/* 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.
 */
static 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 */
static 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(&params->prime)*PR_BITS_PER_BYTE;
    N = PQG_GetLength(&params->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(&params->prime)*PR_BITS_PER_BYTE;
    N = PQG_GetLength(&params->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)
static 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.  */
      unsigned 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);
    PORT_Memset(x, 0, sizeof(x));
    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
*/
static 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.  */
      unsigned 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);
    PORT_Memset(x, 0, sizeof(x));
    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. */
      unsigned 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)) {
	unsigned 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 = NULL;
    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  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 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) );

    /* parameters have been passed in, only generate G */
    if (*pParams != NULL) {
	/* we only support G index generation if generating separate from PQ */
	if ((*pVfy == NULL) || (type == FIPS186_1_TYPE) || 
	    ((*pVfy)->h.len != 1) || ((*pVfy)->h.data == NULL) || 
	    ((*pVfy)->seed.data == NULL) || ((*pVfy)->seed.len == 0)) {
	    PORT_SetError(SEC_ERROR_INVALID_ARGS);
	    return SECFailure;
	}
	params = *pParams;
	verify = *pVfy;

	/* fill in P Q,  */
	SECITEM_TO_MPINT((*pParams)->prime,    &P);
	SECITEM_TO_MPINT((*pParams)->subPrime, &Q);
    	hashtype = getFirstHash(L,N);
	CHECK_SEC_OK(makeGfromIndex(hashtype, &P, &Q, &(*pVfy)->seed, 
						(*pVfy)->h.data[0], &G) );
	MPINT_TO_SECITEM(&G, &(*pParams)->base,     (*pParams)->arena);
	goto cleanup;
    }
    /* 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: (skipped since we don't use b): b = L -1 - (n*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 */
	unsigned 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, &params->prime,    params->arena);
    MPINT_TO_SECITEM(&Q, &params->subPrime, params->arena);
    MPINT_TO_SECITEM(&G, &params->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) {
	if (params) {
	    PORT_FreeArena(params->arena, PR_TRUE);
	}
	if (verify) {
	    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 */
    unsigned 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 };
	unsigned int first_seed_len;
	unsigned 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(&params->prime,    PR_FALSE); /* don't free prime */
	SECITEM_FreeItem(&params->subPrime, PR_FALSE); /* don't free subPrime */
	SECITEM_FreeItem(&params->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);
    }
}
