/* 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/. */
/*
* PQG parameter generation/verification. Based on FIPS 186-3.
*/
#ifdef FREEBL_NO_DEPEND
#include "stubs.h"
#endif
#include "prerr.h"
#include "secerr.h"
#include "prtypes.h"
#include "blapi.h"
#include "secitem.h"
#include "mpi.h"
#include "mpprime.h"
#include "mplogic.h"
#include "secmpi.h"
#define MAX_ITERATIONS 1000 /* Maximum number of iterations of primegen */
typedef enum {
FIPS186_1_TYPE, /* Probablistic */
FIPS186_3_TYPE, /* Probablistic */
FIPS186_3_ST_TYPE /* Shawe-Taylor provable */
} pqgGenType;
/*
* These test iterations are quite a bit larger than we previously had.
* This is because FIPS 186-3 is worried about the primes in PQG generation.
* It may be possible to purposefully construct composites which more
* iterations of Miller-Rabin than the for your normal randomly selected
* numbers.There are 3 ways to counter this: 1) use one of the cool provably
* prime algorithms (which would require a lot more work than DSA-2 deservers.
* 2) add a Lucas primality test (which requires coding a Lucas primality test,
* or 3) use a larger M-R test count. I chose the latter. It increases the time
* that it takes to prove the selected prime, but it shouldn't increase the
* overall time to run the algorithm (non-primes should still faile M-R
* realively quickly). If you want to get that last bit of performance,
* implement Lucas and adjust these two functions. See FIPS 186-3 Appendix C
* and F for more information.
*/
int prime_testcount_p(int L, int N)
{
switch (L) {
case 1024:
return 40;
case 2048:
return 56;
case 3072:
return 64;
default:
break;
}
return 50; /* L = 512-960 */
}
/* The q numbers are different if you run M-R followd by Lucas. I created
* a separate function so if someone wanted to add the Lucas check, they
* could do so fairly easily */
int prime_testcount_q(int L, int N)
{
return prime_testcount_p(L,N);
}
/*
* generic function to make sure our input matches DSA2 requirements
* this gives us one place to go if we need to bump the requirements in the
* future.
*/
static SECStatus
pqg_validate_dsa2(unsigned int L, unsigned int N)
{
switch (L) {
case 1024:
if (N != DSA1_Q_BITS) {
PORT_SetError(SEC_ERROR_INVALID_ARGS);
return SECFailure;
}
break;
case 2048:
if ((N != 224) && (N != 256)) {
PORT_SetError(SEC_ERROR_INVALID_ARGS);
return SECFailure;
}
break;
case 3072:
if (N != 256) {
PORT_SetError(SEC_ERROR_INVALID_ARGS);
return SECFailure;
}
break;
default:
PORT_SetError(SEC_ERROR_INVALID_ARGS);
return SECFailure;
}
return SECSuccess;
}
static unsigned int
pqg_get_default_N(unsigned int L)
{
unsigned int N = 0;
switch (L) {
case 1024:
N = DSA1_Q_BITS;
break;
case 2048:
N = 224;
break;
case 3072:
N = 256;
break;
default:
PORT_SetError(SEC_ERROR_INVALID_ARGS);
break; /* N already set to zero */
}
return N;
}
/*
* Select the lowest hash algorithm usable
*/
static HASH_HashType
getFirstHash(unsigned int L, unsigned int N)
{
if (N < 224) {
return HASH_AlgSHA1;
}
if (N < 256) {
return HASH_AlgSHA224;
}
if (N < 384) {
return HASH_AlgSHA256;
}
if (N < 512) {
return HASH_AlgSHA384;
}
return HASH_AlgSHA512;
}
/*
* find the next usable hash algorthim
*/
static HASH_HashType
getNextHash(HASH_HashType hashtype)
{
switch (hashtype) {
case HASH_AlgSHA1:
hashtype = HASH_AlgSHA224;
break;
case HASH_AlgSHA224:
hashtype = HASH_AlgSHA256;
break;
case HASH_AlgSHA256:
hashtype = HASH_AlgSHA384;
break;
case HASH_AlgSHA384:
hashtype = HASH_AlgSHA512;
break;
case HASH_AlgSHA512:
default:
hashtype = HASH_AlgTOTAL;
break;
}
return hashtype;
}
static unsigned int
HASH_ResultLen(HASH_HashType type)
{
const SECHashObject *hash_obj = HASH_GetRawHashObject(type);
if (hash_obj == NULL) {
return 0;
}
return hash_obj->length;
}
static SECStatus
HASH_HashBuf(HASH_HashType type, unsigned char *dest,
const unsigned char *src, PRUint32 src_len)
{
const SECHashObject *hash_obj = HASH_GetRawHashObject(type);
void *hashcx = NULL;
unsigned int dummy;
if (hash_obj == NULL) {
return SECFailure;
}
hashcx = hash_obj->create();
if (hashcx == NULL) {
return SECFailure;
}
hash_obj->begin(hashcx);
hash_obj->update(hashcx,src,src_len);
hash_obj->end(hashcx,dest, &dummy, hash_obj->length);
hash_obj->destroy(hashcx, PR_TRUE);
return SECSuccess;
}
unsigned int
PQG_GetLength(const SECItem *obj)
{
unsigned int len = obj->len;
if (obj->data == NULL) {
return 0;
}
if (len > 1 && obj->data[0] == 0) {
len--;
}
return len;
}
SECStatus
PQG_Check(const PQGParams *params)
{
unsigned int L,N;
SECStatus rv = SECSuccess;
if (params == NULL) {
PORT_SetError(SEC_ERROR_INVALID_ARGS);
return SECFailure;
}
L = PQG_GetLength(¶ms->prime)*PR_BITS_PER_BYTE;
N = PQG_GetLength(¶ms->subPrime)*PR_BITS_PER_BYTE;
if (L < 1024) {
int j;
/* handle DSA1 pqg parameters with less thatn 1024 bits*/
if ( N != DSA1_Q_BITS ) {
PORT_SetError(SEC_ERROR_INVALID_ARGS);
return SECFailure;
}
j = PQG_PBITS_TO_INDEX(L);
if ( j < 0 ) {
PORT_SetError(SEC_ERROR_INVALID_ARGS);
rv = SECFailure;
}
} else {
/* handle DSA2 parameters (includes DSA1, 1024 bits) */
rv = pqg_validate_dsa2(L, N);
}
return rv;
}
HASH_HashType
PQG_GetHashType(const PQGParams *params)
{
unsigned int L,N;
if (params == NULL) {
PORT_SetError(SEC_ERROR_INVALID_ARGS);
return HASH_AlgNULL;
}
L = PQG_GetLength(¶ms->prime)*PR_BITS_PER_BYTE;
N = PQG_GetLength(¶ms->subPrime)*PR_BITS_PER_BYTE;
return getFirstHash(L, N);
}
/* Get a seed for generating P and Q. If in testing mode, copy in the
** seed from FIPS 186-1 appendix 5. Otherwise, obtain bytes from the
** global random number generator.
*/
static SECStatus
getPQseed(SECItem *seed, PLArenaPool* arena)
{
SECStatus rv;
if (!seed->data) {
seed->data = (unsigned char*)PORT_ArenaZAlloc(arena, seed->len);
}
if (!seed->data) {
PORT_SetError(SEC_ERROR_NO_MEMORY);
return SECFailure;
}
rv = RNG_GenerateGlobalRandomBytes(seed->data, seed->len);
/*
* NIST CMVP disallows a sequence of 20 bytes with the most
* significant byte equal to 0. Perhaps they interpret
* "a sequence of at least 160 bits" as "a number >= 2^159".
* So we always set the most significant bit to 1. (bug 334533)
*/
seed->data[0] |= 0x80;
return rv;
}
/* Generate a candidate h value. If in testing mode, use the h value
** specified in FIPS 186-1 appendix 5, h = 2. Otherwise, obtain bytes
** from the global random number generator.
*/
static SECStatus
generate_h_candidate(SECItem *hit, mp_int *H)
{
SECStatus rv = SECSuccess;
mp_err err = MP_OKAY;
#ifdef FIPS_186_1_A5_TEST
memset(hit->data, 0, hit->len);
hit->data[hit->len-1] = 0x02;
#else
rv = RNG_GenerateGlobalRandomBytes(hit->data, hit->len);
#endif
if (rv)
return SECFailure;
err = mp_read_unsigned_octets(H, hit->data, hit->len);
if (err) {
MP_TO_SEC_ERROR(err);
return SECFailure;
}
return SECSuccess;
}
static SECStatus
addToSeed(const SECItem * seed,
unsigned long addend,
int seedlen, /* g in 186-1 */
SECItem * seedout)
{
mp_int s, sum, modulus, tmp;
mp_err err = MP_OKAY;
SECStatus rv = SECSuccess;
MP_DIGITS(&s) = 0;
MP_DIGITS(&sum) = 0;
MP_DIGITS(&modulus) = 0;
MP_DIGITS(&tmp) = 0;
CHECK_MPI_OK( mp_init(&s) );
CHECK_MPI_OK( mp_init(&sum) );
CHECK_MPI_OK( mp_init(&modulus) );
SECITEM_TO_MPINT(*seed, &s); /* s = seed */
/* seed += addend */
if (addend < MP_DIGIT_MAX) {
CHECK_MPI_OK( mp_add_d(&s, (mp_digit)addend, &s) );
} else {
CHECK_MPI_OK( mp_init(&tmp) );
CHECK_MPI_OK( mp_set_ulong(&tmp, addend) );
CHECK_MPI_OK( mp_add(&s, &tmp, &s) );
}
/*sum = s mod 2**seedlen */
CHECK_MPI_OK( mp_div_2d(&s, (mp_digit)seedlen, NULL, &sum) );
if (seedout->data != NULL) {
SECITEM_ZfreeItem(seedout, PR_FALSE);
}
MPINT_TO_SECITEM(&sum, seedout, NULL);
cleanup:
mp_clear(&s);
mp_clear(&sum);
mp_clear(&modulus);
mp_clear(&tmp);
if (err) {
MP_TO_SEC_ERROR(err);
return SECFailure;
}
return rv;
}
/* Compute Hash[(SEED + addend) mod 2**g]
** Result is placed in shaOutBuf.
** This computation is used in steps 2 and 7 of FIPS 186 Appendix 2.2 and
** step 11.2 of FIPS 186-3 Appendix A.1.1.2 .
*/
static SECStatus
addToSeedThenHash(HASH_HashType hashtype,
const SECItem * seed,
unsigned long addend,
int seedlen, /* g in 186-1 */
unsigned char * hashOutBuf)
{
SECItem str = { 0, 0, 0 };
SECStatus rv;
rv = addToSeed(seed, addend, seedlen, &str);
if (rv != SECSuccess) {
return rv;
}
rv = HASH_HashBuf(hashtype, hashOutBuf, str.data, str.len);/* hash result */
if (str.data)
SECITEM_ZfreeItem(&str, PR_FALSE);
return rv;
}
/*
** Perform steps 2 and 3 of FIPS 186-1, appendix 2.2.
** Generate Q from seed.
*/
static SECStatus
makeQfromSeed(
unsigned int g, /* input. Length of seed in bits. */
const SECItem * seed, /* input. */
mp_int * Q) /* output. */
{
unsigned char sha1[SHA1_LENGTH];
unsigned char sha2[SHA1_LENGTH];
unsigned char U[SHA1_LENGTH];
SECStatus rv = SECSuccess;
mp_err err = MP_OKAY;
int i;
/* ******************************************************************
** Step 2.
** "Compute U = SHA[SEED] XOR SHA[(SEED+1) mod 2**g]."
**/
CHECK_SEC_OK( SHA1_HashBuf(sha1, seed->data, seed->len) );
CHECK_SEC_OK( addToSeedThenHash(HASH_AlgSHA1, seed, 1, g, sha2) );
for (i=0; i<SHA1_LENGTH; ++i)
U[i] = sha1[i] ^ sha2[i];
/* ******************************************************************
** Step 3.
** "Form Q from U by setting the most signficant bit (the 2**159 bit)
** and the least signficant bit to 1. In terms of boolean operations,
** Q = U OR 2**159 OR 1. Note that 2**159 < Q < 2**160."
*/
U[0] |= 0x80; /* U is MSB first */
U[SHA1_LENGTH-1] |= 0x01;
err = mp_read_unsigned_octets(Q, U, SHA1_LENGTH);
cleanup:
memset(U, 0, SHA1_LENGTH);
memset(sha1, 0, SHA1_LENGTH);
memset(sha2, 0, SHA1_LENGTH);
if (err) {
MP_TO_SEC_ERROR(err);
return SECFailure;
}
return rv;
}
/*
** Perform steps 6 and 7 of FIPS 186-3, appendix A.1.1.2.
** Generate Q from seed.
*/
static SECStatus
makeQ2fromSeed(
HASH_HashType hashtype, /* selected Hashing algorithm */
unsigned int N, /* input. Length of q in bits. */
const SECItem * seed, /* input. */
mp_int * Q) /* output. */
{
unsigned char U[HASH_LENGTH_MAX];
SECStatus rv = SECSuccess;
mp_err err = MP_OKAY;
int N_bytes = N/PR_BITS_PER_BYTE; /* length of N in bytes rather than bits */
int hashLen = HASH_ResultLen(hashtype);
int offset = 0;
/* ******************************************************************
** Step 6.
** "Compute U = hash[SEED] mod 2**N-1]."
**/
CHECK_SEC_OK( HASH_HashBuf(hashtype, U, seed->data, seed->len) );
/* mod 2**N . Step 7 will explicitly set the top bit to 1, so no need
* to handle mod 2**N-1 */
if (hashLen > N_bytes) {
offset = hashLen - N_bytes;
}
/* ******************************************************************
** Step 7.
** computed_q = 2**(N-1) + U + 1 - (U mod 2)
**
** This is the same as:
** computed_q = 2**(N-1) | U | 1;
*/
U[offset] |= 0x80; /* U is MSB first */
U[hashLen-1] |= 0x01;
err = mp_read_unsigned_octets(Q, &U[offset], N_bytes);
cleanup:
memset(U, 0, HASH_LENGTH_MAX);
if (err) {
MP_TO_SEC_ERROR(err);
return SECFailure;
}
return rv;
}
/*
** Perform steps from FIPS 186-3, Appendix A.1.2.1 and Appendix C.6
**
** This generates a provable prime from two smaller prime. The resulting
** prime p will have q0 as a multiple of p-1. q0 can be 1.
**
** This implments steps 4 thorough 22 of FIPS 186-3 A.1.2.1 and
** steps 16 through 34 of FIPS 186-2 C.6
*/
#define MAX_ST_SEED_BITS (HASH_LENGTH_MAX*PR_BITS_PER_BYTE)
SECStatus
makePrimefromPrimesShaweTaylor(
HASH_HashType hashtype, /* selected Hashing algorithm */
unsigned int length, /* input. Length of prime in bits. */
mp_int * c0, /* seed prime */
mp_int * q, /* sub prime, can be 1 */
mp_int * prime, /* output. */
SECItem * prime_seed, /* input/output. */
int * prime_gen_counter) /* input/output. */
{
mp_int c;
mp_int c0_2;
mp_int t;
mp_int a;
mp_int z;
mp_int two_length_minus_1;
SECStatus rv = SECFailure;
int hashlen = HASH_ResultLen(hashtype);
int outlen = hashlen*PR_BITS_PER_BYTE;
int offset;
unsigned char bit, mask;
/* x needs to hold roundup(L/outlen)*outlen.
* This can be no larger than L+outlen-1, So we set it's size to
* our max L + max outlen and know we are safe */
unsigned char x[DSA_MAX_P_BITS/8+HASH_LENGTH_MAX];
mp_err err = MP_OKAY;
int i;
int iterations;
int old_counter;
MP_DIGITS(&c) = 0;
MP_DIGITS(&c0_2) = 0;
MP_DIGITS(&t) = 0;
MP_DIGITS(&a) = 0;
MP_DIGITS(&z) = 0;
MP_DIGITS(&two_length_minus_1) = 0;
CHECK_MPI_OK( mp_init(&c) );
CHECK_MPI_OK( mp_init(&c0_2) );
CHECK_MPI_OK( mp_init(&t) );
CHECK_MPI_OK( mp_init(&a) );
CHECK_MPI_OK( mp_init(&z) );
CHECK_MPI_OK( mp_init(&two_length_minus_1) );
/*
** There is a slight mapping of variable names depending on which
** FIPS 186 steps are being carried out. The mapping is as follows:
** variable A.1.2.1 C.6
** c0 p0 c0
** q q 1
** c p c
** c0_2 2*p0*q 2*c0
** length L length
** prime_seed pseed prime_seed
** prime_gen_counter pgen_counter prime_gen_counter
**
** Also note: or iterations variable is actually iterations+1, since
** iterations+1 works better in C.
*/
/* Step 4/16 iterations = ceiling(length/outlen)-1 */
iterations = (length+outlen-1)/outlen; /* NOTE: iterations +1 */
/* Step 5/17 old_counter = prime_gen_counter */
old_counter = *prime_gen_counter;
/*
** Comment: Generate a pseudorandom integer x in the interval
** [2**(lenght-1), 2**length].
**
** Step 6/18 x = 0
*/
PORT_Memset(x, 0, sizeof(x));
/*
** Step 7/19 for i = 0 to iterations do
** x = x + (HASH(prime_seed + i) * 2^(i*outlen))
*/
for (i=0; i < iterations; i++) {
/* is bigger than prime_seed should get to */
CHECK_SEC_OK( addToSeedThenHash(hashtype, prime_seed, i,
MAX_ST_SEED_BITS,&x[(iterations - i - 1)*hashlen]));
}
/* Step 8/20 prime_seed = prime_seed + iterations + 1 */
CHECK_SEC_OK(addToSeed(prime_seed, iterations, MAX_ST_SEED_BITS,
prime_seed));
/*
** Step 9/21 x = 2 ** (length-1) + x mod 2 ** (length-1)
**
** This step mathematically sets the high bit and clears out
** all the other bits higher than length. 'x' is stored
** in the x array, MSB first. The above formula gives us an 'x'
** which is length bytes long and has the high bit set. We also know
** that length <= iterations*outlen since
** iterations=ceiling(length/outlen). First we find the offset in
** bytes into the array where the high bit is.
*/
offset = (outlen*iterations - length)/PR_BITS_PER_BYTE;
/* now we want to set the 'high bit', since length may not be a
* multiple of 8,*/
bit = 1 << ((length-1) & 0x7); /* select the proper bit in the byte */
/* we need to zero out the rest of the bits in the byte above */
mask = (bit-1);
/* now we set it */
x[offset] = (mask & x[offset]) | bit;
/*
** Comment: Generate a candidate prime c in the interval
** [2**(lenght-1), 2**length].
**
** Step 10 t = ceiling(x/(2q(p0)))
** Step 22 t = ceiling(x/(2(c0)))
*/
CHECK_MPI_OK( mp_read_unsigned_octets(&t, &x[offset],
hashlen*iterations - offset ) ); /* t = x */
CHECK_MPI_OK( mp_mul(c0, q, &c0_2) ); /* c0_2 is now c0*q */
CHECK_MPI_OK( mp_add(&c0_2, &c0_2, &c0_2) ); /* c0_2 is now 2*q*c0 */
CHECK_MPI_OK( mp_add(&t, &c0_2, &t) ); /* t = x+2*q*c0 */
CHECK_MPI_OK( mp_sub_d(&t, (mp_digit) 1, &t) ); /* t = x+2*q*c0 -1 */
/* t = floor((x+2qc0-1)/2qc0) = ceil(x/2qc0) */
CHECK_MPI_OK( mp_div(&t, &c0_2, &t, NULL) );
/*
** step 11: if (2tqp0 +1 > 2**length), then t = ceiling(2**(length-1)/2qp0)
** step 12: t = 2tqp0 +1.
**
** step 23: if (2tc0 +1 > 2**length), then t = ceiling(2**(length-1)/2c0)
** step 24: t = 2tc0 +1.
*/
CHECK_MPI_OK( mp_2expt(&two_length_minus_1, length-1) );
step_23:
CHECK_MPI_OK( mp_mul(&t, &c0_2, &c) ); /* c = t*2qc0 */
CHECK_MPI_OK( mp_add_d(&c, (mp_digit)1, &c) ); /* c= 2tqc0 + 1*/
if (mpl_significant_bits(&c) > length) { /* if c > 2**length */
CHECK_MPI_OK( mp_sub_d(&c0_2, (mp_digit) 1, &t) ); /* t = 2qc0-1 */
/* t = 2**(length-1) + 2qc0 -1 */
CHECK_MPI_OK( mp_add(&two_length_minus_1,&t, &t) );
/* t = floor((2**(length-1)+2qc0 -1)/2qco)
* = ceil(2**(lenght-2)/2qc0) */
CHECK_MPI_OK( mp_div(&t, &c0_2, &t, NULL) );
CHECK_MPI_OK( mp_mul(&t, &c0_2, &c) );
CHECK_MPI_OK( mp_add_d(&c, (mp_digit)1, &c) ); /* c= 2tqc0 + 1*/
}
/* Step 13/25 prime_gen_counter = prime_gen_counter + 1*/
(*prime_gen_counter)++;
/*
** Comment: Test the candidate prime c for primality; first pick an
** integer a between 2 and c-2.
**
** Step 14/26 a=0
*/
PORT_Memset(x, 0, sizeof(x)); /* use x for a */
/*
** Step 15/27 for i = 0 to iterations do
** a = a + (HASH(prime_seed + i) * 2^(i*outlen))
**
** NOTE: we reuse the x array for 'a' initially.
*/
for (i=0; i < iterations; i++) {
/* MAX_ST_SEED_BITS is bigger than prime_seed should get to */
CHECK_SEC_OK(addToSeedThenHash(hashtype, prime_seed, i,
MAX_ST_SEED_BITS,&x[(iterations - i - 1)*hashlen]));
}
/* Step 16/28 prime_seed = prime_seed + iterations + 1 */
CHECK_SEC_OK(addToSeed(prime_seed, iterations, MAX_ST_SEED_BITS,
prime_seed));
/* Step 17/29 a = 2 + (a mod (c-3)). */
CHECK_MPI_OK( mp_read_unsigned_octets(&a, x, iterations*hashlen) );
CHECK_MPI_OK( mp_sub_d(&c, (mp_digit) 3, &z) ); /* z = c -3 */
CHECK_MPI_OK( mp_mod(&a, &z, &a) ); /* a = a mod c -3 */
CHECK_MPI_OK( mp_add_d(&a, (mp_digit) 2, &a) ); /* a = 2 + a mod c -3 */
/*
** Step 18 z = a**(2tq) mod p.
** Step 30 z = a**(2t) mod c.
*/
CHECK_MPI_OK( mp_mul(&t, q, &z) ); /* z = tq */
CHECK_MPI_OK( mp_add(&z, &z, &z) ); /* z = 2tq */
CHECK_MPI_OK( mp_exptmod(&a, &z, &c, &z) ); /* z = a**(2tq) mod c */
/*
** Step 19 if (( 1 == GCD(z-1,p)) and ( 1 == z**p0 mod p )), then
** Step 31 if (( 1 == GCD(z-1,c)) and ( 1 == z**c0 mod c )), then
*/
CHECK_MPI_OK( mp_sub_d(&z, (mp_digit) 1, &a) );
CHECK_MPI_OK( mp_gcd(&a,&c,&a ));
if (mp_cmp_d(&a, (mp_digit)1) == 0) {
CHECK_MPI_OK( mp_exptmod(&z, c0, &c, &a) );
if (mp_cmp_d(&a, (mp_digit)1) == 0) {
/* Step 31.1 prime = c */
CHECK_MPI_OK( mp_copy(&c, prime) );
/*
** Step 31.2 return Success, prime, prime_seed,
** prime_gen_counter
*/
rv = SECSuccess;
goto cleanup;
}
}
/*
** Step 20/32 If (prime_gen_counter > 4 * length + old_counter then
** return (FAILURE, 0, 0, 0).
** NOTE: the test is reversed, so we fall through on failure to the
** cleanup routine
*/
if (*prime_gen_counter < (4*length + old_counter)) {
/* Step 21/33 t = t + 1 */
CHECK_MPI_OK( mp_add_d(&t, (mp_digit) 1, &t) );
/* Step 22/34 Go to step 23/11 */
goto step_23;
}
/* if (prime_gencont > (4*length + old_counter), fall through to failure */
rv = SECFailure; /* really is already set, but paranoia is good */
cleanup:
mp_clear(&c);
mp_clear(&c0_2);
mp_clear(&t);
mp_clear(&a);
mp_clear(&z);
mp_clear(&two_length_minus_1);
if (err) {
MP_TO_SEC_ERROR(err);
rv = SECFailure;
}
if (rv == SECFailure) {
mp_zero(prime);
if (prime_seed->data) {
SECITEM_FreeItem(prime_seed, PR_FALSE);
}
*prime_gen_counter = 0;
}
return rv;
}
/*
** Perform steps from FIPS 186-3, Appendix C.6
**
** This generates a provable prime from a seed
*/
SECStatus
makePrimefromSeedShaweTaylor(
HASH_HashType hashtype, /* selected Hashing algorithm */
unsigned int length, /* input. Length of prime in bits. */
const SECItem * input_seed, /* input. */
mp_int * prime, /* output. */
SECItem * prime_seed, /* output. */
int * prime_gen_counter) /* output. */
{
mp_int c;
mp_int c0;
mp_int one;
SECStatus rv = SECFailure;
int hashlen = HASH_ResultLen(hashtype);
int outlen = hashlen*PR_BITS_PER_BYTE;
int offset;
unsigned char bit, mask;
unsigned char x[HASH_LENGTH_MAX*2];
mp_digit dummy;
mp_err err = MP_OKAY;
int i;
MP_DIGITS(&c) = 0;
MP_DIGITS(&c0) = 0;
MP_DIGITS(&one) = 0;
CHECK_MPI_OK( mp_init(&c) );
CHECK_MPI_OK( mp_init(&c0) );
CHECK_MPI_OK( mp_init(&one) );
/* Step 1. if length < 2 then return (FAILURE, 0, 0, 0) */
if (length < 2) {
rv = SECFailure;
goto cleanup;
}
/* Step 2. if length >= 33 then goto step 14 */
if (length >= 33) {
mp_zero(&one);
CHECK_MPI_OK( mp_add_d(&one, (mp_digit) 1, &one) );
/* Step 14 (status, c0, prime_seed, prime_gen_counter) =
** (ST_Random_Prime((ceil(length/2)+1, input_seed)
*/
rv = makePrimefromSeedShaweTaylor(hashtype, (length+1)/2+1,
input_seed, &c0, prime_seed, prime_gen_counter);
/* Step 15 if FAILURE is returned, return (FAILURE, 0, 0, 0). */
if (rv != SECSuccess) {
goto cleanup;
}
/* Steps 16-34 */
rv = makePrimefromPrimesShaweTaylor(hashtype,length, &c0, &one,
prime, prime_seed, prime_gen_counter);
goto cleanup; /* we're done, one way or the other */
}
/* Step 3 prime_seed = input_seed */
CHECK_SEC_OK(SECITEM_CopyItem(NULL, prime_seed, input_seed));
/* Step 4 prime_gen_count = 0 */
*prime_gen_counter = 0;
step_5:
/* Step 5 c = Hash(prime_seed) xor Hash(prime_seed+1). */
CHECK_SEC_OK(HASH_HashBuf(hashtype, x, prime_seed->data, prime_seed->len) );
CHECK_SEC_OK(addToSeedThenHash(hashtype, prime_seed, 1,
MAX_ST_SEED_BITS, &x[hashlen]) );
for (i=0; i < hashlen; i++) {
x[i] = x[i] ^ x[i+hashlen];
}
/* Step 6 c = 2**length-1 + c mod 2**length-1 */
/* This step mathematically sets the high bit and clears out
** all the other bits higher than length. Right now c is stored
** in the x array, MSB first. The above formula gives us a c which
** is length bytes long and has the high bit set. We also know that
** length < outlen since the smallest outlen is 160 bits and the largest
** length at this point is 32 bits. So first we find the offset in bytes
** into the array where the high bit is.
*/
offset = (outlen - length)/PR_BITS_PER_BYTE;
/* now we want to set the 'high bit'. We have to calculate this since
* length may not be a multiple of 8.*/
bit = 1 << ((length-1) & 0x7); /* select the proper bit in the byte */
/* we need to zero out the rest of the bits in the byte above */
mask = (bit-1);
/* now we set it */
x[offset] = (mask & x[offset]) | bit;
/* Step 7 c = c*floor(c/2) + 1 */
/* set the low bit. much easier to find (the end of the array) */
x[hashlen-1] |= 1;
/* now that we've set our bits, we can create our candidate "c" */
CHECK_MPI_OK( mp_read_unsigned_octets(&c, &x[offset], hashlen-offset) );
/* Step 8 prime_gen_counter = prime_gen_counter + 1 */
(*prime_gen_counter)++;
/* Step 9 prime_seed = prime_seed + 2 */
CHECK_SEC_OK(addToSeed(prime_seed, 2, MAX_ST_SEED_BITS, prime_seed));
/* Step 10 Perform deterministic primality test on c. For example, since
** c is small, it's primality can be tested by trial division, See
** See Appendic C.7.
**
** We in fact test with trial division. mpi has a built int trial divider
** that divides all divisors up to 2^16.
*/
if (prime_tab[prime_tab_size-1] < 0xFFF1) {
/* we aren't testing all the primes between 0 and 2^16, we really
* can't use this construction. Just fail. */
rv = SECFailure;
goto cleanup;
}
dummy = prime_tab_size;
err = mpp_divis_primes(&c, &dummy);
/* Step 11 if c is prime then */
if (err == MP_NO) {
/* Step 11.1 prime = c */
CHECK_MPI_OK( mp_copy(&c, prime) );
/* Step 11.2 return SUCCESS prime, prime_seed, prime_gen_counter */
err = MP_OKAY;
rv = SECSuccess;
goto cleanup;
} else if (err != MP_YES) {
goto cleanup; /* function failed, bail out */
} else {
/* reset mp_err */
err = MP_OKAY;
}
/*
** Step 12 if (prime_gen_counter > (4*len))
** then return (FAILURE, 0, 0, 0))
** Step 13 goto step 5
*/
if (*prime_gen_counter <= (4*length)) {
goto step_5;
}
/* if (prime_gencont > 4*length), fall through to failure */
rv = SECFailure; /* really is already set, but paranoia is good */
cleanup:
mp_clear(&c);
mp_clear(&c0);
mp_clear(&one);
if (err) {
MP_TO_SEC_ERROR(err);
rv = SECFailure;
}
if (rv == SECFailure) {
mp_zero(prime);
if (prime_seed->data) {
SECITEM_FreeItem(prime_seed, PR_FALSE);
}
*prime_gen_counter = 0;
}
return rv;
}
/*
* Find a Q and algorithm from Seed.
*/
static SECStatus
findQfromSeed(
unsigned int L, /* input. Length of p in bits. */
unsigned int N, /* input. Length of q in bits. */
unsigned int g, /* input. Length of seed in bits. */
const SECItem * seed, /* input. */
mp_int * Q, /* input. */
mp_int * Q_, /* output. */
int * qseed_len, /* output */
HASH_HashType *hashtypePtr, /* output. Hash uses */
pqgGenType *typePtr) /* output. Generation Type used */
{
HASH_HashType hashtype;
SECItem firstseed = { 0, 0, 0 };
SECItem qseed = { 0, 0, 0 };
SECStatus rv;
*qseed_len = 0; /* only set if FIPS186_3_ST_TYPE */
/* handle legacy small DSA first can only be FIPS186_1_TYPE */
if (L < 1024) {
rv =makeQfromSeed(g,seed,Q_);
if ((rv == SECSuccess) && (mp_cmp(Q,Q_) == 0)) {
*hashtypePtr = HASH_AlgSHA1;
*typePtr = FIPS186_1_TYPE;
return SECSuccess;
}
return SECFailure;
}
/* 1024 could use FIPS186_1 or FIPS186_3 algorithms, we need to try
* them both */
if (L == 1024) {
rv = makeQfromSeed(g,seed,Q_);
if (rv == SECSuccess) {
if (mp_cmp(Q,Q_) == 0) {
*hashtypePtr = HASH_AlgSHA1;
*typePtr = FIPS186_1_TYPE;
return SECSuccess;
}
}
/* fall through for FIPS186_3 types */
}
/* at this point we know we aren't using FIPS186_1, start trying FIPS186_3
* with appropriate hash types */
for (hashtype = getFirstHash(L,N); hashtype != HASH_AlgTOTAL;
hashtype=getNextHash(hashtype)) {
rv = makeQ2fromSeed(hashtype, N, seed, Q_);
if (rv != SECSuccess) {
continue;
}
if (mp_cmp(Q,Q_) == 0) {
*hashtypePtr = hashtype;
*typePtr = FIPS186_3_TYPE;
return SECSuccess;
}
}
/*
* OK finally try FIPS186_3 Shawe-Taylor
*/
firstseed = *seed;
firstseed.len = seed->len/3;
for (hashtype = getFirstHash(L,N); hashtype != HASH_AlgTOTAL;
hashtype=getNextHash(hashtype)) {
int count;
rv = makePrimefromSeedShaweTaylor(hashtype, N, &firstseed, Q_,
&qseed, &count);
if (rv != SECSuccess) {
continue;
}
if (mp_cmp(Q,Q_) == 0) {
/* check qseed as well... */
int offset = seed->len - qseed.len;
if ((offset < 0) ||
(PORT_Memcmp(&seed->data[offset],qseed.data,qseed.len) != 0)) {
/* we found q, but the seeds don't match. This isn't an
* accident, someone has been tweeking with the seeds, just
* fail a this point. */
SECITEM_FreeItem(&qseed,PR_FALSE);
return SECFailure;
}
*qseed_len = qseed.len;
*hashtypePtr = hashtype;
*typePtr = FIPS186_3_ST_TYPE;
SECITEM_FreeItem(&qseed, PR_FALSE);
return SECSuccess;
}
SECITEM_FreeItem(&qseed, PR_FALSE);
}
/* no hash algorithms found which match seed to Q, fail */
return SECFailure;
}
/*
** Perform steps 7, 8 and 9 of FIPS 186, appendix 2.2.
** which are the same as steps 11.1-11.5 of FIPS 186-2, App A.1.1.2
** Generate P from Q, seed, L, and offset.
*/
static SECStatus
makePfromQandSeed(
HASH_HashType hashtype, /* selected Hashing algorithm */
unsigned int L, /* Length of P in bits. Per FIPS 186. */
unsigned int N, /* Length of Q in bits. Per FIPS 186. */
unsigned int offset, /* Per FIPS 186, App 2.2. & 186-3 App A.1.1.2 */
unsigned int seedlen, /* input. Length of seed in bits. (g in 186-1)*/
const SECItem * seed, /* input. */
const mp_int * Q, /* input. */
mp_int * P) /* output. */
{
unsigned int j; /* Per FIPS 186-3 App. A.1.1.2 (k in 186-1)*/
unsigned int n; /* Per FIPS 186, appendix 2.2. */
mp_digit b; /* Per FIPS 186, appendix 2.2. */
unsigned int outlen; /* Per FIPS 186-3 App. A.1.1.2 */
unsigned int hashlen; /* outlen in bytes */
unsigned char V_j[HASH_LENGTH_MAX];
mp_int W, X, c, twoQ, V_n, tmp;
mp_err err = MP_OKAY;
SECStatus rv = SECSuccess;
/* Initialize bignums */
MP_DIGITS(&W) = 0;
MP_DIGITS(&X) = 0;
MP_DIGITS(&c) = 0;
MP_DIGITS(&twoQ) = 0;
MP_DIGITS(&V_n) = 0;
MP_DIGITS(&tmp) = 0;
CHECK_MPI_OK( mp_init(&W) );
CHECK_MPI_OK( mp_init(&X) );
CHECK_MPI_OK( mp_init(&c) );
CHECK_MPI_OK( mp_init(&twoQ) );
CHECK_MPI_OK( mp_init(&tmp) );
CHECK_MPI_OK( mp_init(&V_n) );
hashlen = HASH_ResultLen(hashtype);
outlen = hashlen*PR_BITS_PER_BYTE;
/* L - 1 = n*outlen + b */
n = (L - 1) / outlen;
b = (L - 1) % outlen;
/* ******************************************************************
** Step 11.1 (Step 7 in 186-1)
** "for j = 0 ... n let
** V_j = SHA[(SEED + offset + j) mod 2**seedlen]."
**
** Step 11.2 (Step 8 in 186-1)
** "W = V_0 + (V_1 * 2**outlen) + ... + (V_n-1 * 2**((n-1)*outlen))
** + ((V_n mod 2**b) * 2**(n*outlen))
*/
for (j=0; j<n; ++j) { /* Do the first n terms of V_j */
/* Do step 11.1 for iteration j.
** V_j = HASH[(seed + offset + j) mod 2**g]
*/
CHECK_SEC_OK( addToSeedThenHash(hashtype,seed,offset+j, seedlen, V_j) );
/* Do step 11.2 for iteration j.
** W += V_j * 2**(j*outlen)
*/
OCTETS_TO_MPINT(V_j, &tmp, hashlen); /* get bignum V_j */
CHECK_MPI_OK( mpl_lsh(&tmp, &tmp, j*outlen) );/* tmp=V_j << j*outlen */
CHECK_MPI_OK( mp_add(&W, &tmp, &W) ); /* W += tmp */
}
/* Step 11.2, continued.
** [W += ((V_n mod 2**b) * 2**(n*outlen))]
*/
CHECK_SEC_OK( addToSeedThenHash(hashtype, seed, offset + n, seedlen, V_j) );
OCTETS_TO_MPINT(V_j, &V_n, hashlen); /* get bignum V_n */
CHECK_MPI_OK( mp_div_2d(&V_n, b, NULL, &tmp) ); /* tmp = V_n mod 2**b */
CHECK_MPI_OK( mpl_lsh(&tmp, &tmp, n*outlen) ); /* tmp = tmp << n*outlen */
CHECK_MPI_OK( mp_add(&W, &tmp, &W) ); /* W += tmp */
/* Step 11.3, (Step 8 in 186-1)
** "X = W + 2**(L-1).
** Note that 0 <= W < 2**(L-1) and hence 2**(L-1) <= X < 2**L."
*/
CHECK_MPI_OK( mpl_set_bit(&X, (mp_size)(L-1), 1) ); /* X = 2**(L-1) */
CHECK_MPI_OK( mp_add(&X, &W, &X) ); /* X += W */
/*************************************************************
** Step 11.4. (Step 9 in 186-1)
** "c = X mod 2q"
*/
CHECK_MPI_OK( mp_mul_2(Q, &twoQ) ); /* 2q */
CHECK_MPI_OK( mp_mod(&X, &twoQ, &c) ); /* c = X mod 2q */
/*************************************************************
** Step 11.5. (Step 9 in 186-1)
** "p = X - (c - 1).
** Note that p is congruent to 1 mod 2q."
*/
CHECK_MPI_OK( mp_sub_d(&c, 1, &c) ); /* c -= 1 */
CHECK_MPI_OK( mp_sub(&X, &c, P) ); /* P = X - c */
cleanup:
mp_clear(&W);
mp_clear(&X);
mp_clear(&c);
mp_clear(&twoQ);
mp_clear(&V_n);
mp_clear(&tmp);
if (err) {
MP_TO_SEC_ERROR(err);
return SECFailure;
}
return rv;
}
/*
** Generate G from h, P, and Q.
*/
static SECStatus
makeGfromH(const mp_int *P, /* input. */
const mp_int *Q, /* input. */
mp_int *H, /* input and output. */
mp_int *G, /* output. */
PRBool *passed)
{
mp_int exp, pm1;
mp_err err = MP_OKAY;
SECStatus rv = SECSuccess;
*passed = PR_FALSE;
MP_DIGITS(&exp) = 0;
MP_DIGITS(&pm1) = 0;
CHECK_MPI_OK( mp_init(&exp) );
CHECK_MPI_OK( mp_init(&pm1) );
CHECK_MPI_OK( mp_sub_d(P, 1, &pm1) ); /* P - 1 */
if ( mp_cmp(H, &pm1) >= 0) /* H >= P-1 */
CHECK_MPI_OK( mp_sub(H, &pm1, H) ); /* H = H mod (P-1) */
/* Let b = 2**n (smallest power of 2 greater than P).
** Since P-1 >= b/2, and H < b, quotient(H/(P-1)) = 0 or 1
** so the above operation safely computes H mod (P-1)
*/
/* Check for H = to 0 or 1. Regen H if so. (Regen means return error). */
if (mp_cmp_d(H, 1) <= 0) {
rv = SECFailure;
goto cleanup;
}
/* Compute G, according to the equation G = (H ** ((P-1)/Q)) mod P */
CHECK_MPI_OK( mp_div(&pm1, Q, &exp, NULL) ); /* exp = (P-1)/Q */
CHECK_MPI_OK( mp_exptmod(H, &exp, P, G) ); /* G = H ** exp mod P */
/* Check for G == 0 or G == 1, return error if so. */
if (mp_cmp_d(G, 1) <= 0) {
rv = SECFailure;
goto cleanup;
}
*passed = PR_TRUE;
cleanup:
mp_clear(&exp);
mp_clear(&pm1);
if (err) {
MP_TO_SEC_ERROR(err);
rv = SECFailure;
}
return rv;
}
/*
** Generate G from seed, index, P, and Q.
*/
static SECStatus
makeGfromIndex(HASH_HashType hashtype,
const mp_int *P, /* input. */
const mp_int *Q, /* input. */
const SECItem *seed, /* input. */
unsigned char index, /* input. */
mp_int *G) /* input/output */
{
mp_int e, pm1, W;
unsigned int count;
unsigned char data[HASH_LENGTH_MAX];
unsigned int len;
mp_err err = MP_OKAY;
SECStatus rv = SECSuccess;
const SECHashObject *hashobj;
void *hashcx = NULL;
MP_DIGITS(&e) = 0;
MP_DIGITS(&pm1) = 0;
MP_DIGITS(&W) = 0;
CHECK_MPI_OK( mp_init(&e) );
CHECK_MPI_OK( mp_init(&pm1) );
CHECK_MPI_OK( mp_init(&W) );
/* initialize our hash stuff */
hashobj = HASH_GetRawHashObject(hashtype);
if (hashobj == NULL) {
/* shouldn't happen */
PORT_SetError(SEC_ERROR_LIBRARY_FAILURE);
rv = SECFailure;
goto cleanup;
}
hashcx = hashobj->create();
if (hashcx == NULL) {
rv = SECFailure;
goto cleanup;
}
CHECK_MPI_OK( mp_sub_d(P, 1, &pm1) ); /* P - 1 */
/* Step 3 e = (p-1)/q */
CHECK_MPI_OK( mp_div(&pm1, Q, &e, NULL) ); /* e = (P-1)/Q */
/* Steps 4, 5, and 6 */
/* count is a 16 bit value in the spec. We actually represent count
* as more than 16 bits so we can easily detect the 16 bit overflow */
#define MAX_COUNT 0x10000
for (count = 1; count < MAX_COUNT; count++) {
/* step 7
* U = domain_param_seed || "ggen" || index || count
* step 8
* W = HASH(U)
*/
hashobj->begin(hashcx);
hashobj->update(hashcx,seed->data,seed->len);
hashobj->update(hashcx, (unsigned char *)"ggen", 4);
hashobj->update(hashcx,&index, 1);
data[0] = (count >> 8) & 0xff;
data[1] = count & 0xff;
hashobj->update(hashcx, data, 2);
hashobj->end(hashcx, data, &len, sizeof(data));
OCTETS_TO_MPINT(data, &W, len);
/* step 9. g = W**e mod p */
CHECK_MPI_OK( mp_exptmod(&W, &e, P, G) );
/* step 10. if (g < 2) then goto step 5 */
/* NOTE: this weird construct is to keep the flow according to the spec.
* the continue puts us back to step 5 of the for loop */
if (mp_cmp_d(G, 2) < 0) {
continue;
}
break; /* step 11 follows step 10 if the test condition is false */
}
if (count >= MAX_COUNT) {
rv = SECFailure; /* last part of step 6 */
}
/* step 11.
* return valid G */
cleanup:
PORT_Memset(data, 0, sizeof(data));
if (hashcx) {
hashobj->destroy(hashcx, PR_TRUE);
}
mp_clear(&e);
mp_clear(&pm1);
mp_clear(&W);
if (err) {
MP_TO_SEC_ERROR(err);
rv = SECFailure;
}
return rv;
}
/* This code uses labels and gotos, so that it can follow the numbered
** steps in the algorithms from FIPS 186-3 appendix A.1.1.2 very closely,
** and so that the correctness of this code can be easily verified.
** So, please forgive the ugly c code.
**/
static SECStatus
pqg_ParamGen(unsigned int L, unsigned int N, pqgGenType type,
unsigned int seedBytes, PQGParams **pParams, PQGVerify **pVfy)
{
unsigned int n; /* Per FIPS 186, app 2.2. 186-3 app A.1.1.2 */
unsigned int b; /* Per FIPS 186, app 2.2. 186-3 app A.1.1.2 */
unsigned int seedlen; /* Per FIPS 186-3 app A.1.1.2 (was 'g' 186-1)*/
unsigned int counter; /* Per FIPS 186, app 2.2. 186-3 app A.1.1.2 */
unsigned int offset; /* Per FIPS 186, app 2.2. 186-3 app A.1.1.2 */
unsigned int outlen; /* Per FIPS 186-3, appendix A.1.1.2. */
unsigned int maxCount;
HASH_HashType hashtype;
SECItem *seed; /* Per FIPS 186, app 2.2. 186-3 app A.1.1.2 */
PLArenaPool *arena = NULL;
PQGParams *params = NULL;
PQGVerify *verify = NULL;
PRBool passed;
SECItem hit = { 0, 0, 0 };
SECItem firstseed = { 0, 0, 0 };
SECItem qseed = { 0, 0, 0 };
SECItem pseed = { 0, 0, 0 };
mp_int P, Q, G, H, l, p0;
mp_err err = MP_OKAY;
SECStatus rv = SECFailure;
int iterations = 0;
/* Step 1. L and N already checked by caller*/
/* Step 2. if (seedlen < N) return INVALID; */
if (seedBytes < N/PR_BITS_PER_BYTE || !pParams || !pVfy) {
PORT_SetError(SEC_ERROR_INVALID_ARGS);
return SECFailure;
}
/* Initialize an arena for the params. */
arena = PORT_NewArena(NSS_FREEBL_DEFAULT_CHUNKSIZE);
if (!arena) {
PORT_SetError(SEC_ERROR_NO_MEMORY);
return SECFailure;
}
params = (PQGParams *)PORT_ArenaZAlloc(arena, sizeof(PQGParams));
if (!params) {
PORT_SetError(SEC_ERROR_NO_MEMORY);
PORT_FreeArena(arena, PR_TRUE);
return SECFailure;
}
params->arena = arena;
/* Initialize an arena for the verify. */
arena = PORT_NewArena(NSS_FREEBL_DEFAULT_CHUNKSIZE);
if (!arena) {
PORT_SetError(SEC_ERROR_NO_MEMORY);
PORT_FreeArena(params->arena, PR_TRUE);
return SECFailure;
}
verify = (PQGVerify *)PORT_ArenaZAlloc(arena, sizeof(PQGVerify));
if (!verify) {
PORT_SetError(SEC_ERROR_NO_MEMORY);
PORT_FreeArena(arena, PR_TRUE);
PORT_FreeArena(params->arena, PR_TRUE);
return SECFailure;
}
verify->arena = arena;
seed = &verify->seed;
arena = NULL;
/* Initialize bignums */
MP_DIGITS(&P) = 0;
MP_DIGITS(&Q) = 0;
MP_DIGITS(&G) = 0;
MP_DIGITS(&H) = 0;
MP_DIGITS(&l) = 0;
MP_DIGITS(&p0) = 0;
CHECK_MPI_OK( mp_init(&P) );
CHECK_MPI_OK( mp_init(&Q) );
CHECK_MPI_OK( mp_init(&G) );
CHECK_MPI_OK( mp_init(&H) );
CHECK_MPI_OK( mp_init(&l) );
CHECK_MPI_OK( mp_init(&p0) );
/* Select Hash and Compute lengths. */
/* getFirstHash gives us the smallest acceptable hash for this key
* strength */
hashtype = getFirstHash(L,N);
outlen = HASH_ResultLen(hashtype)*PR_BITS_PER_BYTE;
/* Step 3: n = Ceil(L/outlen)-1; (same as n = Floor((L-1)/outlen)) */
n = (L - 1) / outlen;
/* Step 4: b = L -1 - (n*outlen); (same as n = (L-1) mod outlen) */
b = (L - 1) % outlen;
seedlen = seedBytes * PR_BITS_PER_BYTE; /* bits in seed */
step_5:
/* ******************************************************************
** Step 5. (Step 1 in 186-1)
** "Choose an abitrary sequence of at least N bits and call it SEED.
** Let g be the length of SEED in bits."
*/
if (++iterations > MAX_ITERATIONS) { /* give up after a while */
PORT_SetError(SEC_ERROR_NEED_RANDOM);
goto cleanup;
}
seed->len = seedBytes;
CHECK_SEC_OK( getPQseed(seed, verify->arena) );
/* ******************************************************************
** Step 6. (Step 2 in 186-1)
**
** "Compute U = SHA[SEED] XOR SHA[(SEED+1) mod 2**g]. (186-1)"
** "Compute U = HASH[SEED] 2**(N-1). (186-3)"
**
** Step 7. (Step 3 in 186-1)
** "Form Q from U by setting the most signficant bit (the 2**159 bit)
** and the least signficant bit to 1. In terms of boolean operations,
** Q = U OR 2**159 OR 1. Note that 2**159 < Q < 2**160. (186-1)"
**
** "q = 2**(N-1) + U + 1 - (U mod 2) (186-3)
**
** Note: Both formulations are the same for U < 2**(N-1) and N=160
**
** If using Shawe-Taylor, We do the entire A.1.2.1.2 setps in the block
** FIPS186_3_ST_TYPE.
*/
if (type == FIPS186_1_TYPE) {
CHECK_SEC_OK( makeQfromSeed(seedlen, seed, &Q) );
} else if (type == FIPS186_3_TYPE) {
CHECK_SEC_OK( makeQ2fromSeed(hashtype, N, seed, &Q) );
} else {
/* FIPS186_3_ST_TYPE */
int qgen_counter, pgen_counter;
/* Step 1 (L,N) already checked for acceptability */
firstseed = *seed;
qgen_counter = 0;
/* Step 2. Use N and firstseed to generate random prime q
* using Apendix C.6 */
CHECK_SEC_OK( makePrimefromSeedShaweTaylor(hashtype, N, &firstseed, &Q,
&qseed, &qgen_counter) );
/* Step 3. Use floor(L/2+1) and qseed to generate random prime p0
* using Appendix C.6 */
pgen_counter = 0;
CHECK_SEC_OK( makePrimefromSeedShaweTaylor(hashtype, (L+1)/2+1,
&qseed, &p0, &pseed, &pgen_counter) );
/* Steps 4-22 FIPS 186-3 appendix A.1.2.1.2 */
CHECK_SEC_OK( makePrimefromPrimesShaweTaylor(hashtype, L,
&p0, &Q, &P, &pseed, &pgen_counter) );
/* combine all the seeds */
seed->len = firstseed.len +qseed.len + pseed.len;
seed->data = PORT_ArenaZAlloc(verify->arena, seed->len);
if (seed->data == NULL) {
goto cleanup;
}
PORT_Memcpy(seed->data, firstseed.data, firstseed.len);
PORT_Memcpy(seed->data+firstseed.len, pseed.data, pseed.len);
PORT_Memcpy(seed->data+firstseed.len+pseed.len, qseed.data, qseed.len);
counter = 0 ; /* (qgen_counter << 16) | pgen_counter; */
/* we've generated both P and Q now, skip to generating G */
goto generate_G;
}
/* ******************************************************************
** Step 8. (Step 4 in 186-1)
** "Use a robust primality testing algorithm to test whether q is prime."
**
** Appendix 2.1 states that a Rabin test with at least 50 iterations
** "will give an acceptable probability of error."
*/
/*CHECK_SEC_OK( prm_RabinTest(&Q, &passed) );*/
err = mpp_pprime(&Q, prime_testcount_q(L,N));
passed = (err == MP_YES) ? SECSuccess : SECFailure;
/* ******************************************************************
** Step 9. (Step 5 in 186-1) "If q is not prime, goto step 5 (1 in 186-1)."
*/
if (passed != SECSuccess)
goto step_5;
/* ******************************************************************
** Step 10.
** offset = 1;
**( Step 6b 186-1)"Let counter = 0 and offset = 2."
*/
offset = (type == FIPS186_1_TYPE) ? 2 : 1;
/*
** Step 11. (Step 6a,13a,14 in 186-1)
** For counter - 0 to (4L-1) do
**
*/
maxCount = L >= 1024 ? (4*L - 1) : 4095;
for (counter = 0; counter <= maxCount; counter++) {
/* ******************************************************************
** Step 11.1 (Step 7 in 186-1)
** "for j = 0 ... n let
** V_j = HASH[(SEED + offset + j) mod 2**seedlen]."
**
** Step 11.2 (Step 8 in 186-1)
** "W = V_0 + V_1*2**outlen+...+ V_n-1 * 2**((n-1)*outlen) +
** ((Vn* mod 2**b)*2**(n*outlen))"
** Step 11.3 (Step 8 in 186-1)
** "X = W + 2**(L-1)
** Note that 0 <= W < 2**(L-1) and hence 2**(L-1) <= X < 2**L."
**
** Step 11.4 (Step 9 in 186-1).
** "c = X mod 2q"
**
** Step 11.5 (Step 9 in 186-1).
** " p = X - (c - 1).
** Note that p is congruent to 1 mod 2q."
*/
CHECK_SEC_OK( makePfromQandSeed(hashtype, L, N, offset, seedlen,
seed, &Q, &P) );
/*************************************************************
** Step 11.6. (Step 10 in 186-1)
** "if p < 2**(L-1), then goto step 11.9. (step 13 in 186-1)"
*/
CHECK_MPI_OK( mpl_set_bit(&l, (mp_size)(L-1), 1) ); /* l = 2**(L-1) */
if (mp_cmp(&P, &l) < 0)
goto step_11_9;
/************************************************************
** Step 11.7 (step 11 in 186-1)
** "Perform a robust primality test on p."
*/
/*CHECK_SEC_OK( prm_RabinTest(&P, &passed) );*/
err = mpp_pprime(&P, prime_testcount_p(L, N));
passed = (err == MP_YES) ? SECSuccess : SECFailure;
/* ******************************************************************
** Step 11.8. "If p is determined to be primed return VALID
** values of p, q, seed and counter."
*/
if (passed == SECSuccess)
break;
step_11_9:
/* ******************************************************************
** Step 11.9. "offset = offset + n + 1."
*/
offset += n + 1;
}
/* ******************************************************************
** Step 12. "goto step 5."
**
** NOTE: if counter <= maxCount, then we exited the loop at Step 11.8
** and now need to return p,q, seed, and counter.
*/
if (counter > maxCount)
goto step_5;
generate_G:
/* ******************************************************************
** returning p, q, seed and counter
*/
if (type == FIPS186_1_TYPE) {
/* Generate g, This is called the "Unverifiable Generation of g
* in FIPA186-3 Appedix A.2.1. For compatibility we maintain
* this version of the code */
SECITEM_AllocItem(NULL, &hit, L/8); /* h is no longer than p */
if (!hit.data) goto cleanup;
do {
/* loop generate h until 1<h<p-1 and (h**[(p-1)/q])mod p > 1 */
CHECK_SEC_OK( generate_h_candidate(&hit, &H) );
CHECK_SEC_OK( makeGfromH(&P, &Q, &H, &G, &passed) );
} while (passed != PR_TRUE);
MPINT_TO_SECITEM(&H, &verify->h, verify->arena);
} else {
unsigned char index = 1; /* default to 1 */
verify->h.data = (unsigned char *)PORT_ArenaZAlloc(verify->arena, 1);
if (verify->h.data == NULL) { goto cleanup; }
verify->h.len = 1;
verify->h.data[0] = index;
/* Generate g, using the FIPS 186-3 Appendix A.23 */
CHECK_SEC_OK(makeGfromIndex(hashtype, &P, &Q, seed, index, &G) );
}
/* All generation is done. Now, save the PQG params. */
MPINT_TO_SECITEM(&P, ¶ms->prime, params->arena);
MPINT_TO_SECITEM(&Q, ¶ms->subPrime, params->arena);
MPINT_TO_SECITEM(&G, ¶ms->base, params->arena);
verify->counter = counter;
*pParams = params;
*pVfy = verify;
cleanup:
if (pseed.data) {
PORT_Free(pseed.data);
}
if (qseed.data) {
PORT_Free(qseed.data);
}
mp_clear(&P);
mp_clear(&Q);
mp_clear(&G);
mp_clear(&H);
mp_clear(&l);
mp_clear(&p0);
if (err) {
MP_TO_SEC_ERROR(err);
rv = SECFailure;
}
if (rv) {
PORT_FreeArena(params->arena, PR_TRUE);
PORT_FreeArena(verify->arena, PR_TRUE);
}
if (hit.data) {
SECITEM_FreeItem(&hit, PR_FALSE);
}
return rv;
}
SECStatus
PQG_ParamGen(unsigned int j, PQGParams **pParams, PQGVerify **pVfy)
{
unsigned int L; /* Length of P in bits. Per FIPS 186. */
unsigned int seedBytes;
if (j > 8 || !pParams || !pVfy) {
PORT_SetError(SEC_ERROR_INVALID_ARGS);
return SECFailure;
}
L = 512 + (j * 64); /* bits in P */
seedBytes = L/8;
return pqg_ParamGen(L, DSA1_Q_BITS, FIPS186_1_TYPE, seedBytes,
pParams, pVfy);
}
SECStatus
PQG_ParamGenSeedLen(unsigned int j, unsigned int seedBytes,
PQGParams **pParams, PQGVerify **pVfy)
{
unsigned int L; /* Length of P in bits. Per FIPS 186. */
if (j > 8 || !pParams || !pVfy) {
PORT_SetError(SEC_ERROR_INVALID_ARGS);
return SECFailure;
}
L = 512 + (j * 64); /* bits in P */
return pqg_ParamGen(L, DSA1_Q_BITS, FIPS186_1_TYPE, seedBytes,
pParams, pVfy);
}
SECStatus
PQG_ParamGenV2(unsigned int L, unsigned int N, unsigned int seedBytes,
PQGParams **pParams, PQGVerify **pVfy)
{
if (N == 0) {
N = pqg_get_default_N(L);
}
if (seedBytes == 0) {
/* seedBytes == L/8 for probable primes, N/8 for Shawe-Taylor Primes */
seedBytes = N/8;
}
if (pqg_validate_dsa2(L,N) != SECSuccess) {
/* error code already set */
return SECFailure;
}
return pqg_ParamGen(L, N, FIPS186_3_ST_TYPE, seedBytes, pParams, pVfy);
}
/*
* verify can use vfy structures returned from either FIPS186-1 or
* FIPS186-2, and can handle differences in selected Hash functions to
* generate the parameters.
*/
SECStatus
PQG_VerifyParams(const PQGParams *params,
const PQGVerify *vfy, SECStatus *result)
{
SECStatus rv = SECSuccess;
unsigned int g, n, L, N, offset, outlen;
mp_int p0, P, Q, G, P_, Q_, G_, r, h;
mp_err err = MP_OKAY;
int j;
unsigned int counter_max = 0; /* handle legacy L < 1024 */
int qseed_len;
SECItem pseed_ = {0, 0, 0};
HASH_HashType hashtype;
pqgGenType type;
#define CHECKPARAM(cond) \
if (!(cond)) { \
*result = SECFailure; \
goto cleanup; \
}
if (!params || !vfy || !result) {
PORT_SetError(SEC_ERROR_INVALID_ARGS);
return SECFailure;
}
/* always need at least p, q, and seed for any meaningful check */
if ((params->prime.len == 0) || (params->subPrime.len == 0) ||
(vfy->seed.len == 0)) {
PORT_SetError(SEC_ERROR_INVALID_ARGS);
return SECFailure;
}
/* we want to either check PQ or G or both. If we don't have G, make
* sure we have count so we can check P. */
if ((params->base.len == 0) && (vfy->counter == -1)) {
PORT_SetError(SEC_ERROR_INVALID_ARGS);
return SECFailure;
}
MP_DIGITS(&p0) = 0;
MP_DIGITS(&P) = 0;
MP_DIGITS(&Q) = 0;
MP_DIGITS(&G) = 0;
MP_DIGITS(&P_) = 0;
MP_DIGITS(&Q_) = 0;
MP_DIGITS(&G_) = 0;
MP_DIGITS(&r) = 0;
MP_DIGITS(&h) = 0;
CHECK_MPI_OK( mp_init(&p0) );
CHECK_MPI_OK( mp_init(&P) );
CHECK_MPI_OK( mp_init(&Q) );
CHECK_MPI_OK( mp_init(&G) );
CHECK_MPI_OK( mp_init(&P_) );
CHECK_MPI_OK( mp_init(&Q_) );
CHECK_MPI_OK( mp_init(&G_) );
CHECK_MPI_OK( mp_init(&r) );
CHECK_MPI_OK( mp_init(&h) );
*result = SECSuccess;
SECITEM_TO_MPINT(params->prime, &P);
SECITEM_TO_MPINT(params->subPrime, &Q);
/* if G isn't specified, just check P and Q */
if (params->base.len != 0) {
SECITEM_TO_MPINT(params->base, &G);
}
/* 1. Check (L,N) pair */
N = mpl_significant_bits(&Q);
L = mpl_significant_bits(&P);
if (L < 1024) {
/* handle DSA1 pqg parameters with less thatn 1024 bits*/
CHECKPARAM( N == DSA1_Q_BITS );
j = PQG_PBITS_TO_INDEX(L);
CHECKPARAM( j >= 0 && j <= 8 );
counter_max = 4096;
} else {
/* handle DSA2 parameters (includes DSA1, 1024 bits) */
CHECKPARAM(pqg_validate_dsa2(L, N) == SECSuccess);
counter_max = 4*L;
}
/* 3. G < P */
if (params->base.len != 0) {
CHECKPARAM( mp_cmp(&G, &P) < 0 );
}
/* 4. P % Q == 1 */
CHECK_MPI_OK( mp_mod(&P, &Q, &r) );
CHECKPARAM( mp_cmp_d(&r, 1) == 0 );
/* 5. Q is prime */
CHECKPARAM( mpp_pprime(&Q, prime_testcount_q(L,N)) == MP_YES );
/* 6. P is prime */
CHECKPARAM( mpp_pprime(&P, prime_testcount_p(L,N)) == MP_YES );
/* Steps 7-12 are done only if the optional PQGVerify is supplied. */
/* continue processing P */
/* 7. counter < 4*L */
CHECKPARAM( (vfy->counter == -1) || (vfy->counter < counter_max) );
/* 8. g >= N and g < 2*L (g is length of seed in bits) */
g = vfy->seed.len * 8;
CHECKPARAM( g >= N && g < counter_max/2 );
/* 9. Q generated from SEED matches Q in PQGParams. */
/* This function checks all possible hash and generation types to
* find a Q_ which matches Q. */
CHECKPARAM( findQfromSeed(L, N, g, &vfy->seed, &Q, &Q_, &qseed_len,
&hashtype, &type) == SECSuccess );
CHECKPARAM( mp_cmp(&Q, &Q_) == 0 );
if (type == FIPS186_3_ST_TYPE) {
SECItem qseed = { 0, 0, 0 };
SECItem pseed = { 0, 0, 0 };
int first_seed_len;
int pgen_counter = 0;
/* extract pseed and qseed from domain_parameter_seed, which is
* first_seed || pseed || qseed. qseed is first_seed + small_integer
* pseed is qseed + small_integer. This means most of the time
* first_seed.len == qseed.len == pseed.len. Rarely qseed.len and/or
* pseed.len will be one greater than first_seed.len, so we can
* depend on the fact that
* first_seed.len = floor(domain_parameter_seed.len/3).
* findQfromSeed returned qseed.len, so we can calculate pseed.len as
* pseed.len = domain_parameter_seed.len - first_seed.len - qseed.len
* this is probably over kill, since 99.999% of the time they will all
* be equal.
*
* With the lengths, we can now find the offsets;
* first_seed.data = domain_parameter_seed.data + 0
* pseed.data = domain_parameter_seed.data + first_seed.len
* qseed.data = domain_parameter_seed.data
* + domain_paramter_seed.len - qseed.len
*
*/
first_seed_len = vfy->seed.len/3;
CHECKPARAM(qseed_len < vfy->seed.len);
CHECKPARAM(first_seed_len*8 > N-1);
CHECKPARAM(first_seed_len+qseed_len < vfy->seed.len);
qseed.len = qseed_len;
qseed.data = vfy->seed.data + vfy->seed.len - qseed.len;
pseed.len = vfy->seed.len - (first_seed_len+qseed_len);
pseed.data = vfy->seed.data + first_seed_len;
/*
* now complete FIPS 186-3 A.1.2.1.2. Step 1 was completed
* above in our initial checks, Step 2 was completed by
* findQfromSeed */
/* Step 3 (status, c0, prime_seed, prime_gen_counter) =
** (ST_Random_Prime((ceil(length/2)+1, input_seed)
*/
CHECK_SEC_OK( makePrimefromSeedShaweTaylor(hashtype, (L+1)/2+1,
&qseed, &p0, &pseed_, &pgen_counter) );
/* Steps 4-22 FIPS 186-3 appendix A.1.2.1.2 */
CHECK_SEC_OK( makePrimefromPrimesShaweTaylor(hashtype, L,
&p0, &Q_, &P_, &pseed_, &pgen_counter) );
CHECKPARAM( mp_cmp(&P, &P_) == 0 );
/* make sure pseed wasn't tampered with (since it is part of
* calculating G) */
CHECKPARAM( SECITEM_CompareItem(&pseed, &pseed_) == SECEqual );
} else if (vfy->counter == -1) {
/* If counter is set to -1, we are really only verifying G, skip
* the remainder of the checks for P */
CHECKPARAM(type != FIPS186_1_TYPE); /* we only do this for DSA2 */
} else {
/* 10. P generated from (L, counter, g, SEED, Q) matches P
* in PQGParams. */
outlen = HASH_ResultLen(hashtype)*PR_BITS_PER_BYTE;
n = (L - 1) / outlen;
offset = vfy->counter * (n + 1) + ((type == FIPS186_1_TYPE) ? 2 : 1);
CHECK_SEC_OK( makePfromQandSeed(hashtype, L, N, offset, g, &vfy->seed,
&Q, &P_) );
CHECKPARAM( mp_cmp(&P, &P_) == 0 );
}
/* now check G, skip if don't have a g */
if (params->base.len == 0) goto cleanup;
/* first Always check that G is OK FIPS186-3 A.2.2 & A.2.4*/
/* 1. 2 < G < P-1 */
/* P is prime, p-1 == zero 1st bit */
CHECK_MPI_OK( mpl_set_bit(&P, 0, 0) );
CHECKPARAM( mp_cmp_d(&G, 2) > 0 && mp_cmp(&G, &P) < 0 );
CHECK_MPI_OK( mpl_set_bit(&P, 0, 1) ); /* set it back */
/* 2. verify g**q mod p == 1 */
CHECK_MPI_OK( mp_exptmod(&G, &Q, &P, &h) ); /* h = G ** Q mod P */
CHECKPARAM(mp_cmp_d(&h, 1) == 0);
/* no h, the above is the best we can do */
if (vfy->h.len == 0) {
if (type != FIPS186_1_TYPE) {
*result = SECWouldBlock;
}
goto cleanup;
}
/*
* If h is one byte and FIPS186-3 was used to generate Q (we've verified
* Q was generated from seed already, then we assume that FIPS 186-3
* appendix A.2.3 was used to generate G. Otherwise we assume A.2.1 was
* used to generate G.
*/
if ((vfy->h.len == 1) && (type != FIPS186_1_TYPE)) {
/* A.2.3 */
CHECK_SEC_OK(makeGfromIndex(hashtype, &P, &Q, &vfy->seed,
vfy->h.data[0], &G_) );
CHECKPARAM( mp_cmp(&G, &G_) == 0 );
} else {
int passed;
/* A.2.1 */
SECITEM_TO_MPINT(vfy->h, &h);
/* 11. 1 < h < P-1 */
/* P is prime, p-1 == zero 1st bit */
CHECK_MPI_OK( mpl_set_bit(&P, 0, 0) );
CHECKPARAM( mp_cmp_d(&G, 2) > 0 && mp_cmp(&G, &P) );
CHECK_MPI_OK( mpl_set_bit(&P, 0, 1) ); /* set it back */
/* 12. G generated from h matches G in PQGParams. */
CHECK_SEC_OK( makeGfromH(&P, &Q, &h, &G_, &passed) );
CHECKPARAM( passed && mp_cmp(&G, &G_) == 0 );
}
cleanup:
mp_clear(&p0);
mp_clear(&P);
mp_clear(&Q);
mp_clear(&G);
mp_clear(&P_);
mp_clear(&Q_);
mp_clear(&G_);
mp_clear(&r);
mp_clear(&h);
if (pseed_.data) {
SECITEM_FreeItem(&pseed_,PR_FALSE);
}
if (err) {
MP_TO_SEC_ERROR(err);
rv = SECFailure;
}
return rv;
}
/**************************************************************************
* Free the PQGParams struct and the things it points to. *
**************************************************************************/
void
PQG_DestroyParams(PQGParams *params)
{
if (params == NULL)
return;
if (params->arena != NULL) {
PORT_FreeArena(params->arena, PR_FALSE); /* don't zero it */
} else {
SECITEM_FreeItem(¶ms->prime, PR_FALSE); /* don't free prime */
SECITEM_FreeItem(¶ms->subPrime, PR_FALSE); /* don't free subPrime */
SECITEM_FreeItem(¶ms->base, PR_FALSE); /* don't free base */
PORT_Free(params);
}
}
/**************************************************************************
* Free the PQGVerify struct and the things it points to. *
**************************************************************************/
void
PQG_DestroyVerify(PQGVerify *vfy)
{
if (vfy == NULL)
return;
if (vfy->arena != NULL) {
PORT_FreeArena(vfy->arena, PR_FALSE); /* don't zero it */
} else {
SECITEM_FreeItem(&vfy->seed, PR_FALSE); /* don't free seed */
SECITEM_FreeItem(&vfy->h, PR_FALSE); /* don't free h */
PORT_Free(vfy);
}
}