C++ BN_is_one函數代碼示例

/*
 * pr_fact - print the factors of a number
 *
 * Print the factors of the number, from the lowest to the highest.
 * A factor will be printed multiple times if it divides the value
 * multiple times.
 *
 * Factors are printed with leading tabs.
 */
static void
pr_fact(BIGNUM *val)
{
	const ubig *fact;	/* The factor found. */

	/* Firewall - catch 0 and 1. */
	if (BN_is_zero(val))	/* Historical practice; 0 just exits. */
		exit(0);
	if (BN_is_one(val)) {
		printf("1: 1\n");
		return;
	}

	/* Factor value. */

	if (hflag) {
		fputs("0x", stdout);
		BN_print_fp(stdout, val);
	} else
		BN_print_dec_fp(stdout, val);
	putchar(':');
	for (fact = &prime[0]; !BN_is_one(val); ++fact) {
		/* Look for the smallest factor. */
		do {
			if (BN_mod_word(val, (BN_ULONG)*fact) == 0)
				break;
		} while (++fact <= pr_limit);

		/* Watch for primes larger than the table. */
		if (fact > pr_limit) {
#ifdef HAVE_OPENSSL
			BIGNUM *bnfact;

			bnfact = BN_new();
			BN_set_word(bnfact, *(fact - 1));
			if (!BN_sqr(bnfact, bnfact, ctx))
				errx(1, "error in BN_sqr()");
			if (BN_cmp(bnfact, val) > 0 ||
			    BN_is_prime(val, PRIME_CHECKS,
					NULL, NULL, NULL) == 1)
				pr_print(val);
			else
				pollard_pminus1(val);
#else
			pr_print(val);
#endif
			break;
		}

		/* Divide factor out until none are left. */
		do {
			printf(hflag ? " 0x%lx" : " %lu", *fact);
			BN_div_word(val, (BN_ULONG)*fact);
		} while (BN_mod_word(val, (BN_ULONG)*fact) == 0);

		/* Let the user know we're doing something. */
		fflush(stdout);
	}
	putchar('\n');
}

CHECK_RETVAL_BOOL \
static BOOLEAN selfTestGeneralOps1( void )
	{
	BIGNUM a;

	/* Simple tests that don't need the support of higher-level routines 
	   like importBignum() */
	BN_init( &a );
	if( !BN_zero( &a ) )
		return( FALSE );
	if( !BN_is_zero( &a ) || BN_is_one( &a ) )
		return( FALSE );
	if( !BN_is_word( &a, 0 ) || BN_is_word( &a, 1 ) )
		return( FALSE );
	if( BN_is_odd( &a ) )
		return( FALSE );
	if( BN_get_word( &a ) != 0 )
		return( FALSE );
	if( !BN_one( &a ) )
		return( FALSE );
	if( BN_is_zero( &a ) || !BN_is_one( &a ) )
		return( FALSE );
	if( BN_is_word( &a, 0 ) || !BN_is_word( &a, 1 ) )
		return( FALSE );
	if( !BN_is_odd( &a ) )
		return( FALSE );
	if( BN_num_bytes( &a ) != 1 )
		return( FALSE );
	if( BN_get_word( &a ) != 1 )
		return( FALSE );
	BN_clear( &a );

	return( TRUE );
	}

static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1,
                   const BIGNUM *a1_odd, int k, BN_CTX *ctx,
                   BN_MONT_CTX *mont)
{
    if (!BN_mod_exp_mont(w, w, a1_odd, a, ctx, mont)) /* w := w^a1_odd mod a */
        return -1;
    if (BN_is_one(w))
        return 0;               /* probably prime */
    if (BN_cmp(w, a1) == 0)
        return 0;               /* w == -1 (mod a), 'a' is probably prime */
    while (--k) {
        if (!BN_mod_mul(w, w, w, a, ctx)) /* w := w^2 mod a */
            return -1;
        if (BN_is_one(w))
            return 1;           /* 'a' is composite, otherwise a previous 'w'
                                 * would have been == -1 (mod 'a') */
        if (BN_cmp(w, a1) == 0)
            return 0;           /* w == -1 (mod a), 'a' is probably prime */
    }
    /*
     * If we get here, 'w' is the (a-1)/2-th power of the original 'w', and
     * it is neither -1 nor +1 -- so 'a' cannot be prime
     */
    bn_check_top(w);
    return 1;
}

void test_lehmer_thm(void)
{
  BIGNUM
    *v = BN_new(),
    *v2 = BN_new(),
    *h = BN_new(),
    *n = BN_new(),
    *p = BN_new(),
    *q = BN_new(),
    *g = BN_new();
  BN_CTX *ctx = BN_CTX_new();

  BN_dec2bn(&v, "2");
  BN_dec2bn(&p,
            "181857351165158586099319592412492032999818333818932850952491024"
            "131283899677766672100915923041329384157985577418702469610834914"
            "6296393743554494871840505599");
  BN_dec2bn(&q,
            "220481921324130321200060036818685031159071785249502660004347524"
            "831733577485433929892260897846567483448177204481081755191897197"
            "38283711758138566145322943999");
  BN_mul(n, p, q, ctx);
  /* p + 1 */
  BN_dec2bn(&h,
            "181857351165158586099319592412492032999818333818932850952491024"
            "131283899677766672100915923041329384157985577418702469610834914"
            "6296393743554494871840505600");
  lucas(v, h, n, ctx);
  BN_sub(v2, v, BN_value_two());
  BN_gcd(g, v2, n, ctx);
  assert(!BN_is_one(g));

  /* another test */
  BN_dec2bn(&v, "3");
  BN_dec2bn(&p,
            "181857351165158586099319592412492032999818333818932850952491024"
            "131283899677766672100915923041329384157985577418702469610834914"
            "62963937435544948718405055999");
  BN_generate_prime(q, 512, 1, NULL, NULL, NULL, NULL);
  BN_mul(n, p, q, ctx);

  BN_sub(h, p, BN_value_one());
  BN_mul(h, h, BN_value_two(), ctx);
  lucas(v, h, n, ctx);

  BN_mod_sub(v2, v, BN_value_two(), n, ctx);
  BN_gcd(g, v2, n, ctx);
  assert(!BN_is_one(g));
  assert(BN_cmp(g, n));

  BN_free(q);
  BN_free(p);
  BN_free(v);
  BN_free(v2);
  BN_free(h);

  BN_CTX_free(ctx);
}

/*
 * pr_fact - print the factors of a number
 *
 * If the number is 0 or 1, then print the number and return.
 * If the number is < 0, print -1, negate the number and continue
 * processing.
 *
 * Print the factors of the number, from the lowest to the highest.
 * A factor will be printed numtiple times if it divides the value
 * multiple times.
 *
 * Factors are printed with leading tabs.
 */
static void
pr_fact(BIGNUM *val)
{
	const ubig *fact;		/* The factor found. */

	/* Firewall - catch 0 and 1. */
	if (BN_is_zero(val) || BN_is_one(val))
		errx(1, "numbers <= 1 aren't permitted.");

	/* Factor value. */

	BN_print_dec_fp(stdout, val);
	putchar(':');
	for (fact = &prime[0]; !BN_is_one(val); ++fact) {
		/* Look for the smallest factor. */
		while (fact <= pr_limit) {
			if (BN_mod_word(val, (BN_ULONG)*fact) == 0)
				break;
			fact++;
		}

		/* Watch for primes larger than the table. */
		if (fact > pr_limit) {
#ifdef HAVE_OPENSSL
			BIGNUM *bnfact;

			bnfact = BN_new();
			BN_set_word(bnfact, (BN_ULONG)*(fact - 1));
			BN_sqr(bnfact, bnfact, ctx);
			if (BN_cmp(bnfact, val) > 0
			    || BN_is_prime(val, PRIME_CHECKS, NULL, NULL,
					   NULL) == 1) {
				putchar(' ');
				BN_print_dec_fp(stdout, val);
			} else
				pollard_rho(val);
#else
			printf(" %s", BN_bn2dec(val));
#endif
			break;
		}

		/* Divide factor out until none are left. */
		do {
			printf(" %lu", *fact);
			BN_div_word(val, (BN_ULONG)*fact);
		} while (BN_mod_word(val, (BN_ULONG)*fact) == 0);

		/* Let the user know we're doing something. */
		fflush(stdout);
	}
	putchar('\n');
}

/* pollard p-1, algorithm from Jim Gillogly, May 2000 */
static void
pollard_pminus1(BIGNUM *val)
{
	BIGNUM *base, *rbase, *num, *i, *x;

	base = BN_new();
	rbase = BN_new();
	num = BN_new();
	i = BN_new();
	x = BN_new();

	BN_set_word(rbase, 1);
newbase:
	if (!BN_add_word(rbase, 1))
		errx(1, "error in BN_add_word()");
	BN_set_word(i, 2);
	BN_copy(base, rbase);

	for (;;) {
		BN_mod_exp(base, base, i, val, ctx);
		if (BN_is_one(base))
			goto newbase;

		BN_copy(x, base);
		BN_sub_word(x, 1);
		if (!BN_gcd(x, x, val, ctx))
			errx(1, "error in BN_gcd()");

		if (!BN_is_one(x)) {
			if (BN_is_prime(x, PRIME_CHECKS, NULL, NULL,
			    NULL) == 1)
				pr_print(x);
			else
				pollard_pminus1(x);
			fflush(stdout);

			BN_div(num, NULL, val, x, ctx);
			if (BN_is_one(num))
				return;
			if (BN_is_prime(num, PRIME_CHECKS, NULL, NULL,
			    NULL) == 1) {
				pr_print(num);
				fflush(stdout);
				return;
			}
			BN_copy(val, num);
		}
		if (!BN_add_word(i, 1))
			errx(1, "error in BN_add_word()");
	}
}

static int verifystep1(const JPakeUser * us, const JPakeUserPublic * them,
                       const JPakeParameters * params)
{
    printf("\n%s verifies %s:\n\n", us->p.name, them->name);

    // verify their ZKP(xc)
    if (!VerifyZKP(&us->p.s1c.zkpx, us->p.s1c.gx, them, params->g, params,
                   them->base, ""))
        return 0;

    // verify their ZKP(xd)
    if (!VerifyZKP(&us->p.s1d.zkpx, us->p.s1d.gx, them, params->g, params,
                   them->base + 1, ""))
        return 0;

    // g^xd != 1
    printf("  g^{x%d} != 1: ", them->base + 1);
    if (BN_is_one(us->p.s1d.gx)) {
        puts("FAIL");
        return 0;
    }
    puts("OK");

    return 1;
}

/**
 * \brief Test for a pair of moduluses having a prime factor in common.
 *
 */
int test(BIGNUM *n, BIGNUM *m)
{
  BIGNUM *g;
  BN_CTX *ctx;
  int ret = 0;

  if (!BN_cmp(n, m)) return 1;

  g = BN_new();
  ctx = BN_CTX_new();
  BN_gcd(g, n, m, ctx);

  if (!BN_is_one(g)) {
    fprintf(stdout, "%-8s: ", PRIME);
    BN_print_fp(stdout, n);
    fprintf(stdout, "  ");
    BN_print_fp(stdout, m);
    fprintf(stdout, "\n");
    ret = 1;
  }

  BN_CTX_free(ctx);
  BN_free(g);

  return ret;
}

int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *group,
        EC_POINT *point,
        const BIGNUM *x,
        const BIGNUM *y,
        const BIGNUM *z,
        BN_CTX *ctx)
{
    BN_CTX *new_ctx = NULL;
    int ret = 0;

    if (ctx == NULL) {
        ctx = new_ctx = BN_CTX_new();
        if (ctx == NULL)
            return 0;
    }

    if (x != NULL) {
        if (!BN_nnmod(&point->X, x, &group->field, ctx))
            goto err;
        if (group->meth->field_encode) {
            if (!group->meth->field_encode(group, &point->X, &point->X, ctx))
                goto err;
        }
    }

    if (y != NULL) {
        if (!BN_nnmod(&point->Y, y, &group->field, ctx))
            goto err;
        if (group->meth->field_encode) {
            if (!group->meth->field_encode(group, &point->Y, &point->Y, ctx))
                goto err;
        }
    }

    if (z != NULL) {
        int Z_is_one;

        if (!BN_nnmod(&point->Z, z, &group->field, ctx))
            goto err;
        Z_is_one = BN_is_one(&point->Z);
        if (group->meth->field_encode) {
            if (Z_is_one && (group->meth->field_set_to_one != 0)) {
                if (!group->meth->field_set_to_one(group, &point->Z, ctx))
                    goto err;
            } else {
                if (!group->
                        meth->field_encode(group, &point->Z, &point->Z, ctx))
                    goto err;
            }
        }
        point->Z_is_one = Z_is_one;
    }

    ret = 1;

err:
    if (new_ctx != NULL)
        BN_CTX_free(new_ctx);
    return ret;
}

int main(int argc, char ** argv) {
	/* Generate 2 big random numbers (512 bits) */
	primitive_p = initialize("1011011");
	initialize_rand(SEED);
	BIGNUM *p = get_long_prime_number(RSA_KEY_LENGTH);
	printf("p=%s\n", BN_bn2hex(p));
	BIGNUM *q = get_long_prime_number(RSA_KEY_LENGTH);
	printf("q=%s\n", BN_bn2hex(q));
	/* Compute phi = (p-1)*(q-1) and n = p*q */
	BIGNUM *phi, *n;
	BN_CTX *tmp;
	tmp = BN_CTX_new();
	n = BN_new();
	phi = BN_new();
	BN_copy(n, p);
	BN_mul(n, n, q, tmp);
	printf("n=%s\n", BN_bn2dec(n));
	BN_sub_word(p, 1);
	printf("p-1=%s\n", BN_bn2dec(p));
	BN_sub_word(q, 1);
	printf("q-1=%s\n", BN_bn2dec(q));
	phi = BN_new();
	BN_init(tmp);
	BN_mul(phi, p, q, tmp);
	printf("(p-1)(q-1)=%s\n", BN_bn2dec(phi));
	/* Find the smallest integer coprime with phi */
	BIGNUM * e = BN_new();
	BIGNUM *gcd = BN_new();
	BN_add_word(e, 3);
	for ( ; ; BN_add_word(e, 2)) {
		tmp = BN_CTX_new();
		BN_gcd(gcd, e, phi, tmp);
		if (BN_is_one(gcd))
			break;
	}
	printf("e=%s\n", BN_bn2dec(e));
	/* Find d, the inverse of e in Z_phi */
	BIGNUM * d = BN_new();
	BIGNUM * i = BN_new();
	BIGNUM * rem = BN_new();
	BIGNUM * prod = BN_new();
	BN_add_word(i, 1);
	for ( ; ; BN_add_word(i, 1)) {
		BN_copy(prod, phi);
		tmp = BN_CTX_new();
		BN_mul(prod, prod, i, tmp);
		BN_add_word(prod, 1);
		BN_div(d, rem, prod, e, tmp);
		if (BN_is_zero(rem)) {
			break;
		}
	}
	printf("d=%s\n", BN_bn2dec(d));
	return 0;
}

static int dss_paramcheck(int nmod, BIGNUM *p, BIGNUM *q, BIGNUM *g,
                          BN_CTX *ctx)
{
    BIGNUM *rem = NULL;
    if (BN_num_bits(p) != nmod)
        return 0;
    if (BN_num_bits(q) != 160)
        return 0;
    if (BN_is_prime_ex(p, BN_prime_checks, ctx, NULL) != 1)
        return 0;
    if (BN_is_prime_ex(q, BN_prime_checks, ctx, NULL) != 1)
        return 0;
    rem = BN_new();
    if (!BN_mod(rem, p, q, ctx) || !BN_is_one(rem)
            || (BN_cmp(g, BN_value_one()) <= 0)
            || !BN_mod_exp(rem, g, q, p, ctx) || !BN_is_one(rem)) {
        BN_free(rem);
        return 0;
    }
    /* Todo: check g */
    BN_free(rem);
    return 1;
}

int DH_check_pub_key(const DH *dh, const BIGNUM *pub_key, int *ret) {
  *ret = 0;

  BN_CTX *ctx = BN_CTX_new();
  if (ctx == NULL) {
    return 0;
  }
  BN_CTX_start(ctx);

  int ok = 0;

  /* Check |pub_key| is greater than 1. */
  BIGNUM *tmp = BN_CTX_get(ctx);
  if (tmp == NULL ||
      !BN_set_word(tmp, 1)) {
    goto err;
  }
  if (BN_cmp(pub_key, tmp) <= 0) {
    *ret |= DH_CHECK_PUBKEY_TOO_SMALL;
  }

  /* Check |pub_key| is less than |dh->p| - 1. */
  if (!BN_copy(tmp, dh->p) ||
      !BN_sub_word(tmp, 1)) {
    goto err;
  }
  if (BN_cmp(pub_key, tmp) >= 0) {
    *ret |= DH_CHECK_PUBKEY_TOO_LARGE;
  }

  if (dh->q != NULL) {
    /* Check |pub_key|^|dh->q| is 1 mod |dh->p|. This is necessary for RFC 5114
     * groups which are not safe primes but pick a generator on a prime-order
     * subgroup of size |dh->q|. */
    if (!BN_mod_exp(tmp, pub_key, dh->q, dh->p, ctx)) {
      goto err;
    }
    if (!BN_is_one(tmp)) {
      *ret |= DH_CHECK_PUBKEY_INVALID;
    }
  }

  ok = 1;

err:
  BN_CTX_end(ctx);
  BN_CTX_free(ctx);
  return ok;
}

static bool
bsqrt_stop(const BIGNUM *x, const BIGNUM *y, u_int *onecount)
{
	BIGNUM *r;
	bool ret;

	r = BN_new();
	bn_checkp(r);
	bn_check(BN_sub(r, x, y));
	if (BN_is_one(r))
		(*onecount)++;
	ret = BN_is_zero(r);
	BN_free(r);
	return (ret || *onecount > 1);
}

/* g^x is a legal value */
static int is_legal(const BIGNUM *gx, const JPAKE_CTX *ctx)
    {
    BIGNUM *t;
    int res;
    
    if(BN_is_negative(gx) || BN_is_zero(gx) || BN_cmp(gx, ctx->p.p) >= 0)
	return 0;

    t = BN_new();
    BN_mod_exp(t, gx, ctx->p.q, ctx->p.p, ctx->ctx);
    res = BN_is_one(t);
    BN_free(t);

    return res;
    }

static int check_mod_inverse(int *out_ok, const BIGNUM *a, const BIGNUM *ainv,
                             const BIGNUM *m, int check_reduced, BN_CTX *ctx) {
  BN_CTX_start(ctx);
  BIGNUM *tmp = BN_CTX_get(ctx);
  int ret = tmp != NULL &&
            bn_mul_consttime(tmp, a, ainv, ctx) &&
            bn_div_consttime(NULL, tmp, tmp, m, ctx);
  if (ret) {
    *out_ok = BN_is_one(tmp);
    if (check_reduced && (BN_is_negative(ainv) || BN_cmp(ainv, m) >= 0)) {
      *out_ok = 0;
    }
  }
  BN_CTX_end(ctx);
  return ret;
}