/* $Id: t_bdRSA.c $ */

/*
 * Copyright (C) 2001-26 David Ireland, D.I. Management Services Pty Limited
 * <https://di-mgt.com.au/contact/> <https://di-mgt.com.au/bigdigits.html>
 * SPDX-License-Identifier: MPL-2.0
 *
 * Last updated:
 * $Date: 2026-03-29 05:11:00 $
 * $Revision: 2.7.0 $
 * $Author: dai $
 */

/* 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;
}