PRIMES)/sizeof(DIGIT_T)
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int spIsPrime(DIGIT_T w, size_t t)
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{ /* Returns true if w is a probable prime
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Carries out t iterations
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(Use t = 50 for DSS Standard)
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*/
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/* Uses Rabin-Miller Probabilistic Primality Test,
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Ref: FIPS-186-2 Appendix 2.
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Also Schneier 2nd ed p 260 & Knuth Vol 2, p 379
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and ANSI 9.42-2003 Annex B.1.1.
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*/
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unsigned int i, j;
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DIGIT_T m, a, b, z;
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int failed;
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/* First check for small primes */
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for (i = 0; i < N_SMALL_PRIMES; i++)
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{
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if (w % SMALL_PRIMES[i] == 0)
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return 0; /* Failed */
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}
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/* Now do Rabin-Miller */
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/* Step 2. Find a and m where w = 1 + (2^a)m
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m is odd and 2^a is largest power of 2 dividing w - 1 */
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m = w - 1;
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for (a = 0; ISEVEN(m); a++)
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m >>= 1; /* Divide by 2 until m is odd */
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/*
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assert((1 << a) * m + 1 == w);
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*/
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for (i = 0; i < t; i++)
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{
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failed = 1; /* Assume fail unless passed in loop */
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/* Step 3. Generate a random integer 1 < b < w */
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/* [v2.1] changed to 1 < b < w-1 */
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b = spSimpleRand(2, w - 2);
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/*
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assert(1 < b && b < w-1);
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*/
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/* Step 4. Set j = 0 and z = b^m mod w */
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j = 0;
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spModExp(&z, b, m, w);
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do
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{
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/* Step 5. If j = 0 and z = 1, or if z = w - 1 */
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if ((j == 0 && z == 1) || (z == w - 1))
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{ /* Passes on this loop - go to Step 9 */
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failed = 0;
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break;
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}
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/* Step 6. If j > 0 and z = 1 */
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if (j > 0 && z == 1)
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{ /* Fails - go to Step 8 */
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failed = 1;
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break;
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}
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/* Step 7. j = j + 1. If j < a set z = z^2 mod w */
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j++;
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if (j < a)
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spModMult(&z, z, z, w);
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/* Loop: if j < a go to Step 5 */
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} while (j < a);
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if (failed)
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{ /* Step 8. Not a prime - stop */
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return 0;
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}
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} /* Step 9. Go to Step 3 until i >= n */
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/* If got here, probably prime => success */
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return 1;
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}
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/* spModExp */
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/* Two alternative functions for spModExp */
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int spModExpK(DIGIT_T *exp, DIGIT_T x,
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DIGIT_T n, DIGIT_T d)
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{ /* Computes exp = x^n mod d */
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/* Ref: Knuth Vol 2 Ch 4.6.3 p 462 Algorithm A
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*/
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DIGIT_T y = 1; /* Step A1. Initialise */
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while (n > 0)
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{ /* Step A2. Halve N */
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if (n & 0x1) /* If odd */
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spModMult(&y, y, x, d); /* Step A3. Multiply Y by Z */
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n >>= 1; /* Halve N */
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if (n > 0) /* Step A4. N = 0? Y is answer */
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spModMult(&x, x, x, d); /* Step A5. Square Z */
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}
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*exp = y;
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return 0;
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}
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int spModExpB(DIGIT_T *exp, DIGIT_T x,
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DIGIT_T e, DIGIT_T m)
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{ /* Computes exp = x^e mod m */
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/* Binary left-to-right method
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*/
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DIGIT_T mask;
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DIGIT_T y; /* Temp variable */
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/* Find most significant bit in e */
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for (mask = HIBITMASK; mask > 0; mask >>= 1)
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{
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if (e & mask)
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break;
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}
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y = x;
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/* For j = k-2 downto 0 step -1 */
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for (mask >>= 1; mask > 0; mask >>= 1)
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{
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spModMult(&y, y, y, m); /* Square */
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if (e & mask)
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spModMult(&y, y, x, m); /* Multiply */
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}
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*exp = y;
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return 0;
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}
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int spModInv(DIGIT_T *inv, DIGIT_T u, DIGIT_T v)
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{ /* Computes inv = u^(-1) mod v */
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/* Ref: Knuth Algorithm X Vol 2 p 342
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ignoring u2, v2, t2
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and avoiding negative numbers
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*/
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DIGIT_T u1, u3, v1, v3, t1, t3, q, w;
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int bIterations = 1;
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int result;
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/* Step X1. Initialise */
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u1 = 1;
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u3 = u;
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v1 = 0;
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v3 = v;
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while (v3 != 0) /* Step X2. */
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{ /* Step X3. */
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q = u3 / v3; /* Divide and */
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t3 = u3 % v3;
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w = q * v1; /* "Subtract" */
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t1 = u1 + w;
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/* Swap */
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u1 = v1;
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v1 = t1;
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u3 = v3;
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v3 = t3;
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bIterations = -bIterations;
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}
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if (bIterations < 0)
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*inv = v - u1;
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else
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*inv = u1;
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/* Make sure u3 = gcd(u,v) == 1 */
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if (u3 != 1)
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{
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result = 1;
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*inv = 0;
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}
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else
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result = 0;
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return result;
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}
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/* spExtras.c */
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/***** BEGIN LICENSE BLOCK *****
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||||
*
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||||
* This Source Code Form is subject to the terms of the Mozilla Public
|
||||
* License, v. 2.0. If a copy of the MPL was not distributed with this
|
||||
* file, You can obtain one at http://mozilla.org/MPL/2.0/.
|
||||
*
|
||||
* Copyright (c) 2001-15 David Ireland, D.I. Management Services Pty Limited
|
||||
* <http://www.di-mgt.com.au/bigdigits.html>. All rights reserved.
|
||||
*
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||||
***** END LICENSE BLOCK *****/
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||||
/*
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* Last updated:
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* $Date: 2015-10-22 10:23:00 $
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* $Revision: 2.5.0 $
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* $Author: dai $
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*/
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#include <assert.h>
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#include "bigdigits.h"
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#include "spExtras.h"
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int spModMult(DIGIT_T *a, DIGIT_T x, DIGIT_T y, DIGIT_T m)
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{ /* Computes a = (x * y) mod m */
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/* Calc p[2] = x * y */
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DIGIT_T p[2];
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spMultiply(p, x, y);
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/* Then modulo */
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*a = mpShortMod(p, m, 2);
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return 0;
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}
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DIGIT_T spGcd_old(DIGIT_T x, DIGIT_T y)
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{ /* Returns gcd(x, y) */
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/* Ref: Schneier 2nd ed, p245 */
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DIGIT_T g;
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if (x + y == 0)
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return 0; /* Error */
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g = y;
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while (x > 0)
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{
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g = x;
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x = y % x;
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y = g;
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}
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return g;
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}
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DIGIT_T spGcd(DIGIT_T a, DIGIT_T b)
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{ /* Returns gcd(a, b) */
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/* Ref: Cohen, Algorithm 1.3.5 (Binary GCD)
|
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and Menezes, Algorithm 14.54 */
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DIGIT_T r, t;
|
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unsigned int k;
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|
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/* 1. [Reduce size once] */
|
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if (a < b)
|
||||
{ /* exchange a and b */
|
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t = a;
|
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a = b;
|
||||
b = t;
|
||||
}
|
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if (0 == b)
|
||||
{
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return a;
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}
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r = a % b;
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a = b;
|
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b = r;
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||||
|
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if (0 == b)
|
||||
{
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return a;
|
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}
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/* 2. [Compute power of 2] */
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k = 0;
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while (ISEVEN(a) && ISEVEN(b))
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{
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a >>= 1; /* a <-- a/2 */
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b >>= 1; /* b <-- b/2 */
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k++; /* g <-- 2g */
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}
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while (a != 0)
|
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{
|
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while (ISEVEN(a))
|
||||
{
|
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a >>= 1; /* a <-- a/2 until a is odd */
|
||||
}
|
||||
while (ISEVEN(b))
|
||||
{
|
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b >>= 1; /* b <-- a/2 until b is odd */
|
||||
}
|
||||
/* t <-- |a-b|/2 */
|
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if (b > a)
|
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t = (b - a) >> 1;
|
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else
|
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t = (a - b) >> 1;
|
||||
/* If a >= b then a = t, otherwise b = t */
|
||||
if (a >= b)
|
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a = t;
|
||||
else
|
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b = t;
|
||||
}
|
||||
/* Output (2^k.b) */
|
||||
return (b << k);
|
||||
}
|
||||
|
||||
/* spIsPrime */
|
||||
|
||||
static DIGIT_T SMALL_PRIMES[] = { 2, 3, 5, 7, 11, 13, 17, 19 };
|
||||
#define N_SMALL_PRIMES sizeof(SMALL_PRIMES)/sizeof(DIGIT_T)
|
||||
|
||||
int spIsPrime(DIGIT_T w, size_t t)
|
||||
{ /* Returns true if w is a probable prime
|
||||
Carries out t iterations
|
||||
(Use t = 50 for DSS Standard)
|
||||
*/
|
||||
/* Uses Rabin-Miller Probabilistic Primality Test,
|
||||
Ref: FIPS-186-2 Appendix 2.
|
||||
Also Schneier 2nd ed p 260 & Knuth Vol 2, p 379
|
||||
and ANSI 9.42-2003 Annex B.1.1.
|
||||
*/
|
||||
|
||||
unsigned int i, j;
|
||||
DIGIT_T m, a, b, z;
|
||||
int failed;
|
||||
|
||||
/* First check for small primes */
|
||||
for (i = 0; i < N_SMALL_PRIMES; i++)
|
||||
{
|
||||
if (w % SMALL_PRIMES[i] == 0)
|
||||
return 0; /* Failed */
|
||||
}
|
||||
|
||||
/* Now do Rabin-Miller */
|
||||
/* Step 2. Find a and m where w = 1 + (2^a)m
|
||||
m is odd and 2^a is largest power of 2 dividing w - 1 */
|
||||
|
||||
m = w - 1;
|
||||
for (a = 0; ISEVEN(m); a++)
|
||||
m >>= 1; /* Divide by 2 until m is odd */
|
||||
|
||||
/*
|
||||
assert((1 << a) * m + 1 == w);
|
||||
*/
|
||||
|
||||
for (i = 0; i < t; i++)
|
||||
{
|
||||
failed = 1; /* Assume fail unless passed in loop */
|
||||
/* Step 3. Generate a random integer 1 < b < w */
|
||||
/* [v2.1] changed to 1 < b < w-1 */
|
||||
b = spSimpleRand(2, w - 2);
|
||||
|
||||
/*
|
||||
assert(1 < b && b < w-1);
|
||||
*/
|
||||
|
||||
/* Step 4. Set j = 0 and z = b^m mod w */
|
||||
j = 0;
|
||||
spModExp(&z, b, m, w);
|
||||
do
|
||||
{
|
||||
/* Step 5. If j = 0 and z = 1, or if z = w - 1 */
|
||||
if ((j == 0 && z == 1) || (z == w - 1))
|
||||
{ /* Passes on this loop - go to Step 9 */
|
||||
failed = 0;
|
||||
break;
|
||||
}
|
||||
|
||||
/* Step 6. If j > 0 and z = 1 */
|
||||
if (j > 0 && z == 1)
|
||||
{ /* Fails - go to Step 8 */
|
||||
failed = 1;
|
||||
break;
|
||||
}
|
||||
|
||||
/* Step 7. j = j + 1. If j < a set z = z^2 mod w */
|
||||
j++;
|
||||
if (j < a)
|
||||
spModMult(&z, z, z, w);
|
||||
/* Loop: if j < a go to Step 5 */
|
||||
} while (j < a);
|
||||
|
||||
if (failed)
|
||||
{ /* Step 8. Not a prime - stop */
|
||||
return 0;
|
||||
}
|
||||
} /* Step 9. Go to Step 3 until i >= n */
|
||||
/* If got here, probably prime => success */
|
||||
return 1;
|
||||
}
|
||||
|
||||
/* spModExp */
|
||||
|
||||
/* Two alternative functions for spModExp */
|
||||
|
||||
int spModExpK(DIGIT_T *exp, DIGIT_T x,
|
||||
DIGIT_T n, DIGIT_T d)
|
||||
{ /* Computes exp = x^n mod d */
|
||||
/* Ref: Knuth Vol 2 Ch 4.6.3 p 462 Algorithm A
|
||||
*/
|
||||
DIGIT_T y = 1; /* Step A1. Initialise */
|
||||
|
||||
while (n > 0)
|
||||
{ /* Step A2. Halve N */
|
||||
if (n & 0x1) /* If odd */
|
||||
spModMult(&y, y, x, d); /* Step A3. Multiply Y by Z */
|
||||
|
||||
n >>= 1; /* Halve N */
|
||||
if (n > 0) /* Step A4. N = 0? Y is answer */
|
||||
spModMult(&x, x, x, d); /* Step A5. Square Z */
|
||||
}
|
||||
|
||||
*exp = y;
|
||||
return 0;
|
||||
}
|
||||
|
||||
int spModExpB(DIGIT_T *exp, DIGIT_T x,
|
||||
DIGIT_T e, DIGIT_T m)
|
||||
{ /* Computes exp = x^e mod m */
|
||||
/* Binary left-to-right method
|
||||
*/
|
||||
DIGIT_T mask;
|
||||
DIGIT_T y; /* Temp variable */
|
||||
|
||||
/* Find most significant bit in e */
|
||||
for (mask = HIBITMASK; mask > 0; mask >>= 1)
|
||||
{
|
||||
if (e & mask)
|
||||
break;
|
||||
}
|
||||
|
||||
y = x;
|
||||
/* For j = k-2 downto 0 step -1 */
|
||||
for (mask >>= 1; mask > 0; mask >>= 1)
|
||||
{
|
||||
spModMult(&y, y, y, m); /* Square */
|
||||
if (e & mask)
|
||||
spModMult(&y, y, x, m); /* Multiply */
|
||||
}
|
||||
|
||||
*exp = y;
|
||||
return 0;
|
||||
}
|
||||
|
||||
int spModInv(DIGIT_T *inv, DIGIT_T u, DIGIT_T v)
|
||||
{ /* Computes inv = u^(-1) mod v */
|
||||
/* Ref: Knuth Algorithm X Vol 2 p 342
|
||||
ignoring u2, v2, t2
|
||||
and avoiding negative numbers
|
||||
*/
|
||||
DIGIT_T u1, u3, v1, v3, t1, t3, q, w;
|
||||
int bIterations = 1;
|
||||
int result;
|
||||
|
||||
/* Step X1. Initialise */
|
||||
u1 = 1;
|
||||
u3 = u;
|
||||
v1 = 0;
|
||||
v3 = v;
|
||||
|
||||
while (v3 != 0) /* Step X2. */
|
||||
{ /* Step X3. */
|
||||
q = u3 / v3; /* Divide and */
|
||||
t3 = u3 % v3;
|
||||
w = q * v1; /* "Subtract" */
|
||||
t1 = u1 + w;
|
||||
/* Swap */
|
||||
u1 = v1;
|
||||
v1 = t1;
|
||||
u3 = v3;
|
||||
v3 = t3;
|
||||
bIterations = -bIterations;
|
||||
}
|
||||
|
||||
if (bIterations < 0)
|
||||
*inv = v - u1;
|
||||
else
|
||||
*inv = u1;
|
||||
|
||||
/* Make sure u3 = gcd(u,v) == 1 */
|
||||
if (u3 != 1)
|
||||
{
|
||||
result = 1;
|
||||
*inv = 0;
|
||||
}
|
||||
else
|
||||
result = 0;
|
||||
|
||||
return result;
|
||||
}
|
||||
|
||||
|
||||
Reference in New Issue
Block a user