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Linux_Drivers/fsbl/lib/BigDigits/t_bdRSA.c
forum_service 88cce7a8a2 fsbl: weekly update 2023-03-25 
1. update release func

Change-Id: I221476630ce4f2f6a01e8f89fd96d9ac9701a270
2023-03-27 00:22:46 +08:00

455 lines
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C
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/* $Id: t_bdRSA.c $ */
/* Test BigDigits "bd" functions using a new RSA key and random data */
/***** 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) 2001-15 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: 2015-10-22 10:23:00 $
* $Revision: 2.5.0 $
* $Author: dai $
*/
#if _MSC_VER >= 1100
/* Detect memory leaks in MSVC++ */
#define _CRTDBG_MAP_ALLOC
#include <stdlib.h>
#include <crtdbg.h>
#else
#include <stdlib.h>
#endif
#include <stdio.h>
#include <string.h>
#include <time.h>
#include <assert.h>
#include "bigd.h"
static int my_rand(unsigned char *bytes, size_t nbytes, const unsigned char *seed, size_t seedlen)
/* Our own (very insecure) random generator func using good old rand()
but in the required format for BD_RANDFUNC
-- replace this in practice with your own cryptographically-secure function
-- or use bdRandomOctets() in bigdRand.h
*/
{
unsigned int myseed;
size_t i;
int offset;
/* Use time for 32-bit seed - then blend in user-supplied seed, if any */
myseed = (unsigned)time(NULL) ^ (unsigned)clock();
if (seed)
{
for (offset = 0, i = 0; i < seedlen; i++, offset = (offset + 1) % sizeof(unsigned))
myseed ^= ((unsigned int)seed[i] << (offset * 8));
}
srand(myseed);
while (nbytes--)
{
*bytes++ = rand() & 0xFF;
}
return 0;
}
#define give_a_sign(c) putchar((c))
static bdigit_t SMALL_PRIMES[] = {
3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43,
47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101,
103, 107, 109, 113,
127, 131, 137, 139, 149, 151, 157, 163, 167, 173,
179, 181, 191, 193, 197, 199, 211, 223, 227, 229,
233, 239, 241, 251, 257, 263, 269, 271, 277, 281,
283, 293, 307, 311, 313, 317, 331, 337, 347, 349,
353, 359, 367, 373, 379, 383, 389, 397, 401, 409,
419, 421, 431, 433, 439, 443, 449, 457, 461, 463,
467, 479, 487, 491, 499, 503, 509, 521, 523, 541,
547, 557, 563, 569, 571, 577, 587, 593, 599, 601,
607, 613, 617, 619, 631, 641, 643, 647, 653, 659,
661, 673, 677, 683, 691, 701, 709, 719, 727, 733,
739, 743, 751, 757, 761, 769, 773, 787, 797, 809,
811, 821, 823, 827, 829, 839, 853, 857, 859, 863,
877, 881, 883, 887, 907, 911, 919, 929, 937, 941,
947, 953, 967, 971, 977, 983, 991, 997,
};
#define N_SMALL_PRIMES (sizeof(SMALL_PRIMES)/sizeof(bdigit_t))
int generateRSAPrime(BIGD p, size_t nbits, bdigit_t e, size_t ntests,
const unsigned char *seed, size_t seedlen, BD_RANDFUNC randFunc)
/* Create a prime p such that gcd(p-1, e) = 1.
Returns # prime tests carried out or -1 if failed.
Sets the TWO highest bits to ensure that the
product pq will always have its high bit set.
e MUST be a prime > 2.
This function assumes that e is prime so we can
do the less expensive test p mod e != 1 instead
of gcd(p-1, e) == 1.
Uses improvement in trial division from Menezes 4.51.
*/
{
BIGD u;
size_t i, j, iloop, maxloops, maxodd;
int done, overflow, failedtrial;
int count = 0;
bdigit_t r[N_SMALL_PRIMES];
/* Create a temp */
u = bdNew();
maxodd = nbits * 100;
maxloops = 5;
done = 0;
for (iloop = 0; !done && iloop < maxloops; iloop++)
{
/* Set candidate n0 as random odd number */
bdRandomSeeded(p, nbits, seed, seedlen, randFunc);
/* Set two highest and low bits */
bdSetBit(p, nbits - 1, 1);
bdSetBit(p, nbits - 2, 1);
bdSetBit(p, 0, 1);
/* To improve trial division, compute table R[q] = n0 mod q
for each odd prime q <= B
*/
for (i = 0; i < N_SMALL_PRIMES; i++)
{
r[i] = bdShortMod(u, p, SMALL_PRIMES[i]);
}
done = overflow = 0;
/* Try every odd number n0, n0+2, n0+4,... until we succeed */
for (j = 0; j < maxodd; j++, overflow = bdShortAdd(p, p, 2))
{
/* Check for overflow */
if (overflow)
break;
give_a_sign('.');
count++;
/* Each time 2 is added to the current candidate
update table R[q] = (R[q] + 2) mod q */
if (j > 0)
{
for (i = 0; i < N_SMALL_PRIMES; i++)
{
r[i] = (r[i] + 2) % SMALL_PRIMES[i];
}
}
/* Candidate passes the trial division stage if and only if
NONE of the R[q] values equal zero */
for (failedtrial = 0, i = 0; i < N_SMALL_PRIMES; i++)
{
if (r[i] == 0)
{
failedtrial = 1;
break;
}
}
if (failedtrial)
continue;
/* If p mod e = 1 then gcd(p, e) > 1, so try again */
bdShortMod(u, p, e);
if (bdShortCmp(u, 1) == 0)
continue;
/* Do expensive primality test */
give_a_sign('*');
if (bdRabinMiller(p, ntests))
{ /* Success! - we have a prime */
done = 1;
break;
}
}
}
/* Clear up */
bdFree(&u);
printf("\n");
return (done ? count : -1);
}
int generateRSAKey(BIGD n, BIGD e, BIGD d, BIGD p, BIGD q, BIGD dP, BIGD dQ, BIGD qInv,
size_t nbits, bdigit_t ee, size_t ntests, unsigned char *seed, size_t seedlen,
BD_RANDFUNC randFunc)
{
BIGD g, p1, q1, phi;
size_t np, nq;
unsigned char *myseed = NULL;
clock_t start, finish;
double duration, tmake;
long ptests;
int res;
/* Initialise */
g = bdNew();
p1 = bdNew();
q1 = bdNew();
phi = bdNew();
printf("Generating a %d-bit RSA key...\n", nbits);
/* We add an extra byte to the user-supplied seed */
myseed = malloc(seedlen + 1);
if (!myseed) return -1;
memcpy(myseed, seed, seedlen);
/* Do (p, q) in two halves, approx equal */
nq = nbits / 2 ;
np = nbits - nq;
/* Make sure seeds are slightly different for p and q */
myseed[seedlen] = 0x01;
start = clock();
res = generateRSAPrime(p, np, ee, ntests, myseed, seedlen+1, randFunc);
finish = clock();
bdPrintHex("p=", p, "\n");
assert(res > 0);
duration = (double)(finish - start) / CLOCKS_PER_SEC;
printf("generateRSAPrime took %.3f secs and %d prime candidates (%.4f s/test)\n", duration, res, duration / res);
ptests = res;
tmake = duration;
printf("p is %d bits\n", bdBitLength(p));
myseed[seedlen] = 0xff;
start = clock();
res = generateRSAPrime(q, nq, ee, ntests, myseed, seedlen+1, randFunc);
finish = clock();
bdPrintHex("q=", q, "\n");
assert(res > 0);
duration = (double)(finish - start) / CLOCKS_PER_SEC;
printf("generateRSAPrime took %.3f secs and %d prime candidates (%.4f s/test)\n", duration, res, duration / res);
ptests += res;
tmake += duration;
printf("q is %d bits\n", bdBitLength(q));
/* Check that p != q (if so, RNG is faulty!) */
assert(!bdIsEqual(p, q));
bdSetShort(e, ee);
bdPrintHex("e=", e, "\n");
/* If q > p swap p and q so p > q */
if (bdCompare(p, q) < 1)
{
bdSetEqual(g, p);
bdSetEqual(p, q);
bdSetEqual(q, g);
}
/* Calc p-1 and q-1 */
bdSetEqual(p1, p);
bdDecrement(p1);
bdPrintHex("p-1=\n", p1, "\n");
bdSetEqual(q1, q);
bdDecrement(q1);
bdPrintHex("q-1=\n", q1, "\n");
/* Check gcd(p-1, e) = 1 */
bdGcd(g, p1, e);
bdPrintHex("gcd(p-1,e)=", g, "\n");
assert(bdShortCmp(g, 1) == 0);
bdGcd(g, q1, e);
bdPrintHex("gcd(q-1,e)=", g, "\n");
assert(bdShortCmp(g, 1) == 0);
/* Compute n = pq */
bdMultiply(n, p, q);
bdPrintHex("n=\n", n, "\n");
/* Compute d = e^-1 mod (p-1)(q-1) */
bdMultiply(phi, p1, q1);
bdPrintHex("phi=\n", phi, "\n");
res = bdModInv(d, e, phi);
assert(res == 0);
bdPrintHex("d=\n", d, "\n");
/* Check ed = 1 mod phi */
bdModMult(g, e, d, phi);
bdPrintHex("ed mod phi=", g, "\n");
assert(bdShortCmp(g, 1) == 0);
/* Calculate CRT key values */
printf("CRT values:\n");
bdModInv(dP, e, p1);
bdModInv(dQ, e, q1);
bdModInv(qInv, q, p);
bdPrintHex("dP=", dP, "\n");
bdPrintHex("dQ=", dQ, "\n");
bdPrintHex("qInv=", qInv, "\n");
printf("\nTime to create key = %.3f secs with %ld prime candidates (%.4f s/test)\n\n", tmake, ptests, tmake / ptests);
printf("n is %d bits\n", bdBitLength(n));
/* Clean up */
if (myseed) free(myseed);
bdFree(&g);
bdFree(&p1);
bdFree(&q1);
bdFree(&phi);
return 0;
}
static int debug = 0;
int main(void)
{
size_t nbits = 1025; /* (use an odd modulus size to see if it breaks anything!) */
unsigned ee = 0x3;
size_t ntests = 50;
unsigned char *seed = NULL;
size_t seedlen = 0;
BIGD n, e, d, p, q, dP, dQ, qInv;
BIGD m, c, s, hq, h, m1, m2;
int res;
clock_t start, finish;
double tinv, tcrt;
/* MSVC memory leak checking stuff */
#if _MSC_VER >= 1100
_CrtSetDbgFlag( _CRTDBG_ALLOC_MEM_DF | _CRTDBG_LEAK_CHECK_DF);
_CrtSetReportMode( _CRT_WARN, _CRTDBG_MODE_FILE );
_CrtSetReportFile( _CRT_WARN, _CRTDBG_FILE_STDOUT );
_CrtSetReportMode( _CRT_ERROR, _CRTDBG_MODE_FILE );
_CrtSetReportFile( _CRT_ERROR, _CRTDBG_FILE_STDOUT );
_CrtSetReportMode( _CRT_ASSERT, _CRTDBG_MODE_FILE );
_CrtSetReportFile( _CRT_ASSERT, _CRTDBG_FILE_STDOUT );
#endif
printf("Test BIGDIGITS with a new %d-bit RSA key and random data.\n", nbits);
/* Initialise */
p = bdNew();
q = bdNew();
n = bdNew();
e = bdNew();
d = bdNew();
dP= bdNew();
dQ= bdNew();
qInv= bdNew();
m = bdNew();
c = bdNew();
s = bdNew();
m1 = bdNew();
m2 = bdNew();
h = bdNew();
hq = bdNew();
/* Create RSA key pair (n, e),(d, p, q, dP, dQ, qInv) */
/* NB we use simple my_rand() here -- you should use a proper cryptographically-secure RNG */
res = generateRSAKey(n, e, d, p, q, dP, dQ, qInv, nbits, ee, ntests, seed, seedlen, my_rand);
if (res != 0)
{
printf("Failed to generate RSA key!\n");
goto clean_up;
}
/* Set a random message m < n */
bdRandomSeeded(m, bdBitLength(n)-1, NULL, 0, my_rand);
bdPrintHex("m=\n", m, "\n");
/* Encrypt c = m^e mod n */
bdModExp(c, m, e, n);
bdPrintHex("c=\n", c, "\n");
/* Check decrypt m1 = c^d mod n */
start = clock();
bdModExp(m1, c, d, n);
finish = clock();
tinv = (double)(finish - start) / CLOCKS_PER_SEC;
bdPrintHex("m'=\n", m1, "\n");
res = bdCompare(m1, m);
printf("Decryption %s\n", (res == 0 ? "OK" : "FAILED!"));
assert(res == 0);
printf("Decrypt by inversion took %.3f secs\n", tinv);
/* Sign s = m^d mod n */
bdModExp(s, m, d, n);
bdPrintHex("s=\n", s, "\n");
/* Check verify m1 = s^e mod n */
bdModExp(m1, s, e, n);
bdPrintHex("m'=\n", m1, "\n");
res = bdCompare(m1, m);
printf("Verification %s\n", (res == 0 ? "OK" : "FAILED!"));
assert(res == 0);
/* Decrypt using CRT method - Ref: PKCS #1 */
bdPrintHex("m=", m, "\n");
bdPrintHex("c=", c, "\n");
bdPrintHex("p=", p, "\n");
bdPrintHex("q=", q, "\n");
start = clock();
/* Let m_1 = c^dP mod p. */
bdModExp(m1, c, dP, p);
if(debug)bdPrintHex("m_1=c^dP mod p=", m1, "\n");
/* Let m_2 = c^dQ mod q. */
bdModExp(m2, c, dQ, q);
if(debug)bdPrintHex("m_2=c^dQ mod q=", m2, "\n");
if (bdCompare(m1, m2) < 0)
bdAdd(m1, m1, p);
bdSubtract(m1, m1, m2);
if(debug)bdPrintHex("m_1 - m_2=", m1, "\n");
/* Let h = qInv ( m_1 - m_2 ) mod p. */
bdModMult(h, qInv, m1, p);
if(debug)bdPrintHex("h=qInv(m1-m2) mod p=", h, "\n");
bdMultiply(hq, h, q);
if(debug)bdPrintHex("hq=", hq, "\n");
/* Let m = m_2 + hq. */
bdAdd(m1, m2, hq);
finish = clock();
tcrt = (double)(finish - start) / CLOCKS_PER_SEC;
if(debug)bdPrintHex("m'=m_2 + hq=", m1, "\n");
bdPrintHex("(CRT)m'=\n", m1, "\n");
res = bdCompare(m1, m);
printf("CRT Decryption %s\n", (res == 0 ? "OK" : "FAILED!"));
assert(res == 0);
printf("Decrypt by CRT took %.3f secs\n", tcrt);
printf("c.f. Decrypt by inversion %.3f secs (factor = %.1f)\n",
tinv, (tcrt ? tinv / tcrt : 0));
printf("n is %d bits\n", bdBitLength(n));
/* Clean up */
clean_up:
bdFree(&n);
bdFree(&e);
bdFree(&d);
bdFree(&p);
bdFree(&q);
bdFree(&dP);
bdFree(&dQ);
bdFree(&qInv);
bdFree(&m);
bdFree(&c);
bdFree(&s);
bdFree(&m1);
bdFree(&m2);
bdFree(&h);
bdFree(&hq);
printf("OK, successfully completed tests.\n");
return 0;
}
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