text: /* 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/. */
  
  /*
   * RSA key generation, public key op, private key op.
   */
  #ifdef FREEBL_NO_DEPEND
  #include "stubs.h"
  #endif
  
  #include "secerr.h"
  
  #include "prclist.h"
  #include "nssilock.h"
  #include "prinit.h"
  #include "blapi.h"
  #include "mpi.h"
  #include "mpprime.h"
  #include "mplogic.h"
  #include "secmpi.h"
  #include "secitem.h"
  #include "blapii.h"
  
  /*
  ** Number of times to attempt to generate a prime (p or q) from a random
  ** seed (the seed changes for each iteration).
  */
  #define MAX_PRIME_GEN_ATTEMPTS 10
  /*
  ** Number of times to attempt to generate a key.  The primes p and q change
  ** for each attempt.
  */
  #define MAX_KEY_GEN_ATTEMPTS 10
  
  /* Blinding Parameters max cache size  */
  #define RSA_BLINDING_PARAMS_MAX_CACHE_SIZE 20
  
  /* exponent should not be greater than modulus */
  #define BAD_RSA_KEY_SIZE(modLen, expLen) \
      ((expLen) > (modLen) || (modLen) > RSA_MAX_MODULUS_BITS/8 || \
      (expLen) > RSA_MAX_EXPONENT_BITS/8)
  
  struct blindingParamsStr;
  typedef struct blindingParamsStr blindingParams;
  
  struct blindingParamsStr {
      blindingParams *next;
      mp_int         f, g;             /* blinding parameter                 */
      int            counter;          /* number of remaining uses of (f, g) */
  };
  
  /*
  ** RSABlindingParamsStr
  **
  ** For discussion of Paul Kocher's timing attack against an RSA private key
  ** operation, see http://www.cryptography.com/timingattack/paper.html.  The 
  ** countermeasure to this attack, known as blinding, is also discussed in 
  ** the Handbook of Applied Cryptography, 11.118-11.119.
  */
  struct RSABlindingParamsStr
  {
      /* Blinding-specific parameters */
      PRCList   link;                  /* link to list of structs            */
      SECItem   modulus;               /* list element "key"                 */
      blindingParams *free, *bp;       /* Blinding parameters queue          */
      blindingParams array[RSA_BLINDING_PARAMS_MAX_CACHE_SIZE];
  };
  typedef struct RSABlindingParamsStr RSABlindingParams;
  
  /*
  ** RSABlindingParamsListStr
  **
  ** List of key-specific blinding params.  The arena holds the volatile pool
  ** of memory for each entry and the list itself.  The lock is for list
  ** operations, in this case insertions and iterations, as well as control
  ** of the counter for each set of blinding parameters.
  */
  struct RSABlindingParamsListStr
  {
      PZLock  *lock;   /* Lock for the list   */
      PRCondVar *cVar; /* Condidtion Variable */
      int  waitCount;  /* Number of threads waiting on cVar */
      PRCList  head;   /* Pointer to the list */
  };
  
  /*
  ** The master blinding params list.
  */
  static struct RSABlindingParamsListStr blindingParamsList = { 0 };
  
  /* Number of times to reuse (f, g).  Suggested by Paul Kocher */
  #define RSA_BLINDING_PARAMS_MAX_REUSE 50
  
  /* Global, allows optional use of blinding.  On by default. */
  /* Cannot be changed at the moment, due to thread-safety issues. */
  static PRBool nssRSAUseBlinding = PR_TRUE;
  
  static SECStatus
  rsa_build_from_primes(const mp_int *p, const mp_int *q,
  		mp_int *e, PRBool needPublicExponent,
  		mp_int *d, PRBool needPrivateExponent,
  		RSAPrivateKey *key, unsigned int keySizeInBits)
  {
      mp_int n, phi;
      mp_int psub1, qsub1, tmp;
      mp_err   err = MP_OKAY;
      SECStatus rv = SECSuccess;
      MP_DIGITS(&n)     = 0;
      MP_DIGITS(&phi)   = 0;
      MP_DIGITS(&psub1) = 0;
      MP_DIGITS(&qsub1) = 0;
      MP_DIGITS(&tmp)   = 0;
      CHECK_MPI_OK( mp_init(&n)     );
      CHECK_MPI_OK( mp_init(&phi)   );
      CHECK_MPI_OK( mp_init(&psub1) );
      CHECK_MPI_OK( mp_init(&qsub1) );
      CHECK_MPI_OK( mp_init(&tmp)   );
      /* p and q must be distinct. */
      if (mp_cmp(p, q) == 0) {
  	PORT_SetError(SEC_ERROR_NEED_RANDOM);
  	rv = SECFailure;
  	goto cleanup;
      }
      /* 1.  Compute n = p*q */
      CHECK_MPI_OK( mp_mul(p, q, &n) );
      /*     verify that the modulus has the desired number of bits */
      if ((unsigned)mpl_significant_bits(&n) != keySizeInBits) {
  	PORT_SetError(SEC_ERROR_NEED_RANDOM);
  	rv = SECFailure;
  	goto cleanup;
      }
  
      /* at least one exponent must be given */
      PORT_Assert(!(needPublicExponent && needPrivateExponent));
  
      /* 2.  Compute phi = (p-1)*(q-1) */
      CHECK_MPI_OK( mp_sub_d(p, 1, &psub1) );
      CHECK_MPI_OK( mp_sub_d(q, 1, &qsub1) );
      if (needPublicExponent || needPrivateExponent) {
  	CHECK_MPI_OK( mp_mul(&psub1, &qsub1, &phi) );
  	/* 3.  Compute d = e**-1 mod(phi) */
  	/*     or      e = d**-1 mod(phi) as necessary */
  	if (needPublicExponent) {
  	    err = mp_invmod(d, &phi, e);
  	} else {
  	    err = mp_invmod(e, &phi, d);
  	}
      } else {
  	err = MP_OKAY;
      }
      /*     Verify that phi(n) and e have no common divisors */
      if (err != MP_OKAY) {
  	if (err == MP_UNDEF) {
  	    PORT_SetError(SEC_ERROR_NEED_RANDOM);
  	    err = MP_OKAY; /* to keep PORT_SetError from being called again */
  	    rv = SECFailure;
  	}
  	goto cleanup;
      }
  
      /* 4.  Compute exponent1 = d mod (p-1) */
      CHECK_MPI_OK( mp_mod(d, &psub1, &tmp) );
      MPINT_TO_SECITEM(&tmp, &key->exponent1, key->arena);
      /* 5.  Compute exponent2 = d mod (q-1) */
      CHECK_MPI_OK( mp_mod(d, &qsub1, &tmp) );
      MPINT_TO_SECITEM(&tmp, &key->exponent2, key->arena);
      /* 6.  Compute coefficient = q**-1 mod p */
      CHECK_MPI_OK( mp_invmod(q, p, &tmp) );
      MPINT_TO_SECITEM(&tmp, &key->coefficient, key->arena);
  
      /* copy our calculated results, overwrite what is there */
      key->modulus.data = NULL;
      MPINT_TO_SECITEM(&n, &key->modulus, key->arena);
      key->privateExponent.data = NULL;
      MPINT_TO_SECITEM(d, &key->privateExponent, key->arena);
      key->publicExponent.data = NULL;
      MPINT_TO_SECITEM(e, &key->publicExponent, key->arena);
      key->prime1.data = NULL;
      MPINT_TO_SECITEM(p, &key->prime1, key->arena);
      key->prime2.data = NULL;
      MPINT_TO_SECITEM(q, &key->prime2, key->arena);
  cleanup:
      mp_clear(&n);
      mp_clear(&phi);
      mp_clear(&psub1);
      mp_clear(&qsub1);
      mp_clear(&tmp);
      if (err) {
  	MP_TO_SEC_ERROR(err);
  	rv = SECFailure;
      }
      return rv;
  }
  static SECStatus
  generate_prime(mp_int *prime, int primeLen)
  {
      mp_err   err = MP_OKAY;
      SECStatus rv = SECSuccess;
      unsigned long counter = 0;
      int piter;
      unsigned char *pb = NULL;
      pb = PORT_Alloc(primeLen);
      if (!pb) {
  	PORT_SetError(SEC_ERROR_NO_MEMORY);
  	goto cleanup;
      }
      for (piter = 0; piter < MAX_PRIME_GEN_ATTEMPTS; piter++) {
  	CHECK_SEC_OK( RNG_GenerateGlobalRandomBytes(pb, primeLen) );
  	pb[0]          |= 0xC0; /* set two high-order bits */
  	pb[primeLen-1] |= 0x01; /* set low-order bit       */
  	CHECK_MPI_OK( mp_read_unsigned_octets(prime, pb, primeLen) );
  	err = mpp_make_prime(prime, primeLen * 8, PR_FALSE, &counter);
  	if (err != MP_NO)
  	    goto cleanup;
  	/* keep going while err == MP_NO */
      }
  cleanup:
      if (pb)
  	PORT_ZFree(pb, primeLen);
      if (err) {
  	MP_TO_SEC_ERROR(err);
  	rv = SECFailure;
      }
      return rv;
  }
  
  /*
  ** Generate and return a new RSA public and private key.
  **	Both keys are encoded in a single RSAPrivateKey structure.
  **	"cx" is the random number generator context
  **	"keySizeInBits" is the size of the key to be generated, in bits.
  **	   512, 1024, etc.
  **	"publicExponent" when not NULL is a pointer to some data that
  **	   represents the public exponent to use. The data is a byte
  **	   encoded integer, in "big endian" order.
  */
  RSAPrivateKey *
  RSA_NewKey(int keySizeInBits, SECItem *publicExponent)
  {
      unsigned int primeLen;
      mp_int p, q, e, d;
      int kiter;
      mp_err   err = MP_OKAY;
      SECStatus rv = SECSuccess;
      int prerr = 0;
      RSAPrivateKey *key = NULL;
      PLArenaPool *arena = NULL;
      /* Require key size to be a multiple of 16 bits. */
      if (!publicExponent || keySizeInBits % 16 != 0 ||
  	    BAD_RSA_KEY_SIZE(keySizeInBits/8, publicExponent->len)) {
  	PORT_SetError(SEC_ERROR_INVALID_ARGS);
  	return NULL;
      }
      /* 1. Allocate arena & key */
      arena = PORT_NewArena(NSS_FREEBL_DEFAULT_CHUNKSIZE);
      if (!arena) {
  	PORT_SetError(SEC_ERROR_NO_MEMORY);
  	return NULL;
      }
      key = PORT_ArenaZNew(arena, RSAPrivateKey);
      if (!key) {
  	PORT_SetError(SEC_ERROR_NO_MEMORY);
  	PORT_FreeArena(arena, PR_TRUE);
  	return NULL;
      }
      key->arena = arena;
      /* length of primes p and q (in bytes) */
      primeLen = keySizeInBits / (2 * PR_BITS_PER_BYTE);
      MP_DIGITS(&p) = 0;
      MP_DIGITS(&q) = 0;
      MP_DIGITS(&e) = 0;
      MP_DIGITS(&d) = 0;
      CHECK_MPI_OK( mp_init(&p) );
      CHECK_MPI_OK( mp_init(&q) );
      CHECK_MPI_OK( mp_init(&e) );
      CHECK_MPI_OK( mp_init(&d) );
      /* 2.  Set the version number (PKCS1 v1.5 says it should be zero) */
      SECITEM_AllocItem(arena, &key->version, 1);
      key->version.data[0] = 0;
      /* 3.  Set the public exponent */
      SECITEM_TO_MPINT(*publicExponent, &e);
      kiter = 0;
      do {
  	prerr = 0;
  	PORT_SetError(0);
  	CHECK_SEC_OK( generate_prime(&p, primeLen) );
  	CHECK_SEC_OK( generate_prime(&q, primeLen) );
  	/* Assure p > q */
  	/* NOTE: PKCS #1 does not require p > q, and NSS doesn't use any
  	 * implementation optimization that requires p > q. We can remove
  	 * this code in the future.
  	 */
  	if (mp_cmp(&p, &q) < 0)
  	    mp_exch(&p, &q);
  	/* Attempt to use these primes to generate a key */
  	rv = rsa_build_from_primes(&p, &q, 
  			&e, PR_FALSE,  /* needPublicExponent=false */
  			&d, PR_TRUE,   /* needPrivateExponent=true */
  			key, keySizeInBits);
  	if (rv == SECSuccess)
  	    break; /* generated two good primes */
  	prerr = PORT_GetError();
  	kiter++;
  	/* loop until have primes */
      } while (prerr == SEC_ERROR_NEED_RANDOM && kiter < MAX_KEY_GEN_ATTEMPTS);
      if (prerr)
  	goto cleanup;
  cleanup:
      mp_clear(&p);
      mp_clear(&q);
      mp_clear(&e);
      mp_clear(&d);
      if (err) {
  	MP_TO_SEC_ERROR(err);
  	rv = SECFailure;
      }
      if (rv && arena) {
  	PORT_FreeArena(arena, PR_TRUE);
  	key = NULL;
      }
      return key;
  }
  
  mp_err
  rsa_is_prime(mp_int *p) {
      int res;
  
      /* run a Fermat test */
      res = mpp_fermat(p, 2);
      if (res != MP_OKAY) {
  	return res;
      }
  
      /* If that passed, run some Miller-Rabin tests */
      res = mpp_pprime(p, 2);
      return res;
  }
  
  /*
   * Try to find the two primes based on 2 exponents plus either a prime
   *   or a modulus.
   *
   * In: e, d and either p or n (depending on the setting of hasModulus).
   * Out: p,q.
   * 
   * Step 1, Since d = e**-1 mod phi, we know that d*e == 1 mod phi, or
   *	d*e = 1+k*phi, or d*e-1 = k*phi. since d is less than phi and e is
   *	usually less than d, then k must be an integer between e-1 and 1 
   *	(probably on the order of e).
   * Step 1a, If we were passed just a prime, we can divide k*phi by that
   *      prime-1 and get k*(q-1). This will reduce the size of our division
   *      through the rest of the loop.
   * Step 2, Loop through the values k=e-1 to 1 looking for k. k should be on
   *	the order or e, and e is typically small. This may take a while for
   *	a large random e. We are looking for a k that divides kphi
   *	evenly. Once we find a k that divides kphi evenly, we assume it 
   *	is the true k. It's possible this k is not the 'true' k but has 
   *	swapped factors of p-1 and/or q-1. Because of this, we 
   *	tentatively continue Steps 3-6 inside this loop, and may return looking
   *	for another k on failure.
   * Step 3, Calculate are tentative phi=kphi/k. Note: real phi is (p-1)*(q-1).
   * Step 4a, if we have a prime, kphi is already k*(q-1), so phi is or tenative
   *      q-1. q = phi+1. If k is correct, q should be the right length and 
   *      prime.
   * Step 4b, It's possible q-1 and k could have swapped factors. We now have a
   * 	possible solution that meets our criteria. It may not be the only 
   *      solution, however, so we keep looking. If we find more than one, 
   *      we will fail since we cannot determine which is the correct
   *      solution, and returning the wrong modulus will compromise both
   *      moduli. If no other solution is found, we return the unique solution.
   * Step 5a, If we have the modulus (n=pq), then use the following formula to 
   * 	calculate  s=(p+q): , phi = (p-1)(q-1) = pq  -p-q +1 = n-s+1. so
   *	s=n-phi+1.
   * Step 5b, Use n=pq and s=p+q to solve for p and q as follows:
   *	since q=s-p, then n=p*(s-p)= sp - p^2, rearranging p^2-s*p+n = 0.
   *	from the quadratic equation we have p=1/2*(s+sqrt(s*s-4*n)) and
   *	q=1/2*(s-sqrt(s*s-4*n)) if s*s-4*n is a perfect square, we are DONE.
   *	If it is not, continue in our look looking for another k. NOTE: the
   *	code actually distributes the 1/2 and results in the equations:
   *	sqrt = sqrt(s/2*s/2-n), p=s/2+sqrt, q=s/2-sqrt. The algebra saves us
   *	and extra divide by 2 and a multiply by 4.
   * 
   * This will return p & q. q may be larger than p in the case that p was given
   * and it was the smaller prime.
   */
  static mp_err
  rsa_get_primes_from_exponents(mp_int *e, mp_int *d, mp_int *p, mp_int *q,
  			      mp_int *n, PRBool hasModulus, 
  			      unsigned int keySizeInBits)
  {
      mp_int kphi; /* k*phi */
      mp_int k;    /* current guess at 'k' */
      mp_int phi;  /* (p-1)(q-1) */
      mp_int s;    /* p+q/2 (s/2 in the algebra) */
      mp_int r;    /* remainder */
      mp_int tmp; /* p-1 if p is given, n+1 is modulus is given */
      mp_int sqrt; /* sqrt(s/2*s/2-n) */
      mp_err err = MP_OKAY;
      unsigned int order_k;
  
      MP_DIGITS(&kphi) = 0;
      MP_DIGITS(&phi) = 0;
      MP_DIGITS(&s) = 0;
      MP_DIGITS(&k) = 0;
      MP_DIGITS(&r) = 0;
      MP_DIGITS(&tmp) = 0;
      MP_DIGITS(&sqrt) = 0;
      CHECK_MPI_OK( mp_init(&kphi) );
      CHECK_MPI_OK( mp_init(&phi) );
      CHECK_MPI_OK( mp_init(&s) );
      CHECK_MPI_OK( mp_init(&k) );
      CHECK_MPI_OK( mp_init(&r) );
      CHECK_MPI_OK( mp_init(&tmp) );
      CHECK_MPI_OK( mp_init(&sqrt) );
  
      /* our algorithm looks for a factor k whose maximum size is dependent
       * on the size of our smallest exponent, which had better be the public
       * exponent (if it's the private, the key is vulnerable to a brute force
       * attack).
       * 
       * since our factor search is linear, we need to limit the maximum
       * size of the public key. this should not be a problem normally, since 
       * public keys are usually small. 
       *
       * if we want to handle larger public key sizes, we should have
       * a version which tries to 'completely' factor k*phi (where completely
       * means 'factor into primes, or composites with which are products of
       * large primes). Once we have all the factors, we can sort them out and
       * try different combinations to form our phi. The risk is if (p-1)/2,
       * (q-1)/2, and k are all large primes. In any case if the public key
       * is small (order of 20 some bits), then a linear search for k is 
       * manageable.
       */
      if (mpl_significant_bits(e) > 23) {
  	err=MP_RANGE;
  	goto cleanup;
      }
  
      /* calculate k*phi = e*d - 1 */
      CHECK_MPI_OK( mp_mul(e, d, &kphi) );
      CHECK_MPI_OK( mp_sub_d(&kphi, 1, &kphi) );
  
  
      /* kphi is (e*d)-1, which is the same as k*(p-1)(q-1)
       * d < (p-1)(q-1), therefor k must be less than e-1
       * We can narrow down k even more, though. Since p and q are odd and both 
       * have their high bit set, then we know that phi must be on order of 
       * keySizeBits.
       */
      order_k = (unsigned)mpl_significant_bits(&kphi) - keySizeInBits;
  
      /* for (k=kinit; order(k) >= order_k; k--) { */
      /* k=kinit: k can't be bigger than  kphi/2^(keySizeInBits -1) */
      CHECK_MPI_OK( mp_2expt(&k,keySizeInBits-1) );
      CHECK_MPI_OK( mp_div(&kphi, &k, &k, NULL));
      if (mp_cmp(&k,e) >= 0) {
  	/* also can't be bigger then e-1 */
          CHECK_MPI_OK( mp_sub_d(e, 1, &k) );
      }
  
      /* calculate our temp value */
      /* This saves recalculating this value when the k guess is wrong, which
       * is reasonably frequent. */
      /* for the modulus case, tmp = n+1 (used to calculate p+q = tmp - phi) */
      /* for the prime case, tmp = p-1 (used to calculate q-1= phi/tmp) */
      if (hasModulus) {
  	CHECK_MPI_OK( mp_add_d(n, 1, &tmp) );
      } else {
  	CHECK_MPI_OK( mp_sub_d(p, 1, &tmp) );
  	CHECK_MPI_OK(mp_div(&kphi,&tmp,&kphi,&r));
  	if (mp_cmp_z(&r) != 0) {
  	    /* p-1 doesn't divide kphi, some parameter wasn't correct */
  	    err=MP_RANGE;
  	    goto cleanup;
  	}
  	mp_zero(q);
  	/* kphi is now k*(q-1) */
      }
  
      /* rest of the for loop */
      for (; (err == MP_OKAY) && (mpl_significant_bits(&k) >= order_k); 
  						err = mp_sub_d(&k, 1, &k)) {
  	/* looking for k as a factor of kphi */
  	CHECK_MPI_OK(mp_div(&kphi,&k,&phi,&r));
  	if (mp_cmp_z(&r) != 0) {
  	    /* not a factor, try the next one */
  	    continue;
  	}
  	/* we have a possible phi, see if it works */
  	if (!hasModulus) {
  	    if ((unsigned)mpl_significant_bits(&phi) != keySizeInBits/2) {
  		/* phi is not the right size */
  		continue;
  	    }
  	    /* phi should be divisible by 2, since
  	     * q is odd and phi=(q-1). */
  	    if (mpp_divis_d(&phi,2) == MP_NO) {
  		/* phi is not divisible by 4 */
  		continue;
  	    }
  	    /* we now have a candidate for the second prime */
  	    CHECK_MPI_OK(mp_add_d(&phi, 1, &tmp));
  	    
  	    /* check to make sure it is prime */
  	    err = rsa_is_prime(&tmp);
  	    if (err != MP_OKAY) {
  		if (err == MP_NO) {
  		    /* No, then we still have the wrong phi */
  		    err = MP_OKAY;
          	    continue;
  		}
  		goto cleanup;
  	    }
  	    /*
  	     * It is possible that we have the wrong phi if 
  	     * k_guess*(q_guess-1) = k*(q-1) (k and q-1 have swapped factors).
  	     * since our q_quess is prime, however. We have found a valid
  	     * rsa key because:
  	     *   q is the correct order of magnitude.
  	     *   phi = (p-1)(q-1) where p and q are both primes.
  	     *   e*d mod phi = 1.
  	     * There is no way to know from the info given if this is the 
  	     * original key. We never want to return the wrong key because if
  	     * two moduli with the same factor is known, then euclid's gcd
  	     * algorithm can be used to find that factor. Even though the 
  	     * caller didn't pass the original modulus, it doesn't mean the
  	     * modulus wasn't known or isn't available somewhere. So to be safe
  	     * if we can't be sure we have the right q, we don't return any.
  	     * 
  	     * So to make sure we continue looking for other valid q's. If none
  	     * are found, then we can safely return this one, otherwise we just
  	     * fail */
  	    if (mp_cmp_z(q) != 0) {
  		/* this is the second valid q, don't return either, 
  		 * just fail */
  		err = MP_RANGE;
  		break;
  	    }
  	    /* we only have one q so far, save it and if no others are found,
  	     * it's safe to return it */
  	    CHECK_MPI_OK(mp_copy(&tmp, q));
  	    continue;
  	}
  	/* test our tentative phi */
  	/* phi should be the correct order */
  	if ((unsigned)mpl_significant_bits(&phi) != keySizeInBits) {
  	    /* phi is not the right size */
  	    continue;
  	}
  	/* phi should be divisible by 4, since
  	 * p and q are odd and phi=(p-1)(q-1). */
  	if (mpp_divis_d(&phi,4) == MP_NO) {
  	    /* phi is not divisible by 4 */
  	    continue;
  	}
  	/* n was given, calculate s/2=(p+q)/2 */
  	CHECK_MPI_OK( mp_sub(&tmp, &phi, &s) );
  	CHECK_MPI_OK( mp_div_2(&s, &s) );
  
  	/* calculate sqrt(s/2*s/2-n) */
  	CHECK_MPI_OK(mp_sqr(&s,&sqrt));
  	CHECK_MPI_OK(mp_sub(&sqrt,n,&r));  /* r as a tmp */
  	CHECK_MPI_OK(mp_sqrt(&r,&sqrt));
  	/* make sure it's a perfect square */
  	/* r is our original value we took the square root of */
  	/* q is the square of our tentative square root. They should be equal*/
  	CHECK_MPI_OK(mp_sqr(&sqrt,q)); /* q as a tmp */
  	if (mp_cmp(&r,q) != 0) {
  	    /* sigh according to the doc, mp_sqrt could return sqrt-1 */
  	   CHECK_MPI_OK(mp_add_d(&sqrt,1,&sqrt));
  	   CHECK_MPI_OK(mp_sqr(&sqrt,q));
  	   if (mp_cmp(&r,q) != 0) {
  		/* s*s-n not a perfect square, this phi isn't valid, find 			 * another.*/
  		continue;
  	    }
  	}
  
  	/* NOTE: In this case we know we have the one and only answer.
  	 * "Why?", you ask. Because:
  	 *    1) n is a composite of two large primes (or it wasn't a
  	 *       valid RSA modulus).
  	 *    2) If we know any number such that x^2-n is a perfect square 
  	 *       and x is not (n+1)/2, then we can calculate 2 non-trivial
  	 *       factors of n.
  	 *    3) Since we know that n has only 2 non-trivial prime factors, 
  	 *       we know the two factors we have are the only possible factors.
  	 */
  
  	/* Now we are home free to calculate p and q */
  	/* p = s/2 + sqrt, q= s/2 - sqrt */
  	CHECK_MPI_OK(mp_add(&s,&sqrt,p));
  	CHECK_MPI_OK(mp_sub(&s,&sqrt,q));
  	break;
      }
      if ((unsigned)mpl_significant_bits(&k) < order_k) {
  	if (hasModulus || (mp_cmp_z(q) == 0)) {
  	    /* If we get here, something was wrong with the parameters we 
  	     * were given */
  	    err = MP_RANGE; 
  	}
      }
  cleanup:
      mp_clear(&kphi);
      mp_clear(&phi);
      mp_clear(&s);
      mp_clear(&k);
      mp_clear(&r);
      mp_clear(&tmp);
      mp_clear(&sqrt);
      return err;
  }
       
  /*
   * take a private key with only a few elements and fill out the missing pieces.
   *
   * All the entries will be overwritten with data allocated out of the arena
   * If no arena is supplied, one will be created.
   *
   * The following fields must be supplied in order for this function
   * to succeed:
   *   one of either publicExponent or privateExponent
   *   two more of the following 5 parameters.
   *      modulus (n)
   *      prime1  (p)
   *      prime2  (q)
   *      publicExponent (e)
   *      privateExponent (d)
   *
   * NOTE: if only the publicExponent, privateExponent, and one prime is given,
   * then there may be more than one RSA key that matches that combination.
   *
   * All parameters will be replaced in the key structure with new parameters
   * Allocated out of the arena. There is no attempt to free the old structures.
   * Prime1 will always be greater than prime2 (even if the caller supplies the
   * smaller prime as prime1 or the larger prime as prime2). The parameters are
   * not overwritten on failure.
   *
   *  How it works:
   *     We can generate all the parameters from:
   *        one of the exponents, plus the two primes. (rsa_build_key_from_primes) *
   *     If we are given one of the exponents and both primes, we are done.
   *     If we are given one of the exponents, the modulus and one prime, we 
   *        caclulate the second prime by dividing the modulus by the given 
   *        prime, giving us and exponent and 2 primes.
   *     If we are given 2 exponents and either the modulus or one of the primes
   *        we calculate k*phi = d*e-1, where k is an integer less than d which 
   *        divides d*e-1. We find factor k so we can isolate phi.
   *            phi = (p-1)(q-1)
   *       If one of the primes are given, we can use phi to find the other prime
   *        as follows: q = (phi/(p-1)) + 1. We now have 2 primes and an 
   *        exponent. (NOTE: if more then one prime meets this condition, the
   *        operation will fail. See comments elsewhere in this file about this).
   *       If the modulus is given, then we can calculate the sum of the primes
   *        as follows: s := (p+q), phi = (p-1)(q-1) = pq -p - q +1, pq = n ->
   *        phi = n - s + 1, s = n - phi +1.  Now that we have s = p+q and n=pq,
   *	  we can solve our 2 equations and 2 unknowns as follows: q=s-p ->
   *        n=p*(s-p)= sp -p^2 -> p^2-sp+n = 0. Using the quadratic to solve for
   *        p, p=1/2*(s+ sqrt(s*s-4*n)) [q=1/2*(s-sqrt(s*s-4*n)]. We again have
   *        2 primes and an exponent.
   *
   */
  SECStatus
  RSA_PopulatePrivateKey(RSAPrivateKey *key)
  {
      PLArenaPool *arena = NULL;
      PRBool needPublicExponent = PR_TRUE;
      PRBool needPrivateExponent = PR_TRUE;
      PRBool hasModulus = PR_FALSE;
      unsigned int keySizeInBits = 0;
      int prime_count = 0;
      /* standard RSA nominclature */
      mp_int p, q, e, d, n;
      /* remainder */
      mp_int r;
      mp_err err = 0;
      SECStatus rv = SECFailure;
  
      MP_DIGITS(&p) = 0;
      MP_DIGITS(&q) = 0;
      MP_DIGITS(&e) = 0;
      MP_DIGITS(&d) = 0;
      MP_DIGITS(&n) = 0;
      MP_DIGITS(&r) = 0;
      CHECK_MPI_OK( mp_init(&p) );
      CHECK_MPI_OK( mp_init(&q) );
      CHECK_MPI_OK( mp_init(&e) );
      CHECK_MPI_OK( mp_init(&d) );
      CHECK_MPI_OK( mp_init(&n) );
      CHECK_MPI_OK( mp_init(&r) );
   
      /* if the key didn't already have an arena, create one. */
      if (key->arena == NULL) {
  	arena = PORT_NewArena(NSS_FREEBL_DEFAULT_CHUNKSIZE);
  	if (!arena) {
  	    goto cleanup;
  	}
  	key->arena = arena;
      }
  
      /* load up the known exponents */
      if (key->publicExponent.data) {
          SECITEM_TO_MPINT(key->publicExponent, &e);
  	needPublicExponent = PR_FALSE;
      } 
      if (key->privateExponent.data) {
          SECITEM_TO_MPINT(key->privateExponent, &d);
  	needPrivateExponent = PR_FALSE;
      }
      if (needPrivateExponent && needPublicExponent) {
  	/* Not enough information, we need at least one exponent */
  	err = MP_BADARG;
  	goto cleanup;
      }
  
      /* load up the known primes. If only one prime is given, it will be
       * assigned 'p'. Once we have both primes, well make sure p is the larger.
       * The value prime_count tells us howe many we have acquired.
       */
      if (key->prime1.data) {
  	int primeLen = key->prime1.len;
  	if (key->prime1.data[0] == 0) {
  	   primeLen--;
  	}
  	keySizeInBits = primeLen * 2 * PR_BITS_PER_BYTE;
          SECITEM_TO_MPINT(key->prime1, &p);
  	prime_count++;
      }
      if (key->prime2.data) {
  	int primeLen = key->prime2.len;
  	if (key->prime2.data[0] == 0) {
  	   primeLen--;
  	}
  	keySizeInBits = primeLen * 2 * PR_BITS_PER_BYTE;
          SECITEM_TO_MPINT(key->prime2, prime_count ? &q : &p);
  	prime_count++;
      }
      /* load up the modulus */
      if (key->modulus.data) {
  	int modLen = key->modulus.len;
  	if (key->modulus.data[0] == 0) {
  	   modLen--;
  	}
  	keySizeInBits = modLen * PR_BITS_PER_BYTE;
  	SECITEM_TO_MPINT(key->modulus, &n);
  	hasModulus = PR_TRUE;
      }
      /* if we have the modulus and one prime, calculate the second. */
      if ((prime_count == 1) && (hasModulus)) {
  	mp_div(&n,&p,&q,&r);
  	if (mp_cmp_z(&r) != 0) {
  	   /* p is not a factor or n, fail */
  	   err = MP_BADARG;
  	   goto cleanup;
  	}
  	prime_count++;
      }
  
      /* If we didn't have enough primes try to calculate the primes from
       * the exponents */
      if (prime_count < 2) {
  	/* if we don't have at least 2 primes at this point, then we need both
  	 * exponents and one prime or a modulus*/
  	if (!needPublicExponent && !needPrivateExponent &&
  		((prime_count > 0) || hasModulus)) {
  	    CHECK_MPI_OK(rsa_get_primes_from_exponents(&e,&d,&p,&q,
  			&n,hasModulus,keySizeInBits));
  	} else {
  	    /* not enough given parameters to get both primes */
  	    err = MP_BADARG;
  	    goto cleanup;
  	}
       }
  
       /* Assure p > q */
       /* NOTE: PKCS #1 does not require p > q, and NSS doesn't use any
        * implementation optimization that requires p > q. We can remove
        * this code in the future.
        */
       if (mp_cmp(&p, &q) < 0)
  	mp_exch(&p, &q);
  
       /* we now have our 2 primes and at least one exponent, we can fill
        * in the key */
       rv = rsa_build_from_primes(&p, &q, 
  			&e, needPublicExponent,
  			&d, needPrivateExponent,
  			key, keySizeInBits);
  cleanup:
      mp_clear(&p);
      mp_clear(&q);
      mp_clear(&e);
      mp_clear(&d);
      mp_clear(&n);
      mp_clear(&r);
      if (err) {
  	MP_TO_SEC_ERROR(err);
  	rv = SECFailure;
      }
      if (rv && arena) {
  	PORT_FreeArena(arena, PR_TRUE);
  	key->arena = NULL;
      }
      return rv;
  }
  
  static unsigned int
  rsa_modulusLen(SECItem *modulus)
  {
      unsigned char byteZero = modulus->data[0];
      unsigned int modLen = modulus->len - !byteZero;
      return modLen;
  }
  
  /*
  ** Perform a raw public-key operation 
  **	Length of input and output buffers are equal to key's modulus len.
  */
  SECStatus 
  RSA_PublicKeyOp(RSAPublicKey  *key, 
                  unsigned char *output, 
                  const unsigned char *input)
  {
      unsigned int modLen, expLen, offset;
      mp_int n, e, m, c;
      mp_err err   = MP_OKAY;
      SECStatus rv = SECSuccess;
      if (!key || !output || !input) {
  	PORT_SetError(SEC_ERROR_INVALID_ARGS);
  	return SECFailure;
      }
      MP_DIGITS(&n) = 0;
      MP_DIGITS(&e) = 0;
      MP_DIGITS(&m) = 0;
      MP_DIGITS(&c) = 0;
      CHECK_MPI_OK( mp_init(&n) );
      CHECK_MPI_OK( mp_init(&e) );
      CHECK_MPI_OK( mp_init(&m) );
      CHECK_MPI_OK( mp_init(&c) );
      modLen = rsa_modulusLen(&key->modulus);
      expLen = rsa_modulusLen(&key->publicExponent);
      /* 1.  Obtain public key (n, e) */
      if (BAD_RSA_KEY_SIZE(modLen, expLen)) {
      	PORT_SetError(SEC_ERROR_INVALID_KEY);
  	rv = SECFailure;
  	goto cleanup;
      }
      SECITEM_TO_MPINT(key->modulus, &n);
      SECITEM_TO_MPINT(key->publicExponent, &e);
      if (e.used > n.used) {
  	/* exponent should not be greater than modulus */
      	PORT_SetError(SEC_ERROR_INVALID_KEY);
  	rv = SECFailure;
  	goto cleanup;
      }
      /* 2. check input out of range (needs to be in range [0..n-1]) */
      offset = (key->modulus.data[0] == 0) ? 1 : 0; /* may be leading 0 */
      if (memcmp(input, key->modulus.data + offset, modLen) >= 0) {
          PORT_SetError(SEC_ERROR_INPUT_LEN);
          rv = SECFailure;
          goto cleanup;
      }
      /* 2 bis.  Represent message as integer in range [0..n-1] */
      CHECK_MPI_OK( mp_read_unsigned_octets(&m, input, modLen) );
      /* 3.  Compute c = m**e mod n */
  #ifdef USE_MPI_EXPT_D
      /* XXX see which is faster */
      if (MP_USED(&e) == 1) {
  	CHECK_MPI_OK( mp_exptmod_d(&m, MP_DIGIT(&e, 0), &n, &c) );
      } else
  #endif
      CHECK_MPI_OK( mp_exptmod(&m, &e, &n, &c) );
      /* 4.  result c is ciphertext */
      err = mp_to_fixlen_octets(&c, output, modLen);
      if (err >= 0) err = MP_OKAY;
  cleanup:
      mp_clear(&n);
      mp_clear(&e);
      mp_clear(&m);
      mp_clear(&c);
      if (err) {
  	MP_TO_SEC_ERROR(err);
  	rv = SECFailure;
      }
      return rv;
  }
  
  /*
  **  RSA Private key operation (no CRT).
  */
  static SECStatus 
  rsa_PrivateKeyOpNoCRT(RSAPrivateKey *key, mp_int *m, mp_int *c, mp_int *n,
                        unsigned int modLen)
  {
      mp_int d;
      mp_err   err = MP_OKAY;
      SECStatus rv = SECSuccess;
      MP_DIGITS(&d) = 0;
      CHECK_MPI_OK( mp_init(&d) );
      SECITEM_TO_MPINT(key->privateExponent, &d);
      /* 1. m = c**d mod n */
      CHECK_MPI_OK( mp_exptmod(c, &d, n, m) );
  cleanup:
      mp_clear(&d);
      if (err) {
  	MP_TO_SEC_ERROR(err);
  	rv = SECFailure;
      }
      return rv;
  }
  
  /*
  **  RSA Private key operation using CRT.
  */
  static SECStatus 
  rsa_PrivateKeyOpCRTNoCheck(RSAPrivateKey *key, mp_int *m, mp_int *c)
  {
      mp_int p, q, d_p, d_q, qInv;
      mp_int m1, m2, h, ctmp;
      mp_err   err = MP_OKAY;
      SECStatus rv = SECSuccess;
      MP_DIGITS(&p)    = 0;
      MP_DIGITS(&q)    = 0;
      MP_DIGITS(&d_p)  = 0;
      MP_DIGITS(&d_q)  = 0;
      MP_DIGITS(&qInv) = 0;
      MP_DIGITS(&m1)   = 0;
      MP_DIGITS(&m2)   = 0;
      MP_DIGITS(&h)    = 0;
      MP_DIGITS(&ctmp) = 0;
      CHECK_MPI_OK( mp_init(&p)    );
      CHECK_MPI_OK( mp_init(&q)    );
      CHECK_MPI_OK( mp_init(&d_p)  );
      CHECK_MPI_OK( mp_init(&d_q)  );
      CHECK_MPI_OK( mp_init(&qInv) );
      CHECK_MPI_OK( mp_init(&m1)   );
      CHECK_MPI_OK( mp_init(&m2)   );
      CHECK_MPI_OK( mp_init(&h)    );
      CHECK_MPI_OK( mp_init(&ctmp) );
      /* copy private key parameters into mp integers */
      SECITEM_TO_MPINT(key->prime1,      &p);    /* p */
      SECITEM_TO_MPINT(key->prime2,      &q);    /* q */
      SECITEM_TO_MPINT(key->exponent1,   &d_p);  /* d_p  = d mod (p-1) */
      SECITEM_TO_MPINT(key->exponent2,   &d_q);  /* d_q  = d mod (q-1) */
      SECITEM_TO_MPINT(key->coefficient, &qInv); /* qInv = q**-1 mod p */
      /* 1. m1 = c**d_p mod p */
      CHECK_MPI_OK( mp_mod(c, &p, &ctmp) );
      CHECK_MPI_OK( mp_exptmod(&ctmp, &d_p, &p, &m1) );
      /* 2. m2 = c**d_q mod q */
      CHECK_MPI_OK( mp_mod(c, &q, &ctmp) );
      CHECK_MPI_OK( mp_exptmod(&ctmp, &d_q, &q, &m2) );
      /* 3.  h = (m1 - m2) * qInv mod p */
      CHECK_MPI_OK( mp_submod(&m1, &m2, &p, &h) );
      CHECK_MPI_OK( mp_mulmod(&h, &qInv, &p, &h)  );
      /* 4.  m = m2 + h * q */
      CHECK_MPI_OK( mp_mul(&h, &q, m) );
      CHECK_MPI_OK( mp_add(m, &m2, m) );
  cleanup:
      mp_clear(&p);
      mp_clear(&q);
      mp_clear(&d_p);
      mp_clear(&d_q);
      mp_clear(&qInv);
      mp_clear(&m1);
      mp_clear(&m2);
      mp_clear(&h);
      mp_clear(&ctmp);
      if (err) {
  	MP_TO_SEC_ERROR(err);
  	rv = SECFailure;
      }
      return rv;
  }
  
  /*
  ** An attack against RSA CRT was described by Boneh, DeMillo, and Lipton in:
  ** "On the Importance of Eliminating Errors in Cryptographic Computations",
  ** http://theory.stanford.edu/~dabo/papers/faults.ps.gz
  **
  ** As a defense against the attack, carry out the private key operation, 
  ** followed up with a public key operation to invert the result.  
  ** Verify that result against the input.
  */
  static SECStatus 
  rsa_PrivateKeyOpCRTCheckedPubKey(RSAPrivateKey *key, mp_int *m, mp_int *c)
  {
      mp_int n, e, v;
      mp_err   err = MP_OKAY;
      SECStatus rv = SECSuccess;
      MP_DIGITS(&n) = 0;
      MP_DIGITS(&e) = 0;
      MP_DIGITS(&v) = 0;
      CHECK_MPI_OK( mp_init(&n) );
      CHECK_MPI_OK( mp_init(&e) );
      CHECK_MPI_OK( mp_init(&v) );
      CHECK_SEC_OK( rsa_PrivateKeyOpCRTNoCheck(key, m, c) );
      SECITEM_TO_MPINT(key->modulus,        &n);
      SECITEM_TO_MPINT(key->publicExponent, &e);
      /* Perform a public key operation v = m ** e mod n */
      CHECK_MPI_OK( mp_exptmod(m, &e, &n, &v) );
      if (mp_cmp(&v, c) != 0) {
  	rv = SECFailure;
      }
  cleanup:
      mp_clear(&n);
      mp_clear(&e);
      mp_clear(&v);
      if (err) {
  	MP_TO_SEC_ERROR(err);
  	rv = SECFailure;
      }
      return rv;
  }
  
  static PRCallOnceType coBPInit = { 0, 0, 0 };
  static PRStatus 
  init_blinding_params_list(void)
  {
      blindingParamsList.lock = PZ_NewLock(nssILockOther);
      if (!blindingParamsList.lock) {
  	PORT_SetError(SEC_ERROR_NO_MEMORY);
  	return PR_FAILURE;
      }
      blindingParamsList.cVar = PR_NewCondVar( blindingParamsList.lock );
      if (!blindingParamsList.cVar) {
  	PORT_SetError(SEC_ERROR_NO_MEMORY);
  	return PR_FAILURE;
      }
      blindingParamsList.waitCount = 0;
      PR_INIT_CLIST(&blindingParamsList.head);
      return PR_SUCCESS;
  }
  
  static SECStatus
  generate_blinding_params(RSAPrivateKey *key, mp_int* f, mp_int* g, mp_int *n, 
                           unsigned int modLen)
  {
      SECStatus rv = SECSuccess;
      mp_int e, k;
      mp_err err = MP_OKAY;
      unsigned char *kb = NULL;
  
      MP_DIGITS(&e) = 0;
      MP_DIGITS(&k) = 0;
      CHECK_MPI_OK( mp_init(&e) );
      CHECK_MPI_OK( mp_init(&k) );
      SECITEM_TO_MPINT(key->publicExponent, &e);
      /* generate random k < n */
      kb = PORT_Alloc(modLen);
      if (!kb) {
  	PORT_SetError(SEC_ERROR_NO_MEMORY);
  	goto cleanup;
      }
      CHECK_SEC_OK( RNG_GenerateGlobalRandomBytes(kb, modLen) );
      CHECK_MPI_OK( mp_read_unsigned_octets(&k, kb, modLen) );
      /* k < n */
      CHECK_MPI_OK( mp_mod(&k, n, &k) );
      /* f = k**e mod n */
      CHECK_MPI_OK( mp_exptmod(&k, &e, n, f) );
      /* g = k**-1 mod n */
      CHECK_MPI_OK( mp_invmod(&k, n, g) );
  cleanup:
      if (kb)
  	PORT_ZFree(kb, modLen);
      mp_clear(&k);
      mp_clear(&e);
      if (err) {
  	MP_TO_SEC_ERROR(err);
  	rv = SECFailure;
      }
      return rv;
  }
  
  static SECStatus
  init_blinding_params(RSABlindingParams *rsabp, RSAPrivateKey *key,
                       mp_int *n, unsigned int modLen)
  {
      blindingParams * bp = rsabp->array;
      int i = 0;
  
      /* Initialize the list pointer for the element */
      PR_INIT_CLIST(&rsabp->link);
      for (i = 0; i < RSA_BLINDING_PARAMS_MAX_CACHE_SIZE; ++i, ++bp) {
      	bp->next = bp + 1;
  	MP_DIGITS(&bp->f) = 0;
  	MP_DIGITS(&bp->g) = 0;
  	bp->counter = 0;
      }
      /* The last bp->next value was initialized with out
       * of rsabp->array pointer and must be set to NULL 
       */ 
      rsabp->array[RSA_BLINDING_PARAMS_MAX_CACHE_SIZE - 1].next = NULL;
      
      bp          = rsabp->array;
      rsabp->bp   = NULL;
      rsabp->free = bp;
  
      /* List elements are keyed using the modulus */
      SECITEM_CopyItem(NULL, &rsabp->modulus, &key->modulus);
  
      return SECSuccess;
  }
  
  static SECStatus
  get_blinding_params(RSAPrivateKey *key, mp_int *n, unsigned int modLen,
                      mp_int *f, mp_int *g)
  {
      RSABlindingParams *rsabp           = NULL;
      blindingParams    *bpUnlinked      = NULL;
      blindingParams    *bp;
      PRCList           *el;
      SECStatus          rv              = SECSuccess;
      mp_err             err             = MP_OKAY;
      int                cmp             = -1;
      PRBool             holdingLock     = PR_FALSE;
  
      do {
  	if (blindingParamsList.lock == NULL) {
  	    PORT_SetError(SEC_ERROR_LIBRARY_FAILURE);
  	    return SECFailure;
  	}
  	/* Acquire the list lock */
  	PZ_Lock(blindingParamsList.lock);
  	holdingLock = PR_TRUE;
  
  	/* Walk the list looking for the private key */
  	for (el = PR_NEXT_LINK(&blindingParamsList.head);
  	     el != &blindingParamsList.head;
  	     el = PR_NEXT_LINK(el)) {
  	    rsabp = (RSABlindingParams *)el;
  	    cmp = SECITEM_CompareItem(&rsabp->modulus, &key->modulus);
  	    if (cmp >= 0) {
  		/* The key is found or not in the list. */
  		break;
  	    }
  	}
  
  	if (cmp) {
  	    /* At this point, the key is not in the list.  el should point to 
  	    ** the list element before which this key should be inserted. 
  	    */
  	    rsabp = PORT_ZNew(RSABlindingParams);
  	    if (!rsabp) {
  		PORT_SetError(SEC_ERROR_NO_MEMORY);
  		goto cleanup;
  	    }
  
  	    rv = init_blinding_params(rsabp, key, n, modLen);
  	    if (rv != SECSuccess) {
  		PORT_ZFree(rsabp, sizeof(RSABlindingParams));
  		goto cleanup;
  	    }
  
  	    /* Insert the new element into the list
  	    ** If inserting in the middle of the list, el points to the link
  	    ** to insert before.  Otherwise, the link needs to be appended to
  	    ** the end of the list, which is the same as inserting before the
  	    ** head (since el would have looped back to the head).
  	    */
  	    PR_INSERT_BEFORE(&rsabp->link, el);
  	}
  
  	/* We've found (or created) the RSAblindingParams struct for this key.
  	 * Now, search its list of ready blinding params for a usable one.
  	 */
  	while (0 != (bp = rsabp->bp)) {
  	    if (--(bp->counter) > 0) {
  		/* Found a match and there are still remaining uses left */
  		/* Return the parameters */
  		CHECK_MPI_OK( mp_copy(&bp->f, f) );
  		CHECK_MPI_OK( mp_copy(&bp->g, g) );
  
  		PZ_Unlock(blindingParamsList.lock); 
  		return SECSuccess;
  	    }
  	    /* exhausted this one, give its values to caller, and
  	     * then retire it.
  	     */
  	    mp_exch(&bp->f, f);
  	    mp_exch(&bp->g, g);
  	    mp_clear( &bp->f );
  	    mp_clear( &bp->g );
  	    bp->counter = 0;
  	    /* Move to free list */
  	    rsabp->bp   = bp->next;
  	    bp->next    = rsabp->free;
  	    rsabp->free = bp;
  	    /* In case there're threads waiting for new blinding
  	     * value - notify 1 thread the value is ready
  	     */
  	    if (blindingParamsList.waitCount > 0) {
  		PR_NotifyCondVar( blindingParamsList.cVar );
  		blindingParamsList.waitCount--;
  	    }
  	    PZ_Unlock(blindingParamsList.lock); 
  	    return SECSuccess;
  	}
  	/* We did not find a usable set of blinding params.  Can we make one? */
  	/* Find a free bp struct. */
  	if ((bp = rsabp->free) != NULL) {
  	    /* unlink this bp */
  	    rsabp->free  = bp->next;
  	    bp->next     = NULL;
  	    bpUnlinked   = bp;  /* In case we fail */
  
  	    PZ_Unlock(blindingParamsList.lock); 
  	    holdingLock = PR_FALSE;
  	    /* generate blinding parameter values for the current thread */
  	    CHECK_SEC_OK( generate_blinding_params(key, f, g, n, modLen ) );
  
  	    /* put the blinding parameter values into cache */
  	    CHECK_MPI_OK( mp_init( &bp->f) );
  	    CHECK_MPI_OK( mp_init( &bp->g) );
  	    CHECK_MPI_OK( mp_copy( f, &bp->f) );
  	    CHECK_MPI_OK( mp_copy( g, &bp->g) );
  
  	    /* Put this at head of queue of usable params. */
  	    PZ_Lock(blindingParamsList.lock);
  	    holdingLock = PR_TRUE;
  	    /* initialize RSABlindingParamsStr */
  	    bp->counter = RSA_BLINDING_PARAMS_MAX_REUSE;
  	    bp->next    = rsabp->bp;
  	    rsabp->bp   = bp;
  	    bpUnlinked  = NULL;
  	    /* In case there're threads waiting for new blinding value
  	     * just notify them the value is ready
  	     */
  	    if (blindingParamsList.waitCount > 0) {
  		PR_NotifyAllCondVar( blindingParamsList.cVar );
  		blindingParamsList.waitCount = 0;
  	    }
  	    PZ_Unlock(blindingParamsList.lock);
  	    return SECSuccess;
  	}
  	/* Here, there are no usable blinding parameters available,
  	 * and no free bp blocks, presumably because they're all 
  	 * actively having parameters generated for them.
  	 * So, we need to wait here and not eat up CPU until some 
  	 * change happens. 
  	 */
  	blindingParamsList.waitCount++;
  	PR_WaitCondVar( blindingParamsList.cVar, PR_INTERVAL_NO_TIMEOUT );
  	PZ_Unlock(blindingParamsList.lock); 
  	holdingLock = PR_FALSE;
      } while (1);
  
  cleanup:
      /* It is possible to reach this after the lock is already released.  */
      if (bpUnlinked) {
  	if (!holdingLock) {
  	    PZ_Lock(blindingParamsList.lock);
  	    holdingLock = PR_TRUE;
  	}
  	bp = bpUnlinked;
  	mp_clear( &bp->f );
  	mp_clear( &bp->g );
  	bp->counter = 0;
      	/* Must put the unlinked bp back on the free list */
  	bp->next    = rsabp->free;
  	rsabp->free = bp;
      }
      if (holdingLock) {
  	PZ_Unlock(blindingParamsList.lock);
  	holdingLock = PR_FALSE;
      }
      if (err) {
  	MP_TO_SEC_ERROR(err);
      }
      return SECFailure;
  }
  
  /*
  ** Perform a raw private-key operation 
  **	Length of input and output buffers are equal to key's modulus len.
  */
  static SECStatus 
  rsa_PrivateKeyOp(RSAPrivateKey *key, 
                   unsigned char *output, 
                   const unsigned char *input,
                   PRBool check)
  {
      unsigned int modLen;
      unsigned int offset;
      SECStatus rv = SECSuccess;
      mp_err err;
      mp_int n, c, m;
      mp_int f, g;
      if (!key || !output || !input) {
  	PORT_SetError(SEC_ERROR_INVALID_ARGS);
  	return SECFailure;
      }
      /* check input out of range (needs to be in range [0..n-1]) */
      modLen = rsa_modulusLen(&key->modulus);
      offset = (key->modulus.data[0] == 0) ? 1 : 0; /* may be leading 0 */
      if (memcmp(input, key->modulus.data + offset, modLen) >= 0) {
  	PORT_SetError(SEC_ERROR_INVALID_ARGS);
  	return SECFailure;
      }
      MP_DIGITS(&n) = 0;
      MP_DIGITS(&c) = 0;
      MP_DIGITS(&m) = 0;
      MP_DIGITS(&f) = 0;
      MP_DIGITS(&g) = 0;
      CHECK_MPI_OK( mp_init(&n) );
      CHECK_MPI_OK( mp_init(&c) );
      CHECK_MPI_OK( mp_init(&m) );
      CHECK_MPI_OK( mp_init(&f) );
      CHECK_MPI_OK( mp_init(&g) );
      SECITEM_TO_MPINT(key->modulus, &n);
      OCTETS_TO_MPINT(input, &c, modLen);
      /* If blinding, compute pre-image of ciphertext by multiplying by
      ** blinding factor
      */
      if (nssRSAUseBlinding) {
  	CHECK_SEC_OK( get_blinding_params(key, &n, modLen, &f, &g) );
  	/* c' = c*f mod n */
  	CHECK_MPI_OK( mp_mulmod(&c, &f, &n, &c) );
      }
      /* Do the private key operation m = c**d mod n */
      if ( key->prime1.len      == 0 ||
           key->prime2.len      == 0 ||
           key->exponent1.len   == 0 ||
           key->exponent2.len   == 0 ||
           key->coefficient.len == 0) {
  	CHECK_SEC_OK( rsa_PrivateKeyOpNoCRT(key, &m, &c, &n, modLen) );
      } else if (check) {
  	CHECK_SEC_OK( rsa_PrivateKeyOpCRTCheckedPubKey(key, &m, &c) );
      } else {
  	CHECK_SEC_OK( rsa_PrivateKeyOpCRTNoCheck(key, &m, &c) );
      }
      /* If blinding, compute post-image of plaintext by multiplying by
      ** blinding factor
      */
      if (nssRSAUseBlinding) {
  	/* m = m'*g mod n */
  	CHECK_MPI_OK( mp_mulmod(&m, &g, &n, &m) );
      }
      err = mp_to_fixlen_octets(&m, output, modLen);
      if (err >= 0) err = MP_OKAY;
  cleanup:
      mp_clear(&n);
      mp_clear(&c);
      mp_clear(&m);
      mp_clear(&f);
      mp_clear(&g);
      if (err) {
  	MP_TO_SEC_ERROR(err);
  	rv = SECFailure;
      }
      return rv;
  }
  
  SECStatus 
  RSA_PrivateKeyOp(RSAPrivateKey *key, 
                   unsigned char *output, 
                   const unsigned char *input)
  {
      return rsa_PrivateKeyOp(key, output, input, PR_FALSE);
  }
  
  SECStatus 
  RSA_PrivateKeyOpDoubleChecked(RSAPrivateKey *key, 
                                unsigned char *output, 
                                const unsigned char *input)
  {
      return rsa_PrivateKeyOp(key, output, input, PR_TRUE);
  }
  
  SECStatus
  RSA_PrivateKeyCheck(const RSAPrivateKey *key)
  {
      mp_int p, q, n, psub1, qsub1, e, d, d_p, d_q, qInv, res;
      mp_err   err = MP_OKAY;
      SECStatus rv = SECSuccess;
      MP_DIGITS(&p)    = 0;
      MP_DIGITS(&q)    = 0;
      MP_DIGITS(&n)    = 0;
      MP_DIGITS(&psub1)= 0;
      MP_DIGITS(&qsub1)= 0;
      MP_DIGITS(&e)    = 0;
      MP_DIGITS(&d)    = 0;
      MP_DIGITS(&d_p)  = 0;
      MP_DIGITS(&d_q)  = 0;
      MP_DIGITS(&qInv) = 0;
      MP_DIGITS(&res)  = 0;
      CHECK_MPI_OK( mp_init(&p)    );
      CHECK_MPI_OK( mp_init(&q)    );
      CHECK_MPI_OK( mp_init(&n)    );
      CHECK_MPI_OK( mp_init(&psub1));
      CHECK_MPI_OK( mp_init(&qsub1));
      CHECK_MPI_OK( mp_init(&e)    );
      CHECK_MPI_OK( mp_init(&d)    );
      CHECK_MPI_OK( mp_init(&d_p)  );
      CHECK_MPI_OK( mp_init(&d_q)  );
      CHECK_MPI_OK( mp_init(&qInv) );
      CHECK_MPI_OK( mp_init(&res)  );
  
      if (!key->modulus.data || !key->prime1.data || !key->prime2.data ||
          !key->publicExponent.data || !key->privateExponent.data ||
          !key->exponent1.data || !key->exponent2.data ||
          !key->coefficient.data) {
          /* call RSA_PopulatePrivateKey first, if the application wishes to
           * recover these parameters */
          err = MP_BADARG;
          goto cleanup;
      }
  
      SECITEM_TO_MPINT(key->modulus,         &n);
      SECITEM_TO_MPINT(key->prime1,          &p);
      SECITEM_TO_MPINT(key->prime2,          &q);
      SECITEM_TO_MPINT(key->publicExponent,  &e);
      SECITEM_TO_MPINT(key->privateExponent, &d);
      SECITEM_TO_MPINT(key->exponent1,       &d_p);
      SECITEM_TO_MPINT(key->exponent2,       &d_q);
      SECITEM_TO_MPINT(key->coefficient,     &qInv);
      /* p and q must be distinct. */
      if (mp_cmp(&p, &q) == 0) {
  	rv = SECFailure;
  	goto cleanup;
      }
  #define VERIFY_MPI_EQUAL(m1, m2) \
      if (mp_cmp(m1, m2) != 0) {   \
  	rv = SECFailure;         \
  	goto cleanup;            \
      }
  #define VERIFY_MPI_EQUAL_1(m)    \
      if (mp_cmp_d(m, 1) != 0) {   \
  	rv = SECFailure;         \
  	goto cleanup;            \
      }
      /* n == p * q */
      CHECK_MPI_OK( mp_mul(&p, &q, &res) );
      VERIFY_MPI_EQUAL(&res, &n);
      /* gcd(e, p-1) == 1 */
      CHECK_MPI_OK( mp_sub_d(&p, 1, &psub1) );
      CHECK_MPI_OK( mp_gcd(&e, &psub1, &res) );
      VERIFY_MPI_EQUAL_1(&res);
      /* gcd(e, q-1) == 1 */
      CHECK_MPI_OK( mp_sub_d(&q, 1, &qsub1) );
      CHECK_MPI_OK( mp_gcd(&e, &qsub1, &res) );
      VERIFY_MPI_EQUAL_1(&res);
      /* d*e == 1 mod p-1 */
      CHECK_MPI_OK( mp_mulmod(&d, &e, &psub1, &res) );
      VERIFY_MPI_EQUAL_1(&res);
      /* d*e == 1 mod q-1 */
      CHECK_MPI_OK( mp_mulmod(&d, &e, &qsub1, &res) );
      VERIFY_MPI_EQUAL_1(&res);
      /* d_p == d mod p-1 */
      CHECK_MPI_OK( mp_mod(&d, &psub1, &res) );
      VERIFY_MPI_EQUAL(&res, &d_p);
      /* d_q == d mod q-1 */
      CHECK_MPI_OK( mp_mod(&d, &qsub1, &res) );
      VERIFY_MPI_EQUAL(&res, &d_q);
      /* q * q**-1 == 1 mod p */
      CHECK_MPI_OK( mp_mulmod(&q, &qInv, &p, &res) );
      VERIFY_MPI_EQUAL_1(&res);
  
  cleanup:
      mp_clear(&n);
      mp_clear(&p);
      mp_clear(&q);
      mp_clear(&psub1);
      mp_clear(&qsub1);
      mp_clear(&e);
      mp_clear(&d);
      mp_clear(&d_p);
      mp_clear(&d_q);
      mp_clear(&qInv);
      mp_clear(&res);
      if (err) {
  	MP_TO_SEC_ERROR(err);
  	rv = SECFailure;
      }
      return rv;
  }
  
  static SECStatus RSA_Init(void)
  {
      if (PR_CallOnce(&coBPInit, init_blinding_params_list) != PR_SUCCESS) {
          PORT_SetError(SEC_ERROR_LIBRARY_FAILURE);
          return SECFailure;
      }
      return SECSuccess;
  }
  
  SECStatus BL_Init(void)
  {
      return RSA_Init();
  }
  
  /* cleanup at shutdown */
  void RSA_Cleanup(void)
  {
      blindingParams * bp = NULL;
      if (!coBPInit.initialized)
  	return;
  
      while (!PR_CLIST_IS_EMPTY(&blindingParamsList.head)) {
  	RSABlindingParams *rsabp = 
  	    (RSABlindingParams *)PR_LIST_HEAD(&blindingParamsList.head);
  	PR_REMOVE_LINK(&rsabp->link);
  	/* clear parameters cache */
  	while (rsabp->bp != NULL) {
  	    bp = rsabp->bp;
  	    rsabp->bp = rsabp->bp->next;
  	    mp_clear( &bp->f );
  	    mp_clear( &bp->g );
  	}
  	SECITEM_FreeItem(&rsabp->modulus,PR_FALSE);
  	PORT_Free(rsabp);
      }
  
      if (blindingParamsList.cVar) {
  	PR_DestroyCondVar(blindingParamsList.cVar);
  	blindingParamsList.cVar = NULL;
      }
  
      if (blindingParamsList.lock) {
  	SKIP_AFTER_FORK(PZ_DestroyLock(blindingParamsList.lock));
  	blindingParamsList.lock = NULL;
      }
  
      coBPInit.initialized = 0;
      coBPInit.inProgress = 0;
      coBPInit.status = 0;
  }
  
  /*
   * need a central place for this function to free up all the memory that
   * free_bl may have allocated along the way. Currently only RSA does this,
   * so I've put it here for now.
   */
  void BL_Cleanup(void)
  {
      RSA_Cleanup();
  }
  
  #ifdef NSS_STATIC
  void
  BL_Unload(void)
  {
  }
  #endif
  
  PRBool bl_parentForkedAfterC_Initialize;
  
  /*
   * Set fork flag so it can be tested in SKIP_AFTER_FORK on relevant platforms.
   */
  void BL_SetForkState(PRBool forked)
  {
      bl_parentForkedAfterC_Initialize = forked;
  }
  
  