void
ecdsasign(ECdomain *dom, ECpriv *priv, uchar *dig, int len, mpint *r, mpint *s)
{
ECpriv tmp;
mpint *E, *t;
tmp.x = mpnew(0);
tmp.y = mpnew(0);
tmp.d = mpnew(0);
E = betomp(dig, len, nil);
t = mpnew(0);
if(mpsignif(dom->n) < 8*len)
mpright(E, 8*len - mpsignif(dom->n), E);
for(;;){
ecgen(dom, &tmp);
mpmod(tmp.x, dom->n, r);
if(mpcmp(r, mpzero) == 0)
continue;
mpmul(r, priv->d, s);
mpadd(E, s, s);
mpinvert(tmp.d, dom->n, t);
mpmul(s, t, s);
mpmod(s, dom->n, s);
if(mpcmp(s, mpzero) != 0)
break;
}
mpfree(t);
mpfree(E);
mpfree(tmp.x);
mpfree(tmp.y);
mpfree(tmp.d);
}
// find a prime p of length n and a generator alpha of Z^*_p
// Alg 4.86 Menezes et al () Handbook, p.164
void
gensafeprime(mpint *p, mpint *alpha, int n, int accuracy)
{
mpint *q, *b;
q = mpnew(n-1);
while(1){
genprime(q, n-1, accuracy);
mpleft(q, 1, p);
mpadd(p, mpone, p); // p = 2*q+1
if(probably_prime(p, accuracy))
break;
}
// now find a generator alpha of the multiplicative
// group Z*_p of order p-1=2q
b = mpnew(0);
while(1){
mprand(n, genrandom, alpha);
mpmod(alpha, p, alpha);
mpmul(alpha, alpha, b);
mpmod(b, p, b);
if(mpcmp(b, mpone) == 0)
continue;
mpexp(alpha, q, p, b);
if(mpcmp(b, mpone) != 0)
break;
}
mpfree(b);
mpfree(q);
}
RSApriv*
rsafill(mpint *n, mpint *e, mpint *d, mpint *p, mpint *q)
{
mpint *c2, *kq, *kp, *x;
RSApriv *rsa;
// make sure we're not being hoodwinked
if(!probably_prime(p, 10) || !probably_prime(q, 10)){
werrstr("rsafill: p or q not prime");
return nil;
}
x = mpnew(0);
mpmul(p, q, x);
if(mpcmp(n, x) != 0){
werrstr("rsafill: n != p*q");
mpfree(x);
return nil;
}
c2 = mpnew(0);
mpsub(p, mpone, c2);
mpsub(q, mpone, x);
mpmul(c2, x, x);
mpmul(e, d, c2);
mpmod(c2, x, x);
if(mpcmp(x, mpone) != 0){
werrstr("rsafill: e*d != 1 mod (p-1)*(q-1)");
mpfree(x);
mpfree(c2);
return nil;
}
// compute chinese remainder coefficient
mpinvert(p, q, c2);
// for crt a**k mod p == (a**(k mod p-1)) mod p
kq = mpnew(0);
kp = mpnew(0);
mpsub(p, mpone, x);
mpmod(d, x, kp);
mpsub(q, mpone, x);
mpmod(d, x, kq);
rsa = rsaprivalloc();
rsa->pub.ek = mpcopy(e);
rsa->pub.n = mpcopy(n);
rsa->dk = mpcopy(d);
rsa->kp = kp;
rsa->kq = kq;
rsa->p = mpcopy(p);
rsa->q = mpcopy(q);
rsa->c2 = c2;
mpfree(x);
return rsa;
}
DSApriv*
dsagen(DSApub *opub)
{
DSApub *pub;
DSApriv *priv;
mpint *exp;
mpint *g;
mpint *r;
int bits;
priv = dsaprivalloc();
pub = &priv->pub;
if(opub != nil){
pub->p = mpcopy(opub->p);
pub->q = mpcopy(opub->q);
} else {
pub->p = mpnew(0);
pub->q = mpnew(0);
DSAprimes(pub->q, pub->p, nil);
}
bits = Dbits*pub->p->top;
pub->alpha = mpnew(0);
pub->key = mpnew(0);
priv->secret = mpnew(0);
// find a generator alpha of the multiplicative
// group Z*p, i.e., of order n = p-1. We use the
// fact that q divides p-1 to reduce the exponent.
exp = mpnew(0);
g = mpnew(0);
r = mpnew(0);
mpsub(pub->p, mpone, exp);
mpdiv(exp, pub->q, exp, r);
if(mpcmp(r, mpzero) != 0)
sysfatal("dsagen foul up");
while(1){
mprand(bits, genrandom, g);
mpmod(g, pub->p, g);
mpexp(g, exp, pub->p, pub->alpha);
if(mpcmp(pub->alpha, mpone) != 0)
break;
}
mpfree(g);
mpfree(exp);
// create the secret key
mprand(bits, genrandom, priv->secret);
mpmod(priv->secret, pub->p, priv->secret);
mpexp(pub->alpha, priv->secret, pub->p, pub->key);
return priv;
}
DSAsig*
dsasign(DSApriv *priv, mpint *m)
{
DSApub *pub = &priv->pub;
DSAsig *sig;
mpint *qm1, *k, *kinv, *r, *s;
mpint *q = pub->q, *p = pub->p, *alpha = pub->alpha;
int qlen = mpsignif(q);
qm1 = mpnew(0);
kinv = mpnew(0);
r = mpnew(0);
s = mpnew(0);
k = mpnew(0);
mpsub(pub->q, mpone, qm1);
// find a k that has an inverse mod q
while(1){
mprand(qlen, genrandom, k);
if((mpcmp(mpone, k) > 0) || (mpcmp(k, qm1) >= 0))
continue;
mpextendedgcd(k, q, r, kinv, s);
if(mpcmp(r, mpone) != 0)
continue;
break;
}
// make kinv positive
mpmod(kinv, qm1, kinv);
// r = ((alpha**k) mod p) mod q
mpexp(alpha, k, p, r);
mpmod(r, q, r);
// s = (kinv*(m + ar)) mod q
mpmul(r, priv->secret, s);
mpadd(s, m, s);
mpmul(s, kinv, s);
mpmod(s, q, s);
sig = dsasigalloc();
sig->r = r;
sig->s = s;
mpfree(qm1);
mpfree(k);
mpfree(kinv);
return sig;
}
void
ecmul(ECdomain *dom, ECpoint *a, mpint *k, ECpoint *s)
{
ECpoint ns, na;
mpint *l;
if(a->inf || mpcmp(k, mpzero) == 0){
s->inf = 1;
return;
}
ns.inf = 1;
ns.x = mpnew(0);
ns.y = mpnew(0);
na.x = mpnew(0);
na.y = mpnew(0);
ecassign(dom, a, &na);
l = mpcopy(k);
l->sign = 1;
while(mpcmp(l, mpzero) != 0){
if(l->p[0] & 1)
ecadd(dom, &na, &ns, &ns);
ecadd(dom, &na, &na, &na);
mpright(l, 1, l);
}
if(k->sign < 0){
ns.y->sign = -1;
mpmod(ns.y, dom->p, ns.y);
}
ecassign(dom, &ns, s);
mpfree(ns.x);
mpfree(ns.y);
mpfree(na.x);
mpfree(na.y);
}
int
egverify(EGpub *pub, EGsig *sig, mpint *m)
{
mpint *p = pub->p, *alpha = pub->alpha;
mpint *r = sig->r, *s = sig->s;
mpint *v1, *v2, *rs;
int rv = -1;
if(mpcmp(r, mpone) < 0 || mpcmp(r, p) >= 0)
return rv;
v1 = mpnew(0);
rs = mpnew(0);
v2 = mpnew(0);
mpexp(pub->key, r, p, v1);
mpexp(r, s, p, rs);
mpmul(v1, rs, v1);
mpmod(v1, p, v1);
mpexp(alpha, m, p, v2);
if(mpcmp(v1, v2) == 0)
rv = 0;
mpfree(v1);
mpfree(rs);
mpfree(v2);
return rv;
}
int
dsaverify(DSApub *pub, DSAsig *sig, mpint *m)
{
int rv = -1;
mpint *u1, *u2, *v, *sinv;
if(sig->r->sign < 0 || mpcmp(sig->r, pub->q) >= 0)
return rv;
if(sig->s->sign < 0 || mpcmp(sig->s, pub->q) >= 0)
return rv;
u1 = mpnew(0);
u2 = mpnew(0);
v = mpnew(0);
sinv = mpnew(0);
// find (s**-1) mod q, make sure it exists
mpextendedgcd(sig->s, pub->q, u1, sinv, v);
if(mpcmp(u1, mpone) != 0)
goto out;
// u1 = (sinv * m) mod q, u2 = (r * sinv) mod q
mpmul(sinv, m, u1);
mpmod(u1, pub->q, u1);
mpmul(sig->r, sinv, u2);
mpmod(u2, pub->q, u2);
// v = (((alpha**u1)*(key**u2)) mod p) mod q
mpexp(pub->alpha, u1, pub->p, sinv);
mpexp(pub->key, u2, pub->p, v);
mpmul(sinv, v, v);
mpmod(v, pub->p, v);
mpmod(v, pub->q, v);
if(mpcmp(v, sig->r) == 0)
rv = 0;
out:
mpfree(v);
mpfree(u1);
mpfree(u2);
mpfree(sinv);
return rv;
}
int
ecdsaverify(ECdomain *dom, ECpub *pub, uchar *dig, int len, mpint *r, mpint *s)
{
mpint *E, *t, *u1, *u2;
ECpoint R, S;
int ret;
if(mpcmp(r, mpone) < 0 || mpcmp(s, mpone) < 0 || mpcmp(r, dom->n) >= 0 || mpcmp(r, dom->n) >= 0)
return 0;
E = betomp(dig, len, nil);
if(mpsignif(dom->n) < 8*len)
mpright(E, 8*len - mpsignif(dom->n), E);
t = mpnew(0);
u1 = mpnew(0);
u2 = mpnew(0);
R.x = mpnew(0);
R.y = mpnew(0);
S.x = mpnew(0);
S.y = mpnew(0);
mpinvert(s, dom->n, t);
mpmul(E, t, u1);
mpmod(u1, dom->n, u1);
mpmul(r, t, u2);
mpmod(u2, dom->n, u2);
ecmul(dom, dom->G, u1, &R);
ecmul(dom, pub, u2, &S);
ecadd(dom, &R, &S, &R);
ret = 0;
if(!R.inf){
mpmod(R.x, dom->n, t);
ret = mpcmp(r, t) == 0;
}
mpfree(t);
mpfree(u1);
mpfree(u2);
mpfree(R.x);
mpfree(R.y);
mpfree(S.x);
mpfree(S.y);
return ret;
}
int
ecverify(ECdomain *dom, ECpoint *a)
{
mpint *p, *q;
int r;
if(a->inf)
return 1;
p = mpnew(0);
q = mpnew(0);
mpmul(a->y, a->y, p);
mpmod(p, dom->p, p);
mpmul(a->x, a->x, q);
mpadd(q, dom->a, q);
mpmul(a->x, q, q);
mpadd(q, dom->b, q);
mpmod(q, dom->p, q);
r = mpcmp(p, q);
mpfree(p);
mpfree(q);
return r == 0;
}
// use extended gcd to find the multiplicative inverse
// res = b**-1 mod m
void
mpinvert(mpint *b, mpint *m, mpint *res)
{
mpint *dc1, *dc2; // don't care
dc1 = mpnew(0);
dc2 = mpnew(0);
mpextendedgcd(b, m, dc1, res, dc2);
if(mpcmp(dc1, mpone) != 0)
abort();
mpmod(res, m, res);
mpfree(dc1);
mpfree(dc2);
}
/* convert to residues, returns a newly created structure */
CRTres*
crtin(CRTpre *crt, mpint *x)
{
int i;
CRTres *res;
res = malloc(sizeof(CRTres)+sizeof(mpint)*crt->n);
if(res == nil)
sysfatal("crtin: %r");
res->n = crt->n;
for(i = 0; i < res->n; i++){
res->r[i] = mpnew(0);
mpmod(x, crt->m[i], res->r[i]);
}
return res;
}
/* garners algorithm for converting residue form to linear */
void
crtout(CRTpre *crt, CRTres *res, mpint *x)
{
mpint *u;
int i;
u = mpnew(0);
mpassign(res->r[0], x);
for(i = 1; i < crt->n; i++){
mpsub(res->r[i], x, u);
mpmul(u, crt->c[i], u);
mpmod(u, crt->m[i], u);
mpmul(u, crt->p[i-1], u);
mpadd(x, u, x);
}
mpfree(u);
}
/* setup crt info, returns a newly created structure */
CRTpre*
crtpre(int n, mpint **m)
{
CRTpre *crt;
int i, j;
mpint *u;
crt = malloc(sizeof(CRTpre)+sizeof(mpint)*3*n);
if(crt == nil)
sysfatal("crtpre: %r");
crt->m = crt->a;
crt->c = crt->a+n;
crt->p = crt->c+n;
crt->n = n;
/* make a copy of the moduli */
for(i = 0; i < n; i++)
crt->m[i] = mpcopy(m[i]);
/* precompute the products */
u = mpcopy(mpone);
for(i = 0; i < n; i++){
mpmul(u, m[i], u);
crt->p[i] = mpcopy(u);
}
/* precompute the coefficients */
for(i = 1; i < n; i++){
crt->c[i] = mpcopy(mpone);
for(j = 0; j < i; j++){
mpinvert(m[j], m[i], u);
mpmul(u, crt->c[i], u);
mpmod(u, m[i], crt->c[i]);
}
}
mpfree(u);
return crt;
}
static int
mpleg(mpint *a, mpint *b)
{
int r, k;
mpint *m, *n, *t;
r = 1;
m = mpcopy(a);
n = mpcopy(b);
for(;;){
if(mpcmp(m, n) > 0)
mpmod(m, n, m);
if(mpcmp(m, mpzero) == 0){
r = 0;
break;
}
if(mpcmp(m, mpone) == 0)
break;
k = mplowbits0(m);
if(k > 0){
if(k & 1)
switch(n->p[0] & 15){
case 3: case 5: case 11: case 13:
r = -r;
}
mpright(m, k, m);
}
if((n->p[0] & 3) == 3 && (m->p[0] & 3) == 3)
r = -r;
t = m;
m = n;
n = t;
}
mpfree(m);
mpfree(n);
return r;
}
int dsasign(const mpbarrett* p, const mpbarrett* q, const mpnumber* g, randomGeneratorContext* rgc, const mpnumber* hm, const mpnumber* x, mpnumber* r, mpnumber* s)
{
register size_t psize = p->size;
register size_t qsize = q->size;
register mpw* ptemp;
register mpw* qtemp;
register mpw* pwksp;
register mpw* qwksp;
register int rc = -1;
ptemp = (mpw*) malloc((5*psize+2)*sizeof(mpw));
if (ptemp == (mpw*) 0)
return rc;
qtemp = (mpw*) malloc((9*qsize+6)*sizeof(mpw));
if (qtemp == (mpw*) 0)
{
free(ptemp);
return rc;
}
pwksp = ptemp+psize;
qwksp = qtemp+3*qsize;
/* allocate r */
mpnfree(r);
mpnsize(r, qsize);
/* get a random k, invertible modulo q; store k @ qtemp, inv(k) @ qtemp+qsize */
mpbrndinv_w(q, rgc, qtemp, qtemp+qsize, qwksp);
/* g^k mod p */
mpbpowmod_w(p, g->size, g->data, qsize, qtemp, ptemp, pwksp);
/* (g^k mod p) mod q - simple modulo */
mpmod(qtemp+2*qsize, psize, ptemp, qsize, q->modl, pwksp);
mpcopy(qsize, r->data, qtemp+psize+qsize);
/* allocate s */
mpnfree(s);
mpnsize(s, qsize);
/* x*r mod q */
mpbmulmod_w(q, x->size, x->data, r->size, r->data, qtemp, qwksp);
/* add h(m) mod q */
mpbaddmod_w(q, qsize, qtemp, hm->size, hm->data, qtemp+2*qsize, qwksp);
/* multiply inv(k) mod q */
mpbmulmod_w(q, qsize, qtemp+qsize, qsize, qtemp+2*qsize, s->data, qwksp);
rc = 0;
free(qtemp);
free(ptemp);
return rc;
}
/*
* Miller-Rabin probabilistic primality testing
* Knuth (1981) Seminumerical Algorithms, p.379
* Menezes et al () Handbook, p.39
* 0 if composite; 1 if almost surely prime, Pr(err)<1/4**nrep
*/
int
probably_prime(mpint *n, int nrep)
{
int j, k, rep, nbits, isprime;
mpint *nm1, *q, *x, *y, *r;
if(n->sign < 0)
sysfatal("negative prime candidate");
if(nrep <= 0)
nrep = 18;
k = mptoi(n);
if(k == 2) /* 2 is prime */
return 1;
if(k < 2) /* 1 is not prime */
return 0;
if((n->p[0] & 1) == 0) /* even is not prime */
return 0;
/* test against small prime numbers */
if(smallprimetest(n) < 0)
return 0;
/* fermat test, 2^n mod n == 2 if p is prime */
x = uitomp(2, nil);
y = mpnew(0);
mpexp(x, n, n, y);
k = mptoi(y);
if(k != 2){
mpfree(x);
mpfree(y);
return 0;
}
nbits = mpsignif(n);
nm1 = mpnew(nbits);
mpsub(n, mpone, nm1); /* nm1 = n - 1 */
k = mplowbits0(nm1);
q = mpnew(0);
mpright(nm1, k, q); /* q = (n-1)/2**k */
for(rep = 0; rep < nrep; rep++){
for(;;){
/* find x = random in [2, n-2] */
r = mprand(nbits, prng, nil);
mpmod(r, nm1, x);
mpfree(r);
if(mpcmp(x, mpone) > 0)
break;
}
/* y = x**q mod n */
mpexp(x, q, n, y);
if(mpcmp(y, mpone) == 0 || mpcmp(y, nm1) == 0)
continue;
for(j = 1;; j++){
if(j >= k) {
isprime = 0;
goto done;
}
mpmul(y, y, x);
mpmod(x, n, y); /* y = y*y mod n */
if(mpcmp(y, nm1) == 0)
break;
if(mpcmp(y, mpone) == 0){
isprime = 0;
goto done;
}
}
}
isprime = 1;
done:
mpfree(y);
mpfree(x);
mpfree(q);
mpfree(nm1);
return isprime;
}
// Miller-Rabin probabilistic primality testing
// Knuth (1981) Seminumerical Algorithms, p.379
// Menezes et al () Handbook, p.39
// 0 if composite; 1 if almost surely prime, Pr(err)<1/4**nrep
int
probably_prime(mpint *n, int nrep)
{
int j, k, rep, nbits, isprime = 1;
mpint *nm1, *q, *x, *y, *r;
if(n->sign < 0)
sysfatal("negative prime candidate");
if(nrep <= 0)
nrep = 18;
k = mptoi(n);
if(k == 2) // 2 is prime
return 1;
if(k < 2) // 1 is not prime
return 0;
if((n->p[0] & 1) == 0) // even is not prime
return 0;
// test against small prime numbers
if(smallprimetest(n) < 0)
return 0;
// fermat test, 2^n mod n == 2 if p is prime
x = uitomp(2, nil);
y = mpnew(0);
mpexp(x, n, n, y);
k = mptoi(y);
if(k != 2){
mpfree(x);
mpfree(y);
return 0;
}
nbits = mpsignif(n);
nm1 = mpnew(nbits);
mpsub(n, mpone, nm1); // nm1 = n - 1 */
k = mplowbits0(nm1);
q = mpnew(0);
mpright(nm1, k, q); // q = (n-1)/2**k
for(rep = 0; rep < nrep; rep++){
// x = random in [2, n-2]
r = mprand(nbits, prng, nil);
mpmod(r, nm1, x);
mpfree(r);
if(mpcmp(x, mpone) <= 0)
continue;
// y = x**q mod n
mpexp(x, q, n, y);
if(mpcmp(y, mpone) == 0 || mpcmp(y, nm1) == 0)
goto done;
for(j = 1; j < k; j++){
mpmul(y, y, x);
mpmod(x, n, y); // y = y*y mod n
if(mpcmp(y, nm1) == 0)
goto done;
if(mpcmp(y, mpone) == 0){
isprime = 0;
goto done;
}
}
isprime = 0;
}
done:
mpfree(y);
mpfree(x);
mpfree(q);
mpfree(nm1);
return isprime;
}
static int
mpsqrt(mpint *n, mpint *p, mpint *r)
{
mpint *a, *t, *s, *xp, *xq, *yp, *yq, *zp, *zq, *N;
if(mpleg(n, p) == -1)
return 0;
a = mpnew(0);
t = mpnew(0);
s = mpnew(0);
N = mpnew(0);
xp = mpnew(0);
xq = mpnew(0);
yp = mpnew(0);
yq = mpnew(0);
zp = mpnew(0);
zq = mpnew(0);
for(;;){
for(;;){
mprand(mpsignif(p), genrandom, a);
if(mpcmp(a, mpzero) > 0 && mpcmp(a, p) < 0)
break;
}
mpmul(a, a, t);
mpsub(t, n, t);
mpmod(t, p, t);
if(mpleg(t, p) == -1)
break;
}
mpadd(p, mpone, N);
mpright(N, 1, N);
mpmul(a, a, t);
mpsub(t, n, t);
mpassign(a, xp);
uitomp(1, xq);
uitomp(1, yp);
uitomp(0, yq);
while(mpcmp(N, mpzero) != 0){
if(N->p[0] & 1){
mpmul(xp, yp, zp);
mpmul(xq, yq, zq);
mpmul(zq, t, zq);
mpadd(zp, zq, zp);
mpmod(zp, p, zp);
mpmul(xp, yq, zq);
mpmul(xq, yp, s);
mpadd(zq, s, zq);
mpmod(zq, p, yq);
mpassign(zp, yp);
}
mpmul(xp, xp, zp);
mpmul(xq, xq, zq);
mpmul(zq, t, zq);
mpadd(zp, zq, zp);
mpmod(zp, p, zp);
mpmul(xp, xq, zq);
mpadd(zq, zq, zq);
mpmod(zq, p, xq);
mpassign(zp, xp);
mpright(N, 1, N);
}
if(mpcmp(yq, mpzero) != 0)
abort();
mpassign(yp, r);
mpfree(a);
mpfree(t);
mpfree(s);
mpfree(N);
mpfree(xp);
mpfree(xq);
mpfree(yp);
mpfree(yq);
mpfree(zp);
mpfree(zq);
return 1;
}
void
ecadd(ECdomain *dom, ECpoint *a, ECpoint *b, ECpoint *s)
{
mpint *l, *k, *sx, *sy;
if(a->inf && b->inf){
s->inf = 1;
return;
}
if(a->inf){
ecassign(dom, b, s);
return;
}
if(b->inf){
ecassign(dom, a, s);
return;
}
if(mpcmp(a->x, b->x) == 0 && (mpcmp(a->y, mpzero) == 0 || mpcmp(a->y, b->y) != 0)){
s->inf = 1;
return;
}
l = mpnew(0);
k = mpnew(0);
sx = mpnew(0);
sy = mpnew(0);
if(mpcmp(a->x, b->x) == 0 && mpcmp(a->y, b->y) == 0){
mpadd(mpone, mptwo, k);
mpmul(a->x, a->x, l);
mpmul(l, k, l);
mpadd(l, dom->a, l);
mpleft(a->y, 1, k);
mpmod(k, dom->p, k);
mpinvert(k, dom->p, k);
mpmul(k, l, l);
mpmod(l, dom->p, l);
mpleft(a->x, 1, k);
mpmul(l, l, sx);
mpsub(sx, k, sx);
mpmod(sx, dom->p, sx);
mpsub(a->x, sx, sy);
mpmul(l, sy, sy);
mpsub(sy, a->y, sy);
mpmod(sy, dom->p, sy);
mpassign(sx, s->x);
mpassign(sy, s->y);
mpfree(sx);
mpfree(sy);
mpfree(l);
mpfree(k);
return;
}
mpsub(b->y, a->y, l);
mpmod(l, dom->p, l);
mpsub(b->x, a->x, k);
mpmod(k, dom->p, k);
mpinvert(k, dom->p, k);
mpmul(k, l, l);
mpmod(l, dom->p, l);
mpmul(l, l, sx);
mpsub(sx, a->x, sx);
mpsub(sx, b->x, sx);
mpmod(sx, dom->p, sx);
mpsub(a->x, sx, sy);
mpmul(sy, l, sy);
mpsub(sy, a->y, sy);
mpmod(sy, dom->p, sy);
mpassign(sx, s->x);
mpassign(sy, s->y);
mpfree(sx);
mpfree(sy);
mpfree(l);
mpfree(k);
}
void
mpexp(mpint *b, mpint *e, mpint *m, mpint *res)
{
mpint *t[2];
int tofree;
mpdigit d, bit;
int i, j;
t[0] = mpcopy(b);
t[1] = res;
tofree = 0;
if(res == b){
b = mpcopy(b);
tofree |= Freeb;
}
if(res == e){
e = mpcopy(e);
tofree |= Freee;
}
if(res == m){
m = mpcopy(m);
tofree |= Freem;
}
// skip first bit
i = e->top-1;
d = e->p[i];
for(bit = mpdighi; (bit & d) == 0; bit >>= 1)
;
bit >>= 1;
j = 0;
for(;;){
for(; bit != 0; bit >>= 1){
mpmul(t[j], t[j], t[j^1]);
if(bit & d)
mpmul(t[j^1], b, t[j]);
else
j ^= 1;
if(m != nil && t[j]->top > m->top){
mpmod(t[j], m, t[j^1]);
j ^= 1;
}
}
if(--i < 0)
break;
bit = mpdighi;
d = e->p[i];
}
if(m != nil){
mpmod(t[j], m, t[j^1]);
j ^= 1;
}
if(t[j] == res){
mpfree(t[j^1]);
} else {
mpassign(t[j], res);
mpfree(t[j]);
}
if(tofree){
if(tofree & Freeb)
mpfree(b);
if(tofree & Freee)
mpfree(e);
if(tofree & Freem)
mpfree(m);
}
}
RSApriv*
rsagen(int nlen, int elen, int rounds)
{
mpint *p, *q, *e, *d, *phi, *n, *t1, *t2, *kp, *kq, *c2;
RSApriv *rsa;
p = mpnew(nlen/2);
q = mpnew(nlen/2);
n = mpnew(nlen);
e = mpnew(elen);
d = mpnew(0);
phi = mpnew(nlen);
// create the prime factors and euclid's function
genprime(p, nlen/2, rounds);
genprime(q, nlen - mpsignif(p) + 1, rounds);
mpmul(p, q, n);
mpsub(p, mpone, e);
mpsub(q, mpone, d);
mpmul(e, d, phi);
// find an e relatively prime to phi
t1 = mpnew(0);
t2 = mpnew(0);
mprand(elen, genrandom, e);
if(mpcmp(e,mptwo) <= 0)
itomp(3, e);
// See Menezes et al. p.291 "8.8 Note (selecting primes)" for discussion
// of the merits of various choices of primes and exponents. e=3 is a
// common and recommended exponent, but doesn't necessarily work here
// because we chose strong rather than safe primes.
for(;;){
mpextendedgcd(e, phi, t1, d, t2);
if(mpcmp(t1, mpone) == 0)
break;
mpadd(mpone, e, e);
}
mpfree(t1);
mpfree(t2);
// compute chinese remainder coefficient
c2 = mpnew(0);
mpinvert(p, q, c2);
// for crt a**k mod p == (a**(k mod p-1)) mod p
kq = mpnew(0);
kp = mpnew(0);
mpsub(p, mpone, phi);
mpmod(d, phi, kp);
mpsub(q, mpone, phi);
mpmod(d, phi, kq);
rsa = rsaprivalloc();
rsa->pub.ek = e;
rsa->pub.n = n;
rsa->dk = d;
rsa->kp = kp;
rsa->kq = kq;
rsa->p = p;
rsa->q = q;
rsa->c2 = c2;
mpfree(phi);
return rsa;
}
int dsavrfy(const mpbarrett* p, const mpbarrett* q, const mpnumber* g, const mpnumber* hm, const mpnumber* y, const mpnumber* r, const mpnumber* s)
{
register size_t psize = p->size;
register size_t qsize = q->size;
register mpw* ptemp;
register mpw* qtemp;
register mpw* pwksp;
register mpw* qwksp;
register int rc = 0;
/* h(m) shouldn't contain more bits than q */
if (mpbits(hm->size, hm->data) > mpbits(q->size, q->modl))
return rc;
/* check 0 < r < q */
if (mpz(r->size, r->data))
return rc;
if (mpgex(r->size, r->data, qsize, q->modl))
return rc;
/* check 0 < s < q */
if (mpz(s->size, s->data))
return rc;
if (mpgex(s->size, s->data, qsize, q->modl))
return rc;
ptemp = (mpw*) malloc((6*psize+2)*sizeof(mpw));
if (ptemp == (mpw*) 0)
return rc;
qtemp = (mpw*) malloc((8*qsize+6)*sizeof(mpw));
if (qtemp == (mpw*) 0)
{
free(ptemp);
return rc;
}
pwksp = ptemp+2*psize;
qwksp = qtemp+2*qsize;
mpsetx(qsize, qtemp+qsize, s->size, s->data);
/* compute w = inv(s) mod q */
if (mpextgcd_w(qsize, q->modl, qtemp+qsize, qtemp, qwksp))
{
/* compute u1 = h(m)*w mod q */
mpbmulmod_w(q, hm->size, hm->data, qsize, qtemp, qtemp+qsize, qwksp);
/* compute u2 = r*w mod q */
mpbmulmod_w(q, r->size, r->data, qsize, qtemp, qtemp, qwksp);
/* compute g^u1 mod p */
mpbpowmod_w(p, g->size, g->data, qsize, qtemp+qsize, ptemp, pwksp);
/* compute y^u2 mod p */
mpbpowmod_w(p, y->size, y->data, qsize, qtemp, ptemp+psize, pwksp);
/* multiply mod p */
mpbmulmod_w(p, psize, ptemp, psize, ptemp+psize, ptemp, pwksp);
/* modulo q */
mpmod(ptemp+psize, psize, ptemp, qsize, q->modl, pwksp);
rc = mpeqx(r->size, r->data, psize, ptemp+psize);
}
free(qtemp);
free(ptemp);
return rc;
}
