/*
* computes the loop of the algorithm.
* for k=0 to h-1
* e=0
* for i=kw to kw+w-1
* if the bitIndex bit in ci is set:
* calculate e += 2^(i-kw)
* result = result *preComp[k][e]
*/
epoint* computeLoop(miracl* mip, big* exponentiations, int w, int h, epoint*** preComp, epoint* result, int bitIndex, int n, int field){
int e = 0, k, i, twoPow;
big temp = mirvar(mip, 0);
for (k=0; k<h; k++){
for (i=k*w; i<(k * w + w); i++){
if (i < n){
copy(exponentiations[i], temp);
//check if the bit in bitIndex is set.
//shift the big number bitIndex times
sftbit(mip, temp, bitIndex*-1, temp);
//check if the shifted big is divisible by two. if not - the first bit is set.
if (subdivisible(mip, temp, 2) == 0){
twoPow = pow((double)2, i-k*w);
e += twoPow;
}
}
}
//multiply operation depends on the field
if (field == 1)
ecurve_add(mip, preComp[k][e], result);
else
ecurve2_add(mip, preComp[k][e], result);
e = 0;
}
mirkill(temp);
return result;
}
int main()
{
int ia,ib;
time_t seed;
epoint *g,*ea,*eb;
big a,b,p,q,n,p1,q1,phi,pa,pb,key,e,d,dp,dq,t,m,c,x,y,k,inv;
big primes[2],pm[2];
big_chinese ch;
miracl *mip;
#ifndef MR_NOFULLWIDTH
mip=mirsys(500,0);
#else
mip=mirsys(500,MAXBASE);
#endif
a=mirvar(0);
b=mirvar(0);
p=mirvar(0);
q=mirvar(0);
n=mirvar(0);
p1=mirvar(0);
q1=mirvar(0);
phi=mirvar(0);
pa=mirvar(0);
pb=mirvar(0);
key=mirvar(0);
e=mirvar(0);
d=mirvar(0);
dp=mirvar(0);
dq=mirvar(0);
t=mirvar(0);
m=mirvar(0);
c=mirvar(0);
pm[0]=mirvar(0);
pm[1]=mirvar(0);
x=mirvar(0);
y=mirvar(0);
k=mirvar(0);
inv=mirvar(0);
time(&seed);
irand((unsigned long)seed); /* change parameter for different values */
printf("First Diffie-Hellman Key exchange .... \n");
cinstr(p,primetext);
/* offline calculations could be done quicker using Comb method
- See brick.c. Note use of "truncated exponent" of 160 bits -
could be output of hash function SHA (see mrshs.c) */
printf("\nAlice's offline calculation\n");
bigbits(160,a);
/* 3 generates the sub-group of prime order (p-1)/2 */
powltr(3,a,p,pa);
printf("Bob's offline calculation\n");
bigbits(160,b);
powltr(3,b,p,pb);
printf("Alice calculates Key=\n");
powmod(pb,a,p,key);
cotnum(key,stdout);
printf("Bob calculates Key=\n");
powmod(pa,b,p,key);
cotnum(key,stdout);
printf("Alice and Bob's keys should be the same!\n");
/*
Now Elliptic Curve version of the above.
Curve is y^2=x^3+Ax+B mod p, where A=-3, B and p as above
"Primitive root" is the point (x,y) above, which is of large prime order q.
In this case actually
q=FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831
*/
printf("\nLets try that again using elliptic curves .... \n");
convert(-3,a);
mip->IOBASE=16;
cinstr(b,ecb);
cinstr(p,ecp);
ecurve_init(a,b,p,MR_BEST); /* Use PROJECTIVE if possible, else AFFINE coordinates */
g=epoint_init();
cinstr(x,ecx);
cinstr(y,ecy);
mip->IOBASE=10;
epoint_set(x,y,0,g);
ea=epoint_init();
eb=epoint_init();
epoint_copy(g,ea);
epoint_copy(g,eb);
printf("Alice's offline calculation\n");
bigbits(160,a);
ecurve_mult(a,ea,ea);
ia=epoint_get(ea,pa,pa); /* <ia,pa> is compressed form of public key */
printf("Bob's offline calculation\n");
bigbits(160,b);
ecurve_mult(b,eb,eb);
ib=epoint_get(eb,pb,pb); /* <ib,pb> is compressed form of public key */
printf("Alice calculates Key=\n");
epoint_set(pb,pb,ib,eb); /* decompress eb */
ecurve_mult(a,eb,eb);
epoint_get(eb,key,key);
cotnum(key,stdout);
printf("Bob calculates Key=\n");
epoint_set(pa,pa,ia,ea); /* decompress ea */
ecurve_mult(b,ea,ea);
epoint_get(ea,key,key);
cotnum(key,stdout);
printf("Alice and Bob's keys should be the same! (but much smaller)\n");
epoint_free(g);
epoint_free(ea);
epoint_free(eb);
/* El Gamal's Method */
printf("\nTesting El Gamal's public key method\n");
cinstr(p,primetext);
bigbits(160,x); /* x<p */
powltr(3,x,p,y); /* y=3^x mod p*/
decr(p,1,p1);
mip->IOBASE=128;
cinstr(m,text);
mip->IOBASE=10;
do
{
bigbits(160,k);
} while (egcd(k,p1,t)!=1);
powltr(3,k,p,a); /* a=3^k mod p */
powmod(y,k,p,b);
mad(b,m,m,p,p,b); /* b=m*y^k mod p */
printf("Ciphertext= \n");
cotnum(a,stdout);
cotnum(b,stdout);
zero(m); /* proof of pudding... */
subtract(p1,x,t);
powmod(a,t,p,m);
mad(m,b,b,p,p,m); /* m=b/a^x mod p */
printf("Plaintext= \n");
mip->IOBASE=128;
cotnum(m,stdout);
mip->IOBASE=10;
/* RSA. Generate primes p & q. Use e=65537, and find d=1/e mod (p-1)(q-1) */
printf("\nNow generating 512-bit random primes p and q\n");
do
{
bigbits(512,p);
if (subdivisible(p,2)) incr(p,1,p);
while (!isprime(p)) incr(p,2,p);
bigbits(512,q);
if (subdivisible(q,2)) incr(q,1,q);
while (!isprime(q)) incr(q,2,q);
multiply(p,q,n); /* n=p.q */
lgconv(65537L,e);
decr(p,1,p1);
decr(q,1,q1);
multiply(p1,q1,phi); /* phi =(p-1)*(q-1) */
} while (xgcd(e,phi,d,d,t)!=1);
cotnum(p,stdout);
cotnum(q,stdout);
printf("n = p.q = \n");
cotnum(n,stdout);
/* set up for chinese remainder thereom */
/* primes[0]=p;
primes[1]=q;
crt_init(&ch,2,primes);
*/
/* use simple CRT as only two primes */
xgcd(p,q,inv,inv,inv); /* 1/p mod q */
copy(d,dp);
copy(d,dq);
divide(dp,p1,p1); /* dp=d mod p-1 */
divide(dq,q1,q1); /* dq=d mod q-1 */
mip->IOBASE=128;
cinstr(m,text);
mip->IOBASE=10;
printf("Encrypting test string\n");
powmod(m,e,n,c);
printf("Ciphertext= \n");
cotnum(c,stdout);
zero(m);
printf("Decrypting test string\n");
powmod(c,dp,p,pm[0]); /* get result mod p */
powmod(c,dq,q,pm[1]); /* get result mod q */
subtract(pm[1],pm[0],pm[1]); /* poor man's CRT */
mad(inv,pm[1],inv,q,q,m);
multiply(m,p,m);
add(m,pm[0],m);
/* crt(&ch,pm,m); combine them using CRT */
printf("Plaintext= \n");
mip->IOBASE=128;
cotnum(m,stdout);
/* crt_end(&ch); */
return 0;
}
