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);
}
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;
}
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;
}
/* 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;
}
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);
}
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;
}
