int
base58dec(char *src, uchar *dst, int len)
{
mpint *n, *b, *r;
char *t;
int l;
n = mpnew(0);
r = mpnew(0);
b = uitomp(58, nil);
for(; *src; src++){
t = strchr(code, *src);
if(t == nil){
mpfree(n);
mpfree(r);
mpfree(b);
werrstr("invalid base58 char");
return -1;
}
uitomp(t - code, r);
mpmul(n, b, n);
mpadd(n, r, n);
}
memset(dst, 0, len);
l = (mpsignif(n) + 7) / 8;
mptobe(n, dst + (len - l), l, nil);
mpfree(n);
mpfree(r);
mpfree(b);
return 0;
}
void
main(void)
{
mpint *z = mpnew(0);
mpint *p = mpnew(0);
mpint *q = mpnew(0);
mpint *nine = mpnew(0);
fmtinstall('B', mpconv);
strtomp("2492491", nil, 16, z); // 38347921 = x*y = (2**28-9)/7,
// an example of 3**(n-1)=1 mod n
strtomp("15662C00E811", nil, 16, p);// 23528569104401, a prime
uitomp(9, nine);
if(probably_prime(z, 5) == 1)
fprint(2, "tricked primality test\n");
if(probably_prime(nine, 5) == 1)
fprint(2, "9 passed primality test!\n");
if(probably_prime(p, 25) == 1)
fprint(2, "ok\n");
DSAprimes(q, p, nil);
print("q=%B\np=%B\n", q, p);
exits(0);
}
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;
}
}
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;
}
/*
* 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;
}
