[fsbl] add fsbl for cv181x/cv180x
Change-Id: I6809bc5016d4bc148f62be2ed3f8e928ec111f19
This commit is contained in:
sam.xiang
260
fsbl/lib/BigDigits/t_mpModArith.c
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260
fsbl/lib/BigDigits/t_mpModArith.c
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/* $Id: t_mpModArith.c $ */
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/* Some more tests of the BigDigits "mp" functions. */
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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
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* License, v. 2.0. If a copy of the MPL was not distributed with this
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* file, You can obtain one at http://mozilla.org/MPL/2.0/.
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*
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* Copyright (c) 2001-16 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: 2016-03-31 09:51:00 $
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* $Revision: 2.6.1 $
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* $Author: dai $
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*/
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#ifdef NDEBUG
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#undef NDEBUG
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#endif
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#include <assert.h>
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#include <stdio.h>
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#include "bigdigits.h"
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/** Hard-coded maximum number of bits we choose to handle */
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#define EC_MAXBITS 640
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/** Number of digits needed to represent an integer of EC_MAXBITS bits */
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#define EC_NDIGITS (EC_MAXBITS/BITS_PER_DIGIT)
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/** Unsigned integer of EC_MAXBITS bits */
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typedef DIGIT_T EC_INT[EC_NDIGITS];
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/* This module can be compiled with the global preprocessor definitions
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MSVC: /D "NO_ALLOCS" /D "MAX_FIXED_BIT_LENGTH=640"
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GCC: -D NO_ALLOCS -D MAX_FIXED_BIT_LENGTH=640
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*/
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/** Make a random number of up to `nbits` bits */
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size_t make_random(EC_INT a, size_t nbits)
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{
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size_t n;
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/* Half the time, pick a shorter bitlength at random from [6,nbits] */
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if (spSimpleRand(0, 1)) {
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n = (size_t)spSimpleRand(6, (DIGIT_T)nbits);
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}
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else {
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n = nbits;
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}
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mpQuickRandBits(a, EC_NDIGITS, n);
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return n;
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}
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int main(void)
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{
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/* Note the neat way to declare variables of EC_NDIGITS */
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EC_INT u, v, w, m, p, x, y;
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size_t nbits;
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int r;
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/* Force linker to include copyright notice in
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executable object image
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*/
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copyright_notice();
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printf("Testing BIGDIGITS 'mp' modular arithmetic functions.\n");
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// First show it works for small numbers...
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mpSetDigit(u, 17, EC_NDIGITS);
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mpSetDigit(v, 13, EC_NDIGITS);
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mpSetDigit(m, 25, EC_NDIGITS);
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mpPrintDecimal("u=", u, EC_NDIGITS, ", ");
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mpPrintDecimal("v=", v, EC_NDIGITS, ", ");
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mpPrintDecimal("m=", m, EC_NDIGITS, "\n");
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mpModAdd(w, u, v, m, EC_NDIGITS);
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mpPrintDecimal("w=u+v(mod m)=", w, EC_NDIGITS, "\n");
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/* Check that w == 5 */
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assert(mpShortCmp(w, 5, EC_NDIGITS) == 0);
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// Add assign w+=u [NB (w,w,u) not (w,u,w)]
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mpModAdd(w, w, u, m, EC_NDIGITS);
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mpPrintDecimal("w+=u(mod m)=", w, EC_NDIGITS, "\n");
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// Subtract assign w-=u
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mpModSub(w, w, u, m, EC_NDIGITS);
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mpPrintDecimal("w-=u(mod m)=", w, EC_NDIGITS, "\n");
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// Subtract modulo m
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mpModSub(w, v, u, m, EC_NDIGITS);
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mpPrintDecimal("w=v-u(mod m)=", w, EC_NDIGITS, "\n");
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mpModSub(w, u, v, m, EC_NDIGITS);
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mpPrintDecimal("w=u-v(mod m)=", w, EC_NDIGITS, "\n");
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// Add then subtract modulo m
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mpModAdd(w, u, v, m, EC_NDIGITS);
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mpPrintDecimal("w=u+v(mod m)=", w, EC_NDIGITS, "\n");
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/* y = w - v */
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mpModSub(y, w, v, m, EC_NDIGITS);
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mpPrintDecimal("y=w-v(mod m)=", y, EC_NDIGITS, "\n");
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/* Check y == u */
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printf("y == u => %s\n", (mpEqual(y, u, EC_NDIGITS) ? "OK" : "ERROR"));
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assert(mpEqual(y, u, EC_NDIGITS));
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printf("Select a 192-bit prime number...\n");
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mpConvFromHex(p, EC_NDIGITS, "fffffffffffffffffffffffffffffffeffffffffffffffff");
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mpPrintHex("p=0x", p, EC_NDIGITS, "\n");
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mpPrintDecimal("p=", p, EC_NDIGITS, "\n");
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r = mpIsPrime(p, EC_NDIGITS, 50);
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printf("mpIsPrime(p)=%d\n", r);
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assert(r != 0);
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printf("Find the square root of a quadratic residue modulo p ...\n");
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/* Pick a number, any number, less than p */
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nbits = mpBitLength(p, EC_NDIGITS);
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make_random(u, nbits - 1);
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mpPrintDecimal("u=", u, EC_NDIGITS, "\n");
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/* Square it modulo p => a quadratic residue modulo p */
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mpModSquare(w, u, p, EC_NDIGITS);
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mpPrintDecimal("w=u^2(mod p)=", w, EC_NDIGITS, "\n");
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/* Check we have a quadratic residue */
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r = mpJacobi(w, p, EC_NDIGITS);
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printf("Legendre symbol (w|p)=%d (expected 1)\n", r);
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assert(r == 1);
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/* Compute one modular square root */
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mpModSqrt(x, w, p, EC_NDIGITS);
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mpPrintDecimal("x=sqrt(w)(mod p)=", x, EC_NDIGITS, "\n");
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/* and the other */
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mpSubtract(y, p, x, EC_NDIGITS);
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mpPrintDecimal("y=p-x=", y, EC_NDIGITS, "\n");
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/* One of x or y is the same as u */
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assert(mpEqual(x, u, EC_NDIGITS) || mpEqual(y, u, EC_NDIGITS));
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if (mpEqual(x, u, EC_NDIGITS)) {
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printf("u == x\n");
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}
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else {
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printf("u == p-x\n");
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}
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printf("Find a number that is not a quadratic residue mod p...\n");
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do {
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make_random(v, nbits);
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} while (mpJacobi(v, p, EC_NDIGITS) != -1);
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mpPrintDecimal("v=", v, EC_NDIGITS, "\n");
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printf("Legendre symbol (v|p)=%d (expected -1)\n", mpJacobi(v, p, EC_NDIGITS));
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r = mpModSqrt(x, v, p, EC_NDIGITS);
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printf("mpModSqrt(v) returns %d (-1 => square root does not exist)\n", r);
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assert(r != 0);
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printf("\nAdd and subtract modulo p...\n");
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/* Add two random numbers w = u + v (mod p) */
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make_random(u, nbits - 1);
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make_random(v, nbits - 1);
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mpPrintDecimal("u=", u, EC_NDIGITS, "\n");
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mpPrintDecimal("v=", v, EC_NDIGITS, "\n");
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mpModAdd(w, u, v, p, EC_NDIGITS);
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mpPrintDecimal("w=u+v(mod p)=", w, EC_NDIGITS, "\n");
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/* y = w - v (mod p) */
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mpModSub(y, w, v, p, EC_NDIGITS);
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mpPrintDecimal("y=w-v(mod p)=", y, EC_NDIGITS, "\n");
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/* Check y == u */
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printf("y == u => %s\n", (mpEqual(y, u, EC_NDIGITS) ? "OK" : "ERROR"));
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assert(mpEqual(y, u, EC_NDIGITS));
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printf("Do 'add assign' and 'subtract assign'...\n");
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mpSetEqual(w, u, EC_NDIGITS);
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mpPrintDecimal("y= ", w, EC_NDIGITS, "\n");
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mpPrintDecimal("w=y= ", w, EC_NDIGITS, "\n");
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mpPrintDecimal("v= ", v, EC_NDIGITS, "\n");
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/* Now "add assign" w += v (mod p) */
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mpModAdd(w, w, v, p, EC_NDIGITS);
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mpPrintDecimal("w+=v(mod p)=", w, EC_NDIGITS, "\n");
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/* and "subtract assign" w -= v (mod p) */
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mpModSub(w, w, v, p, EC_NDIGITS);
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mpPrintDecimal("w-=v(mod p)=", w, EC_NDIGITS, "\n");
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/* Check w == y */
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printf("w == y => %s\n", (mpEqual(w, y, EC_NDIGITS) ? "OK" : "ERROR"));
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assert(mpEqual(w, y, EC_NDIGITS));
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printf("\nDivide an integer by 2 modulo p - quick method...\n");
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mpPrintDecimal("u= ", u, EC_NDIGITS, "\n");
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mpModHalve(w, u, p, EC_NDIGITS);
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mpPrintDecimal("w=u/2(mod p)=", w, EC_NDIGITS, "\n");
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// Check result
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mpModAdd(v, w, w, p, EC_NDIGITS);
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mpPrintDecimal("v=w*2(mod p)=", v, EC_NDIGITS, "\n");
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printf("v == u => %s\n", (mpEqual(v, u, EC_NDIGITS) ? "OK" : "ERROR"));
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assert(mpEqual(v, u, EC_NDIGITS));
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/* DEMONSTRATE "QUICK" MODULO REDUCTION FOR SPECIAL CASE */
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printf("\nSpecial case modulo reduction...\n");
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/* Compute v = u mod p for u in range 0 <= u < 4p */
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mpPrintHex("p=", p, EC_NDIGITS, "\n");
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nbits = mpBitLength(p, EC_NDIGITS);
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printf("p is %d bits\n", nbits);
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// Generate a random number approx 2-4x bigger than p
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mpQuickRandBits(u, EC_NDIGITS, nbits + 2);
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mpPrintHex("u=", u, EC_NDIGITS, "\n");
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printf("u is %d bits\n", mpBitLength(u, EC_NDIGITS));
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// Compute v = u mod p for this special case
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mpModSpecial(v, u, p, EC_NDIGITS);
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mpPrintHex("v=u(mod p)=", v, EC_NDIGITS, "\n");
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// Check that result v < p
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assert(mpCompare(v, p, EC_NDIGITS) < 0);
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// And check again using the more expensive mpModulo fn
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mpModulo(w, u, EC_NDIGITS, p, EC_NDIGITS);
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mpPrintHex("mpModulo()=", w, EC_NDIGITS, "\n");
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assert(mpEqual(v, w, EC_NDIGITS));
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printf("\nDemonstrate mpPrintBits():\n");
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mpSetDigit(u, 0xef, EC_NDIGITS);
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mpPrintHex("u=0x", u, EC_NDIGITS, " => ");
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mpPrintBits("'", u, EC_NDIGITS, "'b\n");
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mpSetDigit(u, 0x28, EC_NDIGITS);
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mpPrintHex("u=0x", u, EC_NDIGITS, " => ");
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mpPrintBits("'", u, EC_NDIGITS, "'b\n");
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mpSetDigit(u, 0, EC_NDIGITS);
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mpPrintHex("u=0x", u, EC_NDIGITS, " => ");
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mpPrintBits("'", u, EC_NDIGITS, "'b\n");
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mpSetDigit(u, 0xdeadbeef, EC_NDIGITS);
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mpPrintHex("u=0x", u, EC_NDIGITS, " => ");
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mpPrintBits("'", u, EC_NDIGITS, "'b\n");
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printf("(correct)= %s\n", "11011110101011011011111011101111");
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mpConvFromHex(u, EC_NDIGITS, "04deadbeefcafebabe1");
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mpPrintHex("u=0x", u, EC_NDIGITS, " => ");
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mpPrintBits("\n'", u, EC_NDIGITS, "'b\n");
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mpPrintHex("p=0x", p, EC_NDIGITS, " => ");
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mpPrintBits("\n'", p, EC_NDIGITS, "'b\n");
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/* Display version number */
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printf("\nVERSION=%d\n", mpVersion());
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printf("Compiled on [%s]\n", mpCompileTime());
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printf("OK, successfully completed tests.\n");
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return 0;
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}
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