t_bdRSA.c (original) (raw)

`/* Id:tbdRSA.cId: t_bdRSA.c Id:tb​dRSA.c */

/*

/* Test BigDigits "bd" functions using a new RSA key and random data */

#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;

}`