The Tor Browser: security/nss/lib/freebl/rsa.c@b8a032363ba2 (annotated)

security/nss/lib/freebl/rsa.c@b8a032363ba2 (annotated)

security/nss/lib/freebl/rsa.c

Thu, 22 Jan 2015 13:21:57 +0100

author: Michael Schloh von Bennewitz <michael@schloh.com>
date: Thu, 22 Jan 2015 13:21:57 +0100
branch: TOR_BUG_9701
changeset 15: b8a032363ba2
permissions: -rw-r--r--

Incorporate requested changes from Mozilla in review:
https://bugzilla.mozilla.org/show_bug.cgi?id=1123480#c6

 /* 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();
 }
 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;
 }

The Tor Browser / annotate

security/nss/lib/freebl/rsa.c@b8a032363ba2 (annotated)

security/nss/lib/freebl/rsa.c