fsbl: weekly update 2023-03-25
1. update release func Change-Id: I221476630ce4f2f6a01e8f89fd96d9ac9701a270
This commit is contained in:
forum_service
@ -1,260 +1,260 @@
|
||||
/* $Id: t_mpModArith.c $ */
|
||||
|
||||
/* Some more tests of the BigDigits "mp" functions. */
|
||||
|
||||
/***** BEGIN LICENSE BLOCK *****
|
||||
*
|
||||
* 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) 2001-16 David Ireland, D.I. Management Services Pty Limited
|
||||
* <http://www.di-mgt.com.au/bigdigits.html>. All rights reserved.
|
||||
*
|
||||
***** END LICENSE BLOCK *****/
|
||||
/*
|
||||
* Last updated:
|
||||
* $Date: 2016-03-31 09:51:00 $
|
||||
* $Revision: 2.6.1 $
|
||||
* $Author: dai $
|
||||
*/
|
||||
|
||||
|
||||
#ifdef NDEBUG
|
||||
#undef NDEBUG
|
||||
#endif
|
||||
#include <assert.h>
|
||||
#include <stdio.h>
|
||||
#include "bigdigits.h"
|
||||
|
||||
|
||||
|
||||
/** Hard-coded maximum number of bits we choose to handle */
|
||||
#define EC_MAXBITS 640
|
||||
/** Number of digits needed to represent an integer of EC_MAXBITS bits */
|
||||
#define EC_NDIGITS (EC_MAXBITS/BITS_PER_DIGIT)
|
||||
|
||||
/** Unsigned integer of EC_MAXBITS bits */
|
||||
typedef DIGIT_T EC_INT[EC_NDIGITS];
|
||||
|
||||
/* This module can be compiled with the global preprocessor definitions
|
||||
MSVC: /D "NO_ALLOCS" /D "MAX_FIXED_BIT_LENGTH=640"
|
||||
GCC: -D NO_ALLOCS -D MAX_FIXED_BIT_LENGTH=640
|
||||
*/
|
||||
|
||||
|
||||
/** Make a random number of up to `nbits` bits */
|
||||
size_t make_random(EC_INT a, size_t nbits)
|
||||
{
|
||||
|
||||
size_t n;
|
||||
|
||||
/* Half the time, pick a shorter bitlength at random from [6,nbits] */
|
||||
if (spSimpleRand(0, 1)) {
|
||||
n = (size_t)spSimpleRand(6, (DIGIT_T)nbits);
|
||||
}
|
||||
else {
|
||||
n = nbits;
|
||||
}
|
||||
|
||||
mpQuickRandBits(a, EC_NDIGITS, n);
|
||||
|
||||
return n;
|
||||
}
|
||||
|
||||
|
||||
int main(void)
|
||||
{
|
||||
/* Note the neat way to declare variables of EC_NDIGITS */
|
||||
EC_INT u, v, w, m, p, x, y;
|
||||
size_t nbits;
|
||||
int r;
|
||||
|
||||
/* Force linker to include copyright notice in
|
||||
executable object image
|
||||
*/
|
||||
copyright_notice();
|
||||
|
||||
|
||||
printf("Testing BIGDIGITS 'mp' modular arithmetic functions.\n");
|
||||
|
||||
// First show it works for small numbers...
|
||||
mpSetDigit(u, 17, EC_NDIGITS);
|
||||
mpSetDigit(v, 13, EC_NDIGITS);
|
||||
mpSetDigit(m, 25, EC_NDIGITS);
|
||||
mpPrintDecimal("u=", u, EC_NDIGITS, ", ");
|
||||
mpPrintDecimal("v=", v, EC_NDIGITS, ", ");
|
||||
mpPrintDecimal("m=", m, EC_NDIGITS, "\n");
|
||||
mpModAdd(w, u, v, m, EC_NDIGITS);
|
||||
mpPrintDecimal("w=u+v(mod m)=", w, EC_NDIGITS, "\n");
|
||||
/* Check that w == 5 */
|
||||
assert(mpShortCmp(w, 5, EC_NDIGITS) == 0);
|
||||
|
||||
// Add assign w+=u [NB (w,w,u) not (w,u,w)]
|
||||
mpModAdd(w, w, u, m, EC_NDIGITS);
|
||||
mpPrintDecimal("w+=u(mod m)=", w, EC_NDIGITS, "\n");
|
||||
// Subtract assign w-=u
|
||||
mpModSub(w, w, u, m, EC_NDIGITS);
|
||||
mpPrintDecimal("w-=u(mod m)=", w, EC_NDIGITS, "\n");
|
||||
|
||||
// Subtract modulo m
|
||||
mpModSub(w, v, u, m, EC_NDIGITS);
|
||||
mpPrintDecimal("w=v-u(mod m)=", w, EC_NDIGITS, "\n");
|
||||
mpModSub(w, u, v, m, EC_NDIGITS);
|
||||
mpPrintDecimal("w=u-v(mod m)=", w, EC_NDIGITS, "\n");
|
||||
|
||||
// Add then subtract modulo m
|
||||
mpModAdd(w, u, v, m, EC_NDIGITS);
|
||||
mpPrintDecimal("w=u+v(mod m)=", w, EC_NDIGITS, "\n");
|
||||
/* y = w - v */
|
||||
mpModSub(y, w, v, m, EC_NDIGITS);
|
||||
mpPrintDecimal("y=w-v(mod m)=", y, EC_NDIGITS, "\n");
|
||||
/* Check y == u */
|
||||
printf("y == u => %s\n", (mpEqual(y, u, EC_NDIGITS) ? "OK" : "ERROR"));
|
||||
assert(mpEqual(y, u, EC_NDIGITS));
|
||||
|
||||
|
||||
|
||||
printf("Select a 192-bit prime number...\n");
|
||||
mpConvFromHex(p, EC_NDIGITS, "fffffffffffffffffffffffffffffffeffffffffffffffff");
|
||||
mpPrintHex("p=0x", p, EC_NDIGITS, "\n");
|
||||
mpPrintDecimal("p=", p, EC_NDIGITS, "\n");
|
||||
r = mpIsPrime(p, EC_NDIGITS, 50);
|
||||
printf("mpIsPrime(p)=%d\n", r);
|
||||
assert(r != 0);
|
||||
|
||||
printf("Find the square root of a quadratic residue modulo p ...\n");
|
||||
/* Pick a number, any number, less than p */
|
||||
nbits = mpBitLength(p, EC_NDIGITS);
|
||||
make_random(u, nbits - 1);
|
||||
mpPrintDecimal("u=", u, EC_NDIGITS, "\n");
|
||||
/* Square it modulo p => a quadratic residue modulo p */
|
||||
mpModSquare(w, u, p, EC_NDIGITS);
|
||||
mpPrintDecimal("w=u^2(mod p)=", w, EC_NDIGITS, "\n");
|
||||
/* Check we have a quadratic residue */
|
||||
r = mpJacobi(w, p, EC_NDIGITS);
|
||||
printf("Legendre symbol (w|p)=%d (expected 1)\n", r);
|
||||
assert(r == 1);
|
||||
/* Compute one modular square root */
|
||||
mpModSqrt(x, w, p, EC_NDIGITS);
|
||||
mpPrintDecimal("x=sqrt(w)(mod p)=", x, EC_NDIGITS, "\n");
|
||||
/* and the other */
|
||||
mpSubtract(y, p, x, EC_NDIGITS);
|
||||
mpPrintDecimal("y=p-x=", y, EC_NDIGITS, "\n");
|
||||
/* One of x or y is the same as u */
|
||||
assert(mpEqual(x, u, EC_NDIGITS) || mpEqual(y, u, EC_NDIGITS));
|
||||
if (mpEqual(x, u, EC_NDIGITS)) {
|
||||
printf("u == x\n");
|
||||
}
|
||||
else {
|
||||
printf("u == p-x\n");
|
||||
}
|
||||
|
||||
printf("Find a number that is not a quadratic residue mod p...\n");
|
||||
do {
|
||||
make_random(v, nbits);
|
||||
} while (mpJacobi(v, p, EC_NDIGITS) != -1);
|
||||
mpPrintDecimal("v=", v, EC_NDIGITS, "\n");
|
||||
printf("Legendre symbol (v|p)=%d (expected -1)\n", mpJacobi(v, p, EC_NDIGITS));
|
||||
r = mpModSqrt(x, v, p, EC_NDIGITS);
|
||||
printf("mpModSqrt(v) returns %d (-1 => square root does not exist)\n", r);
|
||||
assert(r != 0);
|
||||
|
||||
|
||||
printf("\nAdd and subtract modulo p...\n");
|
||||
/* Add two random numbers w = u + v (mod p) */
|
||||
make_random(u, nbits - 1);
|
||||
make_random(v, nbits - 1);
|
||||
mpPrintDecimal("u=", u, EC_NDIGITS, "\n");
|
||||
mpPrintDecimal("v=", v, EC_NDIGITS, "\n");
|
||||
mpModAdd(w, u, v, p, EC_NDIGITS);
|
||||
mpPrintDecimal("w=u+v(mod p)=", w, EC_NDIGITS, "\n");
|
||||
/* y = w - v (mod p) */
|
||||
mpModSub(y, w, v, p, EC_NDIGITS);
|
||||
mpPrintDecimal("y=w-v(mod p)=", y, EC_NDIGITS, "\n");
|
||||
/* Check y == u */
|
||||
printf("y == u => %s\n", (mpEqual(y, u, EC_NDIGITS) ? "OK" : "ERROR"));
|
||||
assert(mpEqual(y, u, EC_NDIGITS));
|
||||
|
||||
printf("Do 'add assign' and 'subtract assign'...\n");
|
||||
mpSetEqual(w, u, EC_NDIGITS);
|
||||
mpPrintDecimal("y= ", w, EC_NDIGITS, "\n");
|
||||
mpPrintDecimal("w=y= ", w, EC_NDIGITS, "\n");
|
||||
mpPrintDecimal("v= ", v, EC_NDIGITS, "\n");
|
||||
/* Now "add assign" w += v (mod p) */
|
||||
mpModAdd(w, w, v, p, EC_NDIGITS);
|
||||
mpPrintDecimal("w+=v(mod p)=", w, EC_NDIGITS, "\n");
|
||||
/* and "subtract assign" w -= v (mod p) */
|
||||
mpModSub(w, w, v, p, EC_NDIGITS);
|
||||
mpPrintDecimal("w-=v(mod p)=", w, EC_NDIGITS, "\n");
|
||||
/* Check w == y */
|
||||
printf("w == y => %s\n", (mpEqual(w, y, EC_NDIGITS) ? "OK" : "ERROR"));
|
||||
assert(mpEqual(w, y, EC_NDIGITS));
|
||||
|
||||
printf("\nDivide an integer by 2 modulo p - quick method...\n");
|
||||
mpPrintDecimal("u= ", u, EC_NDIGITS, "\n");
|
||||
mpModHalve(w, u, p, EC_NDIGITS);
|
||||
mpPrintDecimal("w=u/2(mod p)=", w, EC_NDIGITS, "\n");
|
||||
// Check result
|
||||
mpModAdd(v, w, w, p, EC_NDIGITS);
|
||||
mpPrintDecimal("v=w*2(mod p)=", v, EC_NDIGITS, "\n");
|
||||
printf("v == u => %s\n", (mpEqual(v, u, EC_NDIGITS) ? "OK" : "ERROR"));
|
||||
assert(mpEqual(v, u, EC_NDIGITS));
|
||||
|
||||
|
||||
/* DEMONSTRATE "QUICK" MODULO REDUCTION FOR SPECIAL CASE */
|
||||
printf("\nSpecial case modulo reduction...\n");
|
||||
/* Compute v = u mod p for u in range 0 <= u < 4p */
|
||||
mpPrintHex("p=", p, EC_NDIGITS, "\n");
|
||||
nbits = mpBitLength(p, EC_NDIGITS);
|
||||
printf("p is %d bits\n", nbits);
|
||||
// Generate a random number approx 2-4x bigger than p
|
||||
mpQuickRandBits(u, EC_NDIGITS, nbits + 2);
|
||||
mpPrintHex("u=", u, EC_NDIGITS, "\n");
|
||||
printf("u is %d bits\n", mpBitLength(u, EC_NDIGITS));
|
||||
// Compute v = u mod p for this special case
|
||||
mpModSpecial(v, u, p, EC_NDIGITS);
|
||||
mpPrintHex("v=u(mod p)=", v, EC_NDIGITS, "\n");
|
||||
// Check that result v < p
|
||||
assert(mpCompare(v, p, EC_NDIGITS) < 0);
|
||||
// And check again using the more expensive mpModulo fn
|
||||
mpModulo(w, u, EC_NDIGITS, p, EC_NDIGITS);
|
||||
mpPrintHex("mpModulo()=", w, EC_NDIGITS, "\n");
|
||||
assert(mpEqual(v, w, EC_NDIGITS));
|
||||
|
||||
|
||||
printf("\nDemonstrate mpPrintBits():\n");
|
||||
mpSetDigit(u, 0xef, EC_NDIGITS);
|
||||
mpPrintHex("u=0x", u, EC_NDIGITS, " => ");
|
||||
mpPrintBits("'", u, EC_NDIGITS, "'b\n");
|
||||
|
||||
mpSetDigit(u, 0x28, EC_NDIGITS);
|
||||
mpPrintHex("u=0x", u, EC_NDIGITS, " => ");
|
||||
mpPrintBits("'", u, EC_NDIGITS, "'b\n");
|
||||
|
||||
mpSetDigit(u, 0, EC_NDIGITS);
|
||||
mpPrintHex("u=0x", u, EC_NDIGITS, " => ");
|
||||
mpPrintBits("'", u, EC_NDIGITS, "'b\n");
|
||||
|
||||
mpSetDigit(u, 0xdeadbeef, EC_NDIGITS);
|
||||
mpPrintHex("u=0x", u, EC_NDIGITS, " => ");
|
||||
mpPrintBits("'", u, EC_NDIGITS, "'b\n");
|
||||
printf("(correct)= %s\n", "11011110101011011011111011101111");
|
||||
|
||||
mpConvFromHex(u, EC_NDIGITS, "04deadbeefcafebabe1");
|
||||
mpPrintHex("u=0x", u, EC_NDIGITS, " => ");
|
||||
mpPrintBits("\n'", u, EC_NDIGITS, "'b\n");
|
||||
|
||||
mpPrintHex("p=0x", p, EC_NDIGITS, " => ");
|
||||
mpPrintBits("\n'", p, EC_NDIGITS, "'b\n");
|
||||
|
||||
|
||||
/* Display version number */
|
||||
printf("\nVERSION=%d\n", mpVersion());
|
||||
printf("Compiled on [%s]\n", mpCompileTime());
|
||||
|
||||
printf("OK, successfully completed tests.\n");
|
||||
|
||||
return 0;
|
||||
}
|
||||
|
||||
/* $Id: t_mpModArith.c $ */
|
||||
|
||||
/* Some more tests of the BigDigits "mp" functions. */
|
||||
|
||||
/***** BEGIN LICENSE BLOCK *****
|
||||
*
|
||||
* 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) 2001-16 David Ireland, D.I. Management Services Pty Limited
|
||||
* <http://www.di-mgt.com.au/bigdigits.html>. All rights reserved.
|
||||
*
|
||||
***** END LICENSE BLOCK *****/
|
||||
/*
|
||||
* Last updated:
|
||||
* $Date: 2016-03-31 09:51:00 $
|
||||
* $Revision: 2.6.1 $
|
||||
* $Author: dai $
|
||||
*/
|
||||
|
||||
|
||||
#ifdef NDEBUG
|
||||
#undef NDEBUG
|
||||
#endif
|
||||
#include <assert.h>
|
||||
#include <stdio.h>
|
||||
#include "bigdigits.h"
|
||||
|
||||
|
||||
|
||||
/** Hard-coded maximum number of bits we choose to handle */
|
||||
#define EC_MAXBITS 640
|
||||
/** Number of digits needed to represent an integer of EC_MAXBITS bits */
|
||||
#define EC_NDIGITS (EC_MAXBITS/BITS_PER_DIGIT)
|
||||
|
||||
/** Unsigned integer of EC_MAXBITS bits */
|
||||
typedef DIGIT_T EC_INT[EC_NDIGITS];
|
||||
|
||||
/* This module can be compiled with the global preprocessor definitions
|
||||
MSVC: /D "NO_ALLOCS" /D "MAX_FIXED_BIT_LENGTH=640"
|
||||
GCC: -D NO_ALLOCS -D MAX_FIXED_BIT_LENGTH=640
|
||||
*/
|
||||
|
||||
|
||||
/** Make a random number of up to `nbits` bits */
|
||||
size_t make_random(EC_INT a, size_t nbits)
|
||||
{
|
||||
|
||||
size_t n;
|
||||
|
||||
/* Half the time, pick a shorter bitlength at random from [6,nbits] */
|
||||
if (spSimpleRand(0, 1)) {
|
||||
n = (size_t)spSimpleRand(6, (DIGIT_T)nbits);
|
||||
}
|
||||
else {
|
||||
n = nbits;
|
||||
}
|
||||
|
||||
mpQuickRandBits(a, EC_NDIGITS, n);
|
||||
|
||||
return n;
|
||||
}
|
||||
|
||||
|
||||
int main(void)
|
||||
{
|
||||
/* Note the neat way to declare variables of EC_NDIGITS */
|
||||
EC_INT u, v, w, m, p, x, y;
|
||||
size_t nbits;
|
||||
int r;
|
||||
|
||||
/* Force linker to include copyright notice in
|
||||
executable object image
|
||||
*/
|
||||
copyright_notice();
|
||||
|
||||
|
||||
printf("Testing BIGDIGITS 'mp' modular arithmetic functions.\n");
|
||||
|
||||
// First show it works for small numbers...
|
||||
mpSetDigit(u, 17, EC_NDIGITS);
|
||||
mpSetDigit(v, 13, EC_NDIGITS);
|
||||
mpSetDigit(m, 25, EC_NDIGITS);
|
||||
mpPrintDecimal("u=", u, EC_NDIGITS, ", ");
|
||||
mpPrintDecimal("v=", v, EC_NDIGITS, ", ");
|
||||
mpPrintDecimal("m=", m, EC_NDIGITS, "\n");
|
||||
mpModAdd(w, u, v, m, EC_NDIGITS);
|
||||
mpPrintDecimal("w=u+v(mod m)=", w, EC_NDIGITS, "\n");
|
||||
/* Check that w == 5 */
|
||||
assert(mpShortCmp(w, 5, EC_NDIGITS) == 0);
|
||||
|
||||
// Add assign w+=u [NB (w,w,u) not (w,u,w)]
|
||||
mpModAdd(w, w, u, m, EC_NDIGITS);
|
||||
mpPrintDecimal("w+=u(mod m)=", w, EC_NDIGITS, "\n");
|
||||
// Subtract assign w-=u
|
||||
mpModSub(w, w, u, m, EC_NDIGITS);
|
||||
mpPrintDecimal("w-=u(mod m)=", w, EC_NDIGITS, "\n");
|
||||
|
||||
// Subtract modulo m
|
||||
mpModSub(w, v, u, m, EC_NDIGITS);
|
||||
mpPrintDecimal("w=v-u(mod m)=", w, EC_NDIGITS, "\n");
|
||||
mpModSub(w, u, v, m, EC_NDIGITS);
|
||||
mpPrintDecimal("w=u-v(mod m)=", w, EC_NDIGITS, "\n");
|
||||
|
||||
// Add then subtract modulo m
|
||||
mpModAdd(w, u, v, m, EC_NDIGITS);
|
||||
mpPrintDecimal("w=u+v(mod m)=", w, EC_NDIGITS, "\n");
|
||||
/* y = w - v */
|
||||
mpModSub(y, w, v, m, EC_NDIGITS);
|
||||
mpPrintDecimal("y=w-v(mod m)=", y, EC_NDIGITS, "\n");
|
||||
/* Check y == u */
|
||||
printf("y == u => %s\n", (mpEqual(y, u, EC_NDIGITS) ? "OK" : "ERROR"));
|
||||
assert(mpEqual(y, u, EC_NDIGITS));
|
||||
|
||||
|
||||
|
||||
printf("Select a 192-bit prime number...\n");
|
||||
mpConvFromHex(p, EC_NDIGITS, "fffffffffffffffffffffffffffffffeffffffffffffffff");
|
||||
mpPrintHex("p=0x", p, EC_NDIGITS, "\n");
|
||||
mpPrintDecimal("p=", p, EC_NDIGITS, "\n");
|
||||
r = mpIsPrime(p, EC_NDIGITS, 50);
|
||||
printf("mpIsPrime(p)=%d\n", r);
|
||||
assert(r != 0);
|
||||
|
||||
printf("Find the square root of a quadratic residue modulo p ...\n");
|
||||
/* Pick a number, any number, less than p */
|
||||
nbits = mpBitLength(p, EC_NDIGITS);
|
||||
make_random(u, nbits - 1);
|
||||
mpPrintDecimal("u=", u, EC_NDIGITS, "\n");
|
||||
/* Square it modulo p => a quadratic residue modulo p */
|
||||
mpModSquare(w, u, p, EC_NDIGITS);
|
||||
mpPrintDecimal("w=u^2(mod p)=", w, EC_NDIGITS, "\n");
|
||||
/* Check we have a quadratic residue */
|
||||
r = mpJacobi(w, p, EC_NDIGITS);
|
||||
printf("Legendre symbol (w|p)=%d (expected 1)\n", r);
|
||||
assert(r == 1);
|
||||
/* Compute one modular square root */
|
||||
mpModSqrt(x, w, p, EC_NDIGITS);
|
||||
mpPrintDecimal("x=sqrt(w)(mod p)=", x, EC_NDIGITS, "\n");
|
||||
/* and the other */
|
||||
mpSubtract(y, p, x, EC_NDIGITS);
|
||||
mpPrintDecimal("y=p-x=", y, EC_NDIGITS, "\n");
|
||||
/* One of x or y is the same as u */
|
||||
assert(mpEqual(x, u, EC_NDIGITS) || mpEqual(y, u, EC_NDIGITS));
|
||||
if (mpEqual(x, u, EC_NDIGITS)) {
|
||||
printf("u == x\n");
|
||||
}
|
||||
else {
|
||||
printf("u == p-x\n");
|
||||
}
|
||||
|
||||
printf("Find a number that is not a quadratic residue mod p...\n");
|
||||
do {
|
||||
make_random(v, nbits);
|
||||
} while (mpJacobi(v, p, EC_NDIGITS) != -1);
|
||||
mpPrintDecimal("v=", v, EC_NDIGITS, "\n");
|
||||
printf("Legendre symbol (v|p)=%d (expected -1)\n", mpJacobi(v, p, EC_NDIGITS));
|
||||
r = mpModSqrt(x, v, p, EC_NDIGITS);
|
||||
printf("mpModSqrt(v) returns %d (-1 => square root does not exist)\n", r);
|
||||
assert(r != 0);
|
||||
|
||||
|
||||
printf("\nAdd and subtract modulo p...\n");
|
||||
/* Add two random numbers w = u + v (mod p) */
|
||||
make_random(u, nbits - 1);
|
||||
make_random(v, nbits - 1);
|
||||
mpPrintDecimal("u=", u, EC_NDIGITS, "\n");
|
||||
mpPrintDecimal("v=", v, EC_NDIGITS, "\n");
|
||||
mpModAdd(w, u, v, p, EC_NDIGITS);
|
||||
mpPrintDecimal("w=u+v(mod p)=", w, EC_NDIGITS, "\n");
|
||||
/* y = w - v (mod p) */
|
||||
mpModSub(y, w, v, p, EC_NDIGITS);
|
||||
mpPrintDecimal("y=w-v(mod p)=", y, EC_NDIGITS, "\n");
|
||||
/* Check y == u */
|
||||
printf("y == u => %s\n", (mpEqual(y, u, EC_NDIGITS) ? "OK" : "ERROR"));
|
||||
assert(mpEqual(y, u, EC_NDIGITS));
|
||||
|
||||
printf("Do 'add assign' and 'subtract assign'...\n");
|
||||
mpSetEqual(w, u, EC_NDIGITS);
|
||||
mpPrintDecimal("y= ", w, EC_NDIGITS, "\n");
|
||||
mpPrintDecimal("w=y= ", w, EC_NDIGITS, "\n");
|
||||
mpPrintDecimal("v= ", v, EC_NDIGITS, "\n");
|
||||
/* Now "add assign" w += v (mod p) */
|
||||
mpModAdd(w, w, v, p, EC_NDIGITS);
|
||||
mpPrintDecimal("w+=v(mod p)=", w, EC_NDIGITS, "\n");
|
||||
/* and "subtract assign" w -= v (mod p) */
|
||||
mpModSub(w, w, v, p, EC_NDIGITS);
|
||||
mpPrintDecimal("w-=v(mod p)=", w, EC_NDIGITS, "\n");
|
||||
/* Check w == y */
|
||||
printf("w == y => %s\n", (mpEqual(w, y, EC_NDIGITS) ? "OK" : "ERROR"));
|
||||
assert(mpEqual(w, y, EC_NDIGITS));
|
||||
|
||||
printf("\nDivide an integer by 2 modulo p - quick method...\n");
|
||||
mpPrintDecimal("u= ", u, EC_NDIGITS, "\n");
|
||||
mpModHalve(w, u, p, EC_NDIGITS);
|
||||
mpPrintDecimal("w=u/2(mod p)=", w, EC_NDIGITS, "\n");
|
||||
// Check result
|
||||
mpModAdd(v, w, w, p, EC_NDIGITS);
|
||||
mpPrintDecimal("v=w*2(mod p)=", v, EC_NDIGITS, "\n");
|
||||
printf("v == u => %s\n", (mpEqual(v, u, EC_NDIGITS) ? "OK" : "ERROR"));
|
||||
assert(mpEqual(v, u, EC_NDIGITS));
|
||||
|
||||
|
||||
/* DEMONSTRATE "QUICK" MODULO REDUCTION FOR SPECIAL CASE */
|
||||
printf("\nSpecial case modulo reduction...\n");
|
||||
/* Compute v = u mod p for u in range 0 <= u < 4p */
|
||||
mpPrintHex("p=", p, EC_NDIGITS, "\n");
|
||||
nbits = mpBitLength(p, EC_NDIGITS);
|
||||
printf("p is %d bits\n", nbits);
|
||||
// Generate a random number approx 2-4x bigger than p
|
||||
mpQuickRandBits(u, EC_NDIGITS, nbits + 2);
|
||||
mpPrintHex("u=", u, EC_NDIGITS, "\n");
|
||||
printf("u is %d bits\n", mpBitLength(u, EC_NDIGITS));
|
||||
// Compute v = u mod p for this special case
|
||||
mpModSpecial(v, u, p, EC_NDIGITS);
|
||||
mpPrintHex("v=u(mod p)=", v, EC_NDIGITS, "\n");
|
||||
// Check that result v < p
|
||||
assert(mpCompare(v, p, EC_NDIGITS) < 0);
|
||||
// And check again using the more expensive mpModulo fn
|
||||
mpModulo(w, u, EC_NDIGITS, p, EC_NDIGITS);
|
||||
mpPrintHex("mpModulo()=", w, EC_NDIGITS, "\n");
|
||||
assert(mpEqual(v, w, EC_NDIGITS));
|
||||
|
||||
|
||||
printf("\nDemonstrate mpPrintBits():\n");
|
||||
mpSetDigit(u, 0xef, EC_NDIGITS);
|
||||
mpPrintHex("u=0x", u, EC_NDIGITS, " => ");
|
||||
mpPrintBits("'", u, EC_NDIGITS, "'b\n");
|
||||
|
||||
mpSetDigit(u, 0x28, EC_NDIGITS);
|
||||
mpPrintHex("u=0x", u, EC_NDIGITS, " => ");
|
||||
mpPrintBits("'", u, EC_NDIGITS, "'b\n");
|
||||
|
||||
mpSetDigit(u, 0, EC_NDIGITS);
|
||||
mpPrintHex("u=0x", u, EC_NDIGITS, " => ");
|
||||
mpPrintBits("'", u, EC_NDIGITS, "'b\n");
|
||||
|
||||
mpSetDigit(u, 0xdeadbeef, EC_NDIGITS);
|
||||
mpPrintHex("u=0x", u, EC_NDIGITS, " => ");
|
||||
mpPrintBits("'", u, EC_NDIGITS, "'b\n");
|
||||
printf("(correct)= %s\n", "11011110101011011011111011101111");
|
||||
|
||||
mpConvFromHex(u, EC_NDIGITS, "04deadbeefcafebabe1");
|
||||
mpPrintHex("u=0x", u, EC_NDIGITS, " => ");
|
||||
mpPrintBits("\n'", u, EC_NDIGITS, "'b\n");
|
||||
|
||||
mpPrintHex("p=0x", p, EC_NDIGITS, " => ");
|
||||
mpPrintBits("\n'", p, EC_NDIGITS, "'b\n");
|
||||
|
||||
|
||||
/* Display version number */
|
||||
printf("\nVERSION=%d\n", mpVersion());
|
||||
printf("Compiled on [%s]\n", mpCompileTime());
|
||||
|
||||
printf("OK, successfully completed tests.\n");
|
||||
|
||||
return 0;
|
||||
}
|
||||
|
||||
|
||||
Reference in New Issue
Block a user