int
findkey(char *keyfile, char *host, RSApub *key)
{
char *h;
Biobuf *b;
RSApub *k;
if((b = Bopen(keyfile, OREAD)) == nil)
return NoKeyFile;
for(;;){
if((k = readpublickey(b, &h)) == nil){
Bterm(b);
return NoKey;
}
if(match(h, host) != 0){
free(h);
rsapubfree(k);
continue;
}
if(mpcmp(k->n, key->n) != 0 || mpcmp(k->ek, key->ek) != 0){
free(h);
rsapubfree(k);
Bterm(b);
return KeyWrong;
}
free(h);
rsapubfree(k);
Bterm(b);
return KeyOk;
}
}
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);
}
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;
}
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
findkey(char *keyfile, char *host, RSApub *key)
{
char *h;
Biobuf *b;
RSApub *k;
int res;
if ((b = Bopen(keyfile, OREAD)) == nil)
return NoKeyFile;
for (res = NoKey; res != KeyOk;) {
if ((k = readpublickey(b, &h)) == nil)
break;
if (match(h, host) == 0) {
if (mpcmp(k->n, key->n) == 0 &&
mpcmp(k->ek, key->ek) == 0)
res = KeyOk;
else
res = KeyWrong;
}
free(h);
free(k->ek);
free(k->n);
free(k);
}
Bterm(b);
return res;
}
// 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;
}
void
mpdivmodfixfix(Mpint *q, Mpint *r, Mpint *n, Mpint *d)
{
int i, ns, ds;
ns = n->neg;
ds = d->neg;
n->neg = 0;
d->neg = 0;
mpmovefixfix(r, n);
mpmovecfix(q, 0);
// shift denominator until it
// is larger than numerator
for(i=0; i<Mpprec*Mpscale; i++) {
if(mpcmp(d, r) > 0)
break;
mplsh(d);
}
// if it never happens
// denominator is probably zero
if(i >= Mpprec*Mpscale) {
q->ovf = 1;
r->ovf = 1;
n->neg = ns;
d->neg = ds;
yyerror("set ovf in mpdivmodfixfix");
return;
}
// shift denominator back creating
// quotient a bit at a time
// when done the remaining numerator
// will be the remainder
for(; i>0; i--) {
mplsh(q);
mprsh(d);
if(mpcmp(d, r) <= 0) {
mpaddcfix(q, 1);
mpsubfixfix(r, d);
}
}
n->neg = ns;
d->neg = ds;
r->neg = ns;
q->neg = ns^ds;
}
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
mpdivfract(Mpint *a, Mpint *b)
{
Mpint n, d;
int i, j, neg;
long *a1, x;
mpmovefixfix(&n, a); // numerator
mpmovefixfix(&d, b); // denominator
a1 = &a->a[Mpprec]; // quotient
neg = n.neg ^ d.neg;
n.neg = 0;
d.neg = 0;
for(i=0; i<Mpprec; i++) {
x = 0;
for(j=0; j<Mpscale; j++) {
x <<= 1;
if(mpcmp(&d, &n) <= 0) {
x |= 1;
mpsubfixfix(&n, &d);
}
mprsh(&d);
}
*--a1 = x;
}
a->neg = neg;
}
int
rsaverify(RSApub *key, DigestAlg *hash, uchar *digest, uint dlen,
uchar *sig, uint siglen)
{
uchar asn1[512], *buf;
int n, len, pad;
mpint *m, *mm, *s;
/*
* Create ASN.1
*/
n = mkasn1(asn1, hash, digest, dlen);
/*
* Create number to sign.
*/
len = (mpsignif(key->n)+7)/8 - 1;
if(len < n+2) {
werrstr("rsa key too short");
return -1;
}
pad = len - (n+2);
if(siglen < len) {
werrstr("signature buffer too short");
return -1;
}
buf = malloc(len);
if(buf == nil)
return -1;
buf[0] = 0x01;
memset(buf+1, 0xFF, pad);
buf[1+pad] = 0x00;
memmove(buf+1+pad+1, asn1, n);
m = betomp(buf, len, nil);
free(buf);
if(m == nil)
return -1;
/*
* Extract plaintext of signature.
*/
s = betomp(sig, siglen, nil);
if(s == nil)
return -1;
mm = rsaencrypt(key, s, nil);
mpfree(s);
if(mm == nil)
return -1;
if(mpcmp(m, mm) != 0) {
werrstr("signature did not verify");
mpfree(mm);
mpfree(m);
return -1;
}
mpfree(mm);
mpfree(m);
return 0;
}
ECpriv*
ecgen(ECdomain *dom, ECpriv *p)
{
if(p == nil){
p = mallocz(sizeof(*p), 1);
if(p == nil)
return nil;
p->x = mpnew(0);
p->y = mpnew(0);
p->d = mpnew(0);
}
for(;;){
mprand(mpsignif(dom->n), genrandom, p->d);
if(mpcmp(p->d, mpzero) > 0 && mpcmp(p->d, dom->n) < 0)
break;
}
ecmul(dom, dom->G, p->d, p);
return p;
}
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;
}
static int
rsa_verify(mpint* m, void *sig, void *key)
{
mpint *t;
int r;
t = rsaencrypt((RSApub*)key, (mpint*)sig, nil);
r = mpcmp(t, m) == 0;
mpfree(t);
return r;
}
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;
}
// 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);
}
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;
}
static int
metacond(ASTNode *c)
{
c = onlyone(metarun(c));
if(c == nil){
error(nil, "metacond: nil");
return -1;
}
if(c->t == ASTCINT)
return c->i != 0;
if(c->t == ASTCONST)
return mpcmp(c->cons.n, mpzero) != 0;
error(c, "if: unresolved %n", c);
return -1;
}
int
mptestfix(Mpint *a)
{
Mpint b;
int r;
mpmovecfix(&b, 0);
r = mpcmp(a, &b);
if(a->neg) {
if(r > 0)
return -1;
if(r < 0)
return +1;
}
return r;
}
void
base58enc(uchar *src, char *dst, int len)
{
mpint *n, *r, *b;
char *sdst, t;
sdst = dst;
n = betomp(src, len, nil);
b = uitomp(58, nil);
r = mpnew(0);
while(mpcmp(n, mpzero) != 0){
mpdiv(n, b, n, r);
*dst++ = code[mptoui(r)];
}
for(; *src == 0; src++)
*dst++ = code[0];
dst--;
while(dst > sdst){
t = *sdst;
*sdst++ = *dst;
*dst-- = t;
}
}
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;
}
/*
* 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;
}
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
mpaddfixfix(Mpint *a, Mpint *b)
{
int i, c;
long x, *a1, *b1;
if(a->ovf || b->ovf) {
yyerror("ovf in mpaddxx");
a->ovf = 1;
return;
}
c = 0;
a1 = &a->a[0];
b1 = &b->a[0];
if(a->neg != b->neg)
goto sub;
// perform a+b
for(i=0; i<Mpprec; i++) {
x = *a1 + *b1++ + c;
c = 0;
if(x >= Mpbase) {
x -= Mpbase;
c = 1;
}
*a1++ = x;
}
a->ovf = c;
if(a->ovf)
yyerror("set ovf in mpaddxx");
return;
sub:
// perform a-b
switch(mpcmp(a, b)) {
case 0:
mpmovecfix(a, 0);
break;
case 1:
for(i=0; i<Mpprec; i++) {
x = *a1 - *b1++ - c;
c = 0;
if(x < 0) {
x += Mpbase;
c = 1;
}
*a1++ = x;
}
break;
case -1:
a->neg ^= 1;
for(i=0; i<Mpprec; i++) {
x = *b1++ - *a1 - c;
c = 0;
if(x < 0) {
x += Mpbase;
c = 1;
}
*a1++ = x;
}
break;
}
}
// extended binary gcd
//
// For a anv b it solves, v = gcd(a,b) and finds x and y s.t.
// ax + by = v
//
// Handbook of Applied Cryptography, Menezes et al, 1997, pg 608.
void
mpextendedgcd(mpint *a, mpint *b, mpint *v, mpint *x, mpint *y)
{
mpint *u, *A, *B, *C, *D;
int g;
if(a->top == 0){
mpassign(b, v);
mpassign(mpone, y);
mpassign(mpzero, x);
return;
}
if(b->top == 0){
mpassign(a, v);
mpassign(mpone, x);
mpassign(mpzero, y);
return;
}
g = 0;
a = mpcopy(a);
b = mpcopy(b);
while(iseven(a) && iseven(b)){
mpright(a, 1, a);
mpright(b, 1, b);
g++;
}
u = mpcopy(a);
mpassign(b, v);
A = mpcopy(mpone);
B = mpcopy(mpzero);
C = mpcopy(mpzero);
D = mpcopy(mpone);
for(;;) {
// print("%B %B %B %B %B %B\n", u, v, A, B, C, D);
while(iseven(u)){
mpright(u, 1, u);
if(!iseven(A) || !iseven(B)) {
mpadd(A, b, A);
mpsub(B, a, B);
}
mpright(A, 1, A);
mpright(B, 1, B);
}
// print("%B %B %B %B %B %B\n", u, v, A, B, C, D);
while(iseven(v)){
mpright(v, 1, v);
if(!iseven(C) || !iseven(D)) {
mpadd(C, b, C);
mpsub(D, a, D);
}
mpright(C, 1, C);
mpright(D, 1, D);
}
// print("%B %B %B %B %B %B\n", u, v, A, B, C, D);
if(mpcmp(u, v) >= 0){
mpsub(u, v, u);
mpsub(A, C, A);
mpsub(B, D, B);
} else {
mpsub(v, u, v);
mpsub(C, A, C);
mpsub(D, B, D);
}
if(u->top == 0)
break;
}
mpassign(C, x);
mpassign(D, y);
mpleft(v, g, v);
mpfree(A);
mpfree(B);
mpfree(C);
mpfree(D);
mpfree(u);
mpfree(a);
mpfree(b);
}
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;
}
static int
dorsa(mpint *mod, mpint *exp, mpint *chal, uint8_t chalbuf[32])
{
int afd;
AuthRpc *rpc;
mpint *m;
char buf[4096], *p;
mpint *decr, *unpad;
USED(exp);
snprint(buf, sizeof buf, "proto=rsa service=ssh role=client");
if((afd = open("/mnt/factotum/rpc", ORDWR)) < 0){
debug(DBG_AUTH, "open /mnt/factotum/rpc: %r\n");
return -1;
}
if((rpc = auth_allocrpc(afd)) == nil){
debug(DBG_AUTH, "auth_allocrpc: %r\n");
close(afd);
return -1;
}
if(auth_rpc(rpc, "start", buf, strlen(buf)) != ARok){
debug(DBG_AUTH, "auth_rpc start failed: %r\n");
Die:
auth_freerpc(rpc);
close(afd);
return -1;
}
m = nil;
debug(DBG_AUTH, "trying factotum rsa keys\n");
while(auth_rpc(rpc, "read", nil, 0) == ARok){
debug(DBG_AUTH, "try %s\n", (char*)rpc->arg);
m = strtomp(rpc->arg, nil, 16, nil);
if(mpcmp(m, mod) == 0)
break;
mpfree(m);
m = nil;
}
if(m == nil)
goto Die;
mpfree(m);
p = mptoa(chal, 16, nil, 0);
if(p == nil){
debug(DBG_AUTH, "\tmptoa failed: %r\n");
goto Die;
}
if(auth_rpc(rpc, "write", p, strlen(p)) != ARok){
debug(DBG_AUTH, "\tauth_rpc write failed: %r\n");
free(p);
goto Die;
}
free(p);
if(auth_rpc(rpc, "read", nil, 0) != ARok){
debug(DBG_AUTH, "\tauth_rpc read failed: %r\n");
goto Die;
}
decr = strtomp(rpc->arg, nil, 16, nil);
if(decr == nil){
debug(DBG_AUTH, "\tdecr %s failed\n", rpc->arg);
goto Die;
}
debug(DBG_AUTH, "\tdecrypted %B\n", decr);
unpad = rsaunpad(decr);
if(unpad == nil){
debug(DBG_AUTH, "\tunpad %B failed\n", decr);
mpfree(decr);
goto Die;
}
debug(DBG_AUTH, "\tunpadded %B\n", unpad);
mpfree(decr);
mptoberjust(unpad, chalbuf, 32);
mpfree(unpad);
auth_freerpc(rpc);
close(afd);
return 0;
}
void
sshserverhandshake(Conn *c)
{
char *p, buf[128];
Biobuf *b;
Attr *a;
int i, afd;
mpint *m;
AuthRpc *rpc;
RSApub *key;
/*
* BUG: should use `attr' to get the key attributes
* after the read, but that's not implemented yet.
*/
if((b = Bopen("/mnt/factotum/ctl", OREAD)) == nil)
sysfatal("open /mnt/factotum/ctl: %r");
while((p = Brdline(b, '\n')) != nil){
p[Blinelen(b)-1] = '\0';
if(strstr(p, " proto=rsa ") && strstr(p, " service=sshserve "))
break;
}
if(p == nil)
sysfatal("no sshserve keys found in /mnt/factotum/ctl");
a = _parseattr(p);
Bterm(b);
key = emalloc(sizeof(*key));
if((p = _strfindattr(a, "n")) == nil)
sysfatal("no n in sshserve key");
if((key->n = strtomp(p, &p, 16, nil)) == nil || *p != 0)
sysfatal("bad n in sshserve key");
if((p = _strfindattr(a, "ek")) == nil)
sysfatal("no ek in sshserve key");
if((key->ek = strtomp(p, &p, 16, nil)) == nil || *p != 0)
sysfatal("bad ek in sshserve key");
_freeattr(a);
if((afd = open("/mnt/factotum/rpc", ORDWR)) < 0)
sysfatal("open /mnt/factotum/rpc: %r");
if((rpc = auth_allocrpc(afd)) == nil)
sysfatal("auth_allocrpc: %r");
p = "proto=rsa role=client service=sshserve";
if(auth_rpc(rpc, "start", p, strlen(p)) != ARok)
sysfatal("auth_rpc start %s: %r", p);
if(auth_rpc(rpc, "read", nil, 0) != ARok)
sysfatal("auth_rpc read: %r");
m = strtomp(rpc->arg, nil, 16, nil);
if(mpcmp(m, key->n) != 0)
sysfatal("key in /mnt/factotum/ctl does not match rpc key");
mpfree(m);
c->hostkey = key;
/* send id string */
fprint(c->fd[0], "SSH-1.5-Plan9\n");
/* receive id string */
if(readstrnl(c->fd[0], buf, sizeof buf) < 0)
sysfatal("reading server version: %r");
/* id string is "SSH-m.n-comment". We need m=1, n>=5. */
if(strncmp(buf, "SSH-", 4) != 0
|| strtol(buf+4, &p, 10) != 1
|| *p != '.'
|| strtol(p+1, &p, 10) < 5
|| *p != '-')
sysfatal("protocol mismatch; got %s, need SSH-1.x for x>=5", buf);
for(i=0; i<COOKIELEN; i++)
c->cookie[i] = fastrand();
calcsessid(c);
send_ssh_smsg_public_key(c);
recv_ssh_cmsg_session_key(c, rpc);
auth_freerpc(rpc);
close(afd);
c->cstate = (*c->cipher->init)(c, 1); /* turns on encryption */
sendmsg(allocmsg(c, SSH_SMSG_SUCCESS, 0));
authsrvuser(c);
}
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);
}
