void PairingGroup::init(ZR & r, char *value)
{
big x = mirvar(0);
cinstr(x, value);
r = ZR(x); //should copy this
mr_free(x);
}
static BOOL next(int ch)
{ /* get next digit - returns FALSE if there is a problem */
int cv;
result=FALSE;
if (ipt>=dlen) return FALSE;
if (ch=='/' || ch=='.')
{
if (delim || (ch=='/' && ipt==0)) return FALSE;
delim=TRUE;
}
else
{
if (ch>='A' && ch<='F') cv=10+(ch-'A');
else cv=ch-'0';
if (mip->IOBASE<=cv) return FALSE;
}
if (ipt==0 && ch=='0') clr();
else
{
mybuff[ipt++]=ch;
mybuff[ipt]='\0';
}
just(mybuff);
cinstr(x,mybuff);
newx=TRUE;
return TRUE;
}
/* parse a range given for LbyR or T from the command line.
* Examples:
* 1) "value" => list = { value, value, 1, SCALE_LIN }
* 2) "start,stop,N" => list = { start, stop, N, SCALE_LIN }
* 3) "start,stop,N,log" => list = { start, stop, N, SCALE_LOG }
*/
void parse_range(const char param, const char *_optarg, double list[])
{
int elems = cinstr(_optarg, ','); /* commas in _optarg */
list[3] = SCALE_LIN;
switch(elems)
{
case 0:
/* no comma => example 1) */
list[0] = list[1] = atof(_optarg);
list[2] = 1;
break;
case 3:
/* 3 commas => example 3) */
if(strncasecmp(indexn(_optarg, ',', 3)+1, "log", 3) == 0)
list[3] = SCALE_LOG;
/* here no break! */
case 2:
/* 2 commas => example 2) */
list[0] = atof(_optarg);
list[1] = atof(indexn(_optarg, ',', 1)+1);
list[2] = atoi(indexn(_optarg, ',', 2)+1);
/* N must be positive */
if(list[2] <= 0)
{
fprintf(stderr, "error parsing parameter -%c\n\n", param);
usage(stderr);
exit(1);
}
/* ensure that start < stop */
if(list[0] > list[1])
swap(&list[0], &list[1]);
break;
default:
fprintf(stderr, "Can't parse range %s.\n\n", _optarg);
usage(stderr);
exit(1);
}
}
void envirment_init() {
big a, b, p, x, y;
#if MIRACL==16
#ifdef MR_FLASH
miracl *mip = mirsys(500,10); /* initialise system to base 10, 500 digits per "big" */
#else
miracl *mip = mirsys(5000,10); /* bigger numbers possible if no flash arithmetic */
#endif
#else
miracl *mip = mirsys(5000,10); /* 5000 digits per "big" */
#endif
// init
a = mirvar(-3);
b = mirvar(0);
ECC_N = mirvar(0);
p = mirvar(0);
x = mirvar(0);
y = mirvar(0);
ECC_G = epoint_init();
ECC_H = epoint_init();
mip->IOBASE = 10;
// init curve
cinstr(b, bChar);
cinstr(ECC_N, nChar);
cinstr(p, pChar);
ecurve_init(a, b, p, MR_PROJECTIVE);
// init point: G, H
cinstr(x, gxChar);
cinstr(y, gyChar);
epoint_set(x, y, 0, ECC_G);
cinstr(x, hxChar);
cinstr(y, hyChar);
epoint_set(x, y, 0, ECC_H);
mip->IOBASE = 16;
mirkill(a);
mirkill(b);
mirkill(p);
mirkill(x);
mirkill(y);
}
int main()
{ /* MIRACL rational calculator */
int i,j,k,p,q,c,hpos;
BOOL over,help;
screen();
#if MIRACL==16
mip=mirsys(10,0); /*** 16-bit computer ***/
#else
mip=mirsys(6,0); /*** 32-bit computer ***/
#endif
mip->ERCON=TRUE;
x=mirvar(0);
for (i=0;i<=top;i++) y[i]=mirvar(0);
m=mirvar(0);
t=mirvar(0);
radeg=mirvar(0);
loge2=mirvar(0);
loge10=mirvar(0);
eps=mirvar(0);
mip->pi=mirvar(0);
cinstr(mip->pi,cpi); /* read in constants */
fpmul(mip->pi,1,180,radeg);
cinstr(loge2,clg2);
cinstr(loge10,clg10);
cinstr(eps,ceps);
help=OFF;
show(TRUE);
p=6;
q=0;
flag=OFF;
newx=OFF;
over=FALSE;
setopts();
clrall();
drawit();
while (!over)
{ /* main loop */
if (mip->ERNUM)
{
aprint(ORDINARY,4+5*p,6+3*q,keys[q][p]);
p=5,q=0;
}
if (width==80 || !help)
{
aprint(INVER,4+5*p,6+3*q,keys[q][p]);
curser(1,24);
c=gethit();
aprint(ORDINARY,4+5*p,6+3*q,keys[q][p]);
}
else while ((c=gethit())!='H') ;
result=TRUE;
if ((k=arrow(c))!=0)
{ /* arrow key hit */
if (k==1 && q>0) q--;
if (k==2 && q<5) q++;
if (k==3 && p<6) p++;
if (k==4 && p>0) p--;
continue;
}
if (c=='H')
{ /* switch help on/off */
help=!help;
for (i=1;i<=24;i++)
{
if (width==80) hpos=41;
else hpos=1;
if (help) aprint(HELPCOL,hpos,i,htext[i-1]);
else lclr(hpos,i);
}
if (width==40 && !help) drawit();
continue;
}
if (c>='A' && c<='F')
{ /* hex only */
if (!next(c)) putchar(BELL);
else show(FALSE);
continue;
}
for (j=0;j<6;j++)
for (i=0;i<7;i++)
if (c==qkeys[j][i]) p=i,q=j,c=' ';
if (c==8 || c==127) p=6,q=1,c=' '; /* aliases */
if (c==',' || c=='a') p=5,q=5,c=' ';
if (c=='O' || c==ESC) p=6,q=0,c=' ';
if (c==13) p=6,q=5,c=' ';
if (c=='[' || c=='{') p=3,q=5,c=' ';
if (c==']' || c=='}') p=4,q=5,c=' ';
if (c=='d') p=5,q=2,c=' ';
if (c=='b') p=5,q=3,c=' ';
if (c=='^') p=3,q=2,c=' ';
if (c==' ') over=act(p,q);
else continue;
absol(x,t);
if (fcomp(t,eps)<0) zero(x);
if (result)
{ /* output result to display */
cotstr(x,mip->IOBUFF);
just((char *)mip->IOBUFF);
if (mip->ERNUM<0)
{ /* convert to radix and try again */
mip->ERNUM=0;
mip->RPOINT=ON;
cotstr(x,mip->IOBUFF);
putchar(BELL);
just((char *)mip->IOBUFF);
}
clr();
}
if (newx)
{ /* update display */
getstat();
show(FALSE);
}
}
curser(1,24);
restore();
return 0;
}
static BOOL act(int p,int q)
{ /* act on selected key */
int k,n,c;
aprint(PRESSED,4+5*p,6+3*q,keys[q][p]);
switch(p+7*q)
{
case 0: if (degrees) fmul(x,radeg,x);
if (hyp) fsinh(x,x);
else fsin(x,x);
newx=TRUE;
break;
case 1: if (degrees) fmul(x,radeg,x);
if (hyp) fcosh(x,x);
else fcos(x,x);
newx=TRUE;
break;
case 2: if (degrees) fmul(x,radeg,x);
if (hyp) ftanh(x,x);
else ftan(x,x);
newx=TRUE;
break;
case 3: if (lgbase>0)
{
n=size(x);
if (abs(n)<MR_TOOBIG)
{
convert(lgbase,x);
if (n<0) frecip(x,x);
fpower(x,abs(n),x);
newx=TRUE;
break;
}
if (lgbase==2) fmul(x,loge2,x);
if (lgbase==10) fmul(x,loge10,x);
}
fexp(x,x);
newx=TRUE;
break;
case 4: mip->RPOINT=!mip->RPOINT;
newx=TRUE;
break;
case 5: clrall();
newx=TRUE;
break;
case 6: return TRUE;
case 7: if (hyp) fasinh(x,x);
else fasin(x,x);
if (degrees) fdiv(x,radeg,x);
newx=TRUE;
break;
case 8: if (hyp) facosh(x,x);
else facos(x,x);
if (degrees) fdiv(x,radeg,x);
newx=TRUE;
break;
case 9: if (hyp) fatanh(x,x);
else fatan(x,x);
if (degrees) fdiv(x,radeg,x);
newx=TRUE;
break;
case 10: flog(x,x);
if (lgbase==2) fdiv(x,loge2,x);
if (lgbase==10) fdiv(x,loge10,x);
newx=TRUE;
break;
case 11: newx=TRUE;
k=3;
forever
{
aprint(INVER,2+stptr[k],2,settings[k][option[k]]);
curser(2+stptr[k],2);
c=arrow(gethit());
if (c==1)
{
if (option[k]==nops[k]) option[k]=0;
else option[k]+=1;
continue;
}
aprint(STATCOL,2+stptr[k],2,settings[k][option[k]]);
if (c==0 || c==2) break;
if (c==4 && k>0) k--;
if (c==3 && k<3) k++;
}
setopts();
break;
case 12: chekit(7);
break;
case 13: result=FALSE;
if (ipt==0) break;
ipt--;
mybuff[ipt]='\0';
if (ipt==0) clr();
just(mybuff);
cinstr(x,mybuff);
newx=TRUE;
break;
case 14: if (!next('7')) putchar(BELL);
break;
case 15: if (!next('8')) putchar(BELL);
break;
case 16: if (!next('9')) putchar(BELL);
break;
case 17: chekit(6);
break;
case 18: chekit(5);
break;
case 19: chekit(4);
break;
case 20: copy(m,x);
newx=TRUE;
break;
case 21: if (!next('4')) putchar(BELL);
break;
case 22: if (!next('5')) putchar(BELL);
break;
case 23: if (!next('6')) putchar(BELL);
break;
case 24: fmul(x,x,x);
newx=TRUE;
break;
case 25: froot(x,2,x);
newx=TRUE;
break;
case 26: chekit(3);
break;
case 27: brkt=0;
chekit(0);
flag=OFF;
fadd(m,x,m);
newx=TRUE;
break;
case 28: if (!next('1')) putchar(BELL);
break;
case 29: if (!next('2')) putchar(BELL);
break;
case 30: if (!next('3')) putchar(BELL);
break;
case 31: frecip(x,x);
newx=TRUE;
break;
case 32: fpi(x);
newx=TRUE;
break;
case 33: chekit(2);
break;
case 34: negify(x,x);
newx=TRUE;
break;
case 35: if (!next('0')) putchar(BELL);
break;
case 36: if (!next('/')) putchar(BELL);
break;
case 37: if (!next('.')) putchar(BELL);
break;
case 38: if (ipt>0)
{
putchar(BELL);
result=FALSE;
}
else
{
zero(x);
brkt+=1;
newx=TRUE;
}
break;
case 39: if (brkt>0)
{
chekit(0);
brkt-=1;
}
else
{
putchar(BELL);
result=FALSE;
}
break;
case 40: chekit(1);
break;
case 41: brkt=0;
equals(0);
flag=OFF;
break;
}
return FALSE;
}
int main()
{ /* encode using public key */
big e,m,y,ke,mn,mx;
FILE *ifile;
FILE *ofile;
static char line[500];
static char buff[256];
char ifname[13],ofname[13];
BOOL fli,last;
int i,ipt,klen;
mip=mirsys(100,0);
e=mirvar(0);
m=mirvar(0);
y=mirvar(0);
ke=mirvar(0);
mn=mirvar(0);
mx=mirvar(0);
if ((ifile=fopen("public.key","rt"))==NULL)
{
printf("Unable to open file public.key\n");
return 0;
}
mip->IOBASE=16;
cinnum(ke,ifile);
fclose(ifile);
nroot(ke,3,mn);
multiply(mn,mn,m);
multiply(mn,m,mx);
subtract(mx,m,mx);
klen=0;
copy(mx,m);
while (size(m)>0)
{ /* find key length in characters */
klen++;
subdiv(m,128,m);
}
klen--;
printf("file to be encoded = ");
gets(ifname);
fli=FALSE;
if (strlen(ifname)>0) fli=TRUE;
if (fli)
{ /* set up input file */
strcpy(ofname,ifname);
strip(ofname);
strcat(ofname,".rsa");
if ((ifile=fopen(ifname,"rt"))==NULL)
{
printf("Unable to open file %s\n",ifname);
return 0;
}
printf("encoding message\n");
}
else
{ /* accept input from keyboard */
ifile=stdin;
do
{
printf("output filename = ");
gets(ofname);
} while (strlen(ofname)==0);
strip(ofname);
strcat(ofname,".rsa");
printf("input message - finish with cntrl z\n");
}
ofile=fopen(ofname,"wt");
ipt=0;
last=FALSE;
while (!last)
{ /* encode line by line */
if (fgets(&line[ipt],132,ifile)==NULL) last=TRUE;
if (line[ipt]==EOF) last=TRUE;
ipt=strlen(line);
if (ipt<klen && !last) continue;
while (ipt>=klen)
{ /* chop up into klen-sized chunks and encode */
for (i=0;i<klen;i++)
buff[i]=line[i];
buff[klen]='\0';
for (i=klen;i<=ipt;i++)
line[i-klen]=line[i];
ipt-=klen;
mip->IOBASE=128;
cinstr(m,buff);
power(m,3,ke,e);
mip->IOBASE=16;
cotnum(e,ofile);
}
if (last && ipt>0)
{ /* now deal with left overs */
mip->IOBASE=128;
cinstr(m,line);
if (compare(m,mn)<0)
{ /* pad out with random number if necessary */
bigrand(mn,y);
multiply(mn,mn,e);
subtract(e,y,e);
multiply(mn,e,y);
add(m,y,m);
}
power(m,3,ke,e);
mip->IOBASE=16;
cotnum(e,ofile);
}
}
fclose(ofile);
if (fli) fclose(ifile);
return 0;
}
JNIEXPORT jobjectArray JNICALL
Java_com_sunshuzhou_experiment_1miracl_Verify_computeForServer(JNIEnv *env, jobject instance,
jstring ux_, jstring uy_,
jstring u1x_, jstring u1y_,
jstring wx_, jstring wy_,
jstring com1x_, jstring com1y_,
jstring N1_, jstring sid_,
jstring alpha_, jstring beta_,
jstring zeta_) {
const char *ux = (*env)->GetStringUTFChars(env, ux_, 0);
const char *uy = (*env)->GetStringUTFChars(env, uy_, 0);
const char *u1x = (*env)->GetStringUTFChars(env, u1x_, 0);
const char *u1y = (*env)->GetStringUTFChars(env, u1y_, 0);
const char *wx = (*env)->GetStringUTFChars(env, wx_, 0);
const char *wy = (*env)->GetStringUTFChars(env, wy_, 0);
const char *com1x = (*env)->GetStringUTFChars(env, com1x_, 0);
const char *com1y = (*env)->GetStringUTFChars(env, com1y_, 0);
const char *N1 = (*env)->GetStringUTFChars(env, N1_, 0);
const char *sid = (*env)->GetStringUTFChars(env, sid_, 0);
const char *alpha = (*env)->GetStringUTFChars(env, alpha_, 0);
const char *beta = (*env)->GetStringUTFChars(env, beta_, 0);
const char *zeta = (*env)->GetStringUTFChars(env, zeta_, 0);
big x, y, d, k1, N2, sum, big1;
epoint *u, *u1, *w, *com1, *w1, *epoint1, *com, *K;
int message_len, i;
unsigned char key[300], tag[SHA1_HASH_SIZE], hexdigest[SHA1_HASH_SIZE * 2 + 1], message[1000], tempChars[300];
jclass jclass1 = (*env)->FindClass(env, "java/lang/String");
jobjectArray result;
envirment_init();
x = mirvar(0);
y = mirvar(0);
d = mirvar(0);
k1 = mirvar(0);
N2 = mirvar(0);
sum = mirvar(0);
big1 = mirvar(0);
u = epoint_init();
u1 = epoint_init();
w = epoint_init();
com1 = epoint_init();
w1 = epoint_init();
epoint1 = epoint_init();
com = epoint_init();
K = epoint_init();
cinstr(x, ux);
cinstr(y, uy);
epoint_set(x, y, 0, u);
cinstr(x, u1x);
cinstr(y, u1y);
epoint_set(x, y, 0, u1);
cinstr(x, wx);
cinstr(y, wy);
epoint_set(x, y, 0, w);
cinstr(x, com1x);
cinstr(y, com1y);
epoint_set(x, y, 0, com1);
irand((long)time(0));
bigrand(ECC_N, d);
bigrand(ECC_N, k1);
bigbits(80, N2);
// sum = alpha + beta + zeta
cinstr(big1, alpha);
cinstr(sum, beta);
add(big1, sum, sum);
cinstr(big1, zeta);
add(big1, sum, sum);
// w1 = k1 * H
ecurve_mult(k1, ECC_H, w1);
// com = (alpha + beta + zeta) * u + d * H
ecurve_mult(sum, u, com);
ecurve_mult(d, ECC_H, epoint1);
ecurve_add(epoint1, com);
// K = d * w + k1 * (com1 - sum * u1)
ecurve_mult(d, w, K);
ecurve_mult(sum, u1, epoint1);
ecurve_sub(epoint1, com1);
ecurve_mult(k1, com1, com1);
ecurve_add(com1, K);
// K.y as key
epoint_get(K, x, y);
cotstr(y, key);
// message: u.y || u1.y || w.y || com1.y || N1 || sid
epoint_get(u, x, y);
cotstr(y, message);
message_len = strlen(message);
epoint_get(u1, x, y);
cotstr(y, &message[message_len]);
message_len = strlen(message);
epoint_get(w, x, y);
cotstr(y, &message[message_len]);
message_len = strlen(message);
epoint_get(com1, x, y);
cotstr(x, &message[message_len]);
message_len = strlen(message);
strcpy(&message[message_len], N1);
message_len = strlen(message);
strcpy(&message[message_len], sid);
message_len = strlen(message);
hmac_sha1(key, strlen(key), message, message_len, tag, SHA1_HASH_SIZE);
for (i = 0; i < SHA1_HASH_SIZE; ++i) {
sprintf(&hexdigest[i * 2], "%02x", tag[i]);
}
hexdigest[40] = '\0';
(*env)->ReleaseStringUTFChars(env, ux_, ux);
(*env)->ReleaseStringUTFChars(env, uy_, uy);
(*env)->ReleaseStringUTFChars(env, u1x_, u1x);
(*env)->ReleaseStringUTFChars(env, u1y_, u1y);
(*env)->ReleaseStringUTFChars(env, wx_, wx);
(*env)->ReleaseStringUTFChars(env, wy_, wy);
(*env)->ReleaseStringUTFChars(env, com1x_, com1x);
(*env)->ReleaseStringUTFChars(env, com1y_, com1y);
(*env)->ReleaseStringUTFChars(env, N1_, N1);
(*env)->ReleaseStringUTFChars(env, sid_, sid);
(*env)->ReleaseStringUTFChars(env, alpha_, alpha);
(*env)->ReleaseStringUTFChars(env, beta_, beta);
(*env)->ReleaseStringUTFChars(env, zeta_, zeta);
result = (*env)->NewObjectArray(env, 8, jclass1, (*env)->NewStringUTF(env, ""));
epoint_get(w1, x, y);
cotstr(x, tempChars);
(*env)->SetObjectArrayElement(env, result, 0, (*env)->NewStringUTF(env, tempChars));
cotstr(y, tempChars);
(*env)->SetObjectArrayElement(env, result, 1, (*env)->NewStringUTF(env, tempChars));
epoint_get(com, x, y);
cotstr(x, tempChars);
(*env)->SetObjectArrayElement(env, result, 2, (*env)->NewStringUTF(env, tempChars));
cotstr(y, tempChars);
(*env)->SetObjectArrayElement(env, result, 3, (*env)->NewStringUTF(env, tempChars));
cotstr(N2, tempChars);
(*env)->SetObjectArrayElement(env, result, 4, (*env)->NewStringUTF(env, tempChars));
(*env)->SetObjectArrayElement(env, result, 5, (*env)->NewStringUTF(env, message));
(*env)->SetObjectArrayElement(env, result, 6, (*env)->NewStringUTF(env, hexdigest));
(*env)->SetObjectArrayElement(env, result, 7, (*env)->NewStringUTF(env, key));
mirkill(x);
mirkill(y);
mirkill(d);
mirkill(k1);
mirkill(N2);
mirkill(sum);
mirkill(big1);
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;
}
int main()
{
int j,k;
big a,b,x,y,p,A2;
time_t seed;
epoint *g;
double tr1,tr2,ts,tv1,tv2,tp,td;
#ifndef MR_NOFULLWIDTH
miracl *mip=mirsys(300,0);
#else
miracl *mip=mirsys(300,MAXBASE);
#endif
p=mirvar(0);
a=mirvar(-3);
b=mirvar(0);
x=mirvar(1);
y=mirvar(0);
A2=mirvar(0);
mip->IOBASE=60;
time(&seed);
irand((long)seed);
printf("MIRACL - %d bit version\n",MIRACL);
#ifdef MR_LITTLE_ENDIAN
printf("Little Endian processor\n");
#endif
#ifdef MR_BIG_ENDIAN
printf("Big Endian processor\n");
#endif
#ifdef MR_NOASM
printf("C-Only Version of MIRACL\n");
#else
printf("Using some assembly language\n");
#endif
#ifdef MR_STRIPPED_DOWN
printf("Stripped down version of MIRACL - no error messages\n");
#endif
#ifdef MR_KCM
k=MR_KCM*MIRACL;
printf("Using KCM method \n");
printf("Optimized for %d, %d, %d, %d...etc. bit moduli\n",k,k*2,k*4,k*8);
#endif
#ifdef MR_COMBA
k=MR_COMBA*MIRACL;
printf("Using COMBA method \n");
printf("Optimized for %d bit moduli\n",k);
#endif
#ifdef MR_PENTIUM
printf("Floating-point co-processor arithmetic used for Pentium\n");
#endif
#ifndef MR_KCM
#ifndef MR_COMBA
#ifndef MR_PENTIUM
printf("No special optimizations\n");
#endif
#endif
#endif
printf("Precomputation uses fixed Window size = %d\n",WINDOW);
printf("So %d values are precomputed and stored\n",(1<<WINDOW));
#ifdef MR_NOFULLWIDTH
printf("No Fullwidth base possible\n");
#else
printf("NOTE: No optimizations/assembly language apply to GF(2^m) Elliptic Curves\n");
#endif
printf("NOTE: times are elapsed real-times - so make sure nothing else is running!\n\n");
printf("Modular exponentiation benchmarks - calculating g^e mod p\n");
printf("From these figures it should be possible to roughly estimate the time\n");
printf("required for your favourite PK algorithm, RSA, DSA, DH, etc.\n");
printf("Key R - random base bits/random exponent bits \n");
printf(" V - random base bits/(small exponent e) \n");
printf(" S - (small base g) /random exponent bits \n");
printf(" P - exponentiation with precomputation (fixed base g)\n");
printf(" D - double exponentiation g^e.a^b mod p\n");
printf("F3 = 257, F4 = 65537\n");
printf("RSA - Rivest-Shamir-Adleman\n");
printf("DH - Diffie Hellman Key exchange\n");
printf("DSA - Digital Signature Algorithm\n");
printf("\n512 bit prime....\n");
cinstr(p,p512);
k=512;
j=160;
tr1=powers(k,j,p);
td=powers_double(k,j,p);
tr2=powers(k,k,p);
ts=powers_small_base(3,j,p);
tp=powers_precomp(k,j,p);
printf("\n");
printf("%4d bit RSA decryption %8.2lf ms \n",2*k,2*tr2);
printf("%4d bit DH %d bit exponent:-\n",k,j);
printf(" offline, no precomputation %8.2lf ms \n",tr1);
printf(" offline, small base %8.2lf ms \n",ts);
printf(" offline, w. precomputation %8.2lf ms \n",tp);
printf(" online %8.2lf ms \n",tr1);
printf("%4d bit DSA %d bit exponent:-\n",k,j);
printf(" signature no precomputation %8.2lf ms \n",tr1);
printf(" signature w. precomputation %8.2lf ms \n",tp);
printf(" verification %8.2lf ms \n",td);
printf("\n1024 bit prime....\n");
cinstr(p,p1024);
k=1024; j=160;
tr1=powers(k,j,p);
td=powers_double(k,j,p);
tr2=powers(k,k,p);
tv1=powers_small_exp(k,3,p);
tv2=powers_small_exp(k,65537L,p);
ts=powers_small_base(3,j,p);
tp=powers_precomp(k,j,p);
printf("\n");
printf("%4d bit RSA decryption %8.2lf ms \n",2*k,2*tr2);
printf("%4d bit RSA encryption e=3 %8.2lf ms \n",k,tv1);
printf("%4d bit RSA encryption e=65537 %8.2lf ms \n",k,tv2);
printf("%4d bit DH %d bit exponent:-\n",k,j);
printf(" offline, no precomputation %8.2lf ms \n",tr1);
printf(" offline, small base %8.2lf ms \n",ts);
printf(" offline, w. precomputation %8.2lf ms \n",tp);
printf(" online %8.2lf ms \n",tr1);
printf("%4d bit DSA %d bit exponent:-\n",k,j);
printf(" signature no precomputation %8.2lf ms \n",tr1);
printf(" signature w. precomputation %8.2lf ms \n",tp);
printf(" verification %8.2lf ms \n",td);
printf("\n2048 bit prime....\n");
cinstr(p,p2048);
k=2048; j=256;
tr1=powers(k,j,p);
td=powers_double(k,j,p);
powers(k,k,p);
tv1=powers_small_exp(k,3,p);
tv2=powers_small_exp(k,65537L,p);
ts=powers_small_base(3,j,p);
tp=powers_precomp(k,j,p);
printf("\n");
printf("%4d bit RSA encryption e=3 %8.2lf ms \n",k,tv1);
printf("%4d bit RSA encryption e=65537 %8.2lf ms \n",k,tv2);
printf("%4d bit DH %d bit exponent:-\n",k,j);
printf(" offline, no precomputation %8.2lf ms \n",tr1);
printf(" offline, small base %8.2lf ms \n",ts);
printf(" offline, w. precomputation %8.2lf ms \n",tp);
printf(" online %8.2lf ms \n",tr1);
printf("%4d bit DSA %d bit exponent:-\n",k,j);
printf(" signature no precomputation %8.2lf ms \n",tr1);
printf(" signature w. precomputation %8.2lf ms \n",tp);
printf(" verification %8.2lf ms \n",td);
printf("\n");
printf("Elliptic Curve point multiplication benchmarks - calculating r.P\n");
printf("From these figures it should be possible to roughly estimate the time\n");
printf("required for your favourite EC PK algorithm, ECDSA, ECDH, etc.\n");
printf("Key - ER - Elliptic Curve point multiplication r.P\n");
printf(" ED - Elliptic Curve double multiplication r.P + s.Q\n");
printf(" EP - Elliptic Curve multiplication with precomputation\n");
printf("EC - Elliptic curve GF(p) - p of no special form \n");
printf("ECDH - Diffie Hellman Key exchange\n");
printf("ECDSA - Digital Signature Algorithm\n");
mip->IOBASE=10;
printf("\n160 bit GF(p) Elliptic Curve....\n");
k=160;
cinstr(p,p160);
cinstr(b,b160);
cinstr(y,y160);
ecurve_init(a,b,p,MR_PROJECTIVE);
g=epoint_init();
if (!epoint_set(x,y,0,g))
{
printf("This is not a point on the curve!\n");
exit(0);
}
tr1=mults(k,g);
td=mult_double(k,g);
tp=mult_precomp(k,x,y,a,b,p);
printf("\n");
printf("%4d bit ECDH :-\n",k);
printf(" offline, no precomputation %8.2lf ms \n",tr1);
printf(" offline, w. precomputation %8.2lf ms \n",tp);
printf(" online %8.2lf ms \n",tr1);
printf("%4d bit ECDSA :-\n",k);
printf(" signature no precomputation %8.2lf ms \n",tr1);
printf(" signature w. precomputation %8.2lf ms \n",tp);
printf(" verification %8.2lf ms \n",td);
printf("\n192 bit GF(p) Elliptic Curve....\n");
k=192;
cinstr(p,p192);
cinstr(b,b192);
cinstr(y,y192);
ecurve_init(a,b,p,MR_PROJECTIVE);
g=epoint_init();
if (!epoint_set(x,y,0,g))
{
printf("This is not a point on the curve!\n");
exit(0);
}
tr1=mults(k,g);
td=mult_double(k,g);
tp=mult_precomp(k,x,y,a,b,p);
printf("\n");
printf("%4d bit ECDH :-\n",k);
printf(" offline, no precomputation %8.2lf ms \n",tr1);
printf(" offline, w. precomputation %8.2lf ms \n",tp);
printf(" online %8.2lf ms \n",tr1);
printf("%4d bit ECDSA :-\n",k);
printf(" signature no precomputation %8.2lf ms \n",tr1);
printf(" signature w. precomputation %8.2lf ms \n",tp);
printf(" verification %8.2lf ms \n",td);
printf("\n224 bit GF(p) Elliptic Curve....\n");
k=224;
cinstr(p,p224);
cinstr(b,b224);
cinstr(y,y224);
ecurve_init(a,b,p,MR_PROJECTIVE);
g=epoint_init();
if (!epoint_set(x,y,0,g))
{
printf("This is not a point on the curve!\n");
exit(0);
}
tr1=mults(k,g);
td=mult_double(k,g);
tp=mult_precomp(k,x,y,a,b,p);
printf("\n");
printf("%4d bit ECDH :-\n",k);
printf(" offline, no precomputation %8.2lf ms \n",tr1);
printf(" offline, w. precomputation %8.2lf ms \n",tp);
printf(" online %8.2lf ms \n",tr1);
printf("%4d bit ECDSA :-\n",k);
printf(" signature no precomputation %8.2lf ms \n",tr1);
printf(" signature w. precomputation %8.2lf ms \n",tp);
printf(" verification %8.2lf ms \n",td);
printf("\n256 bit GF(p) Elliptic Curve....\n");
k=256;
cinstr(p,p256);
cinstr(b,b256);
cinstr(y,y256);
ecurve_init(a,b,p,MR_PROJECTIVE);
g=epoint_init();
if (!epoint_set(x,y,0,g))
{
printf("This is not a point on the curve!\n");
exit(0);
}
tr1=mults(k,g);
td=mult_double(k,g);
tp=mult_precomp(k,x,y,a,b,p);
printf("\n");
printf("%4d bit ECDH :-\n",k);
printf(" offline, no precomputation %8.2lf ms \n",tr1);
printf(" offline, w. precomputation %8.2lf ms \n",tp);
printf(" online %8.2lf ms \n",tr1);
printf("%4d bit ECDSA :-\n",k);
printf(" signature no precomputation %8.2lf ms \n",tr1);
printf(" signature w. precomputation %8.2lf ms \n",tp);
printf(" verification %8.2lf ms \n",td);
#ifndef MR_FP
printf("\n163 bit GF(2^m) Elliptic Curve....\n");
k=163;
mip->IOBASE=16;
cinstr(b,B163);
cinstr(x,x163);
cinstr(y,y163);
mip->IOBASE=10;
convert(A163,A2);
ecurve2_init(m163,a163,b163,c163,A2,b,FALSE,MR_PROJECTIVE);
g=epoint_init();
if (!epoint2_set(x,y,0,g))
{
printf("This is not a point on the curve!\n");
exit(0);
}
tr1=mults2(k,g);
td=mult2_double(k,g);
tp=mult2_precomp(k,x,y,A2,b,m163,a163,b163,c163);
printf("\n");
printf("%4d bit ECDH :-\n",k);
printf(" offline, no precomputation %8.2lf ms \n",tr1);
printf(" offline, w. precomputation %8.2lf ms \n",tp);
printf(" online %8.2lf ms \n",tr1);
printf("%4d bit ECDSA :-\n",k);
printf(" signature no precomputation %8.2lf ms \n",tr1);
printf(" signature w. precomputation %8.2lf ms \n",tp);
printf(" verification %8.2lf ms \n",td);
printf("\n163 bit GF(2^m) Koblitz Elliptic Curve....\n");
k=163;
mip->IOBASE=16;
cinstr(b,KB163);
cinstr(x,Kx163);
cinstr(y,Ky163);
mip->IOBASE=10;
convert(KA163,A2);
ecurve2_init(m163,a163,b163,c163,A2,b,FALSE,MR_PROJECTIVE);
g=epoint_init();
if (!epoint2_set(x,y,0,g))
{
printf("This is not a point on the curve!\n");
exit(0);
}
tr1=mults2(k,g);
td=mult2_double(k,g);
tp=mult2_precomp(k,x,y,A2,b,m163,a163,b163,c163);
printf("\n");
printf("%4d bit ECDH :-\n",k);
printf(" offline, no precomputation %8.2lf ms \n",tr1);
printf(" offline, w. precomputation %8.2lf ms \n",tp);
printf(" online %8.2lf ms \n",tr1);
printf("%4d bit ECDSA :-\n",k);
printf(" signature no precomputation %8.2lf ms \n",tr1);
printf(" signature w. precomputation %8.2lf ms \n",tp);
printf(" verification %8.2lf ms \n",td);
printf("\n233 bit GF(2^m) Elliptic Curve....\n");
k=233;
mip->IOBASE=16;
cinstr(b,B233);
cinstr(x,x233);
cinstr(y,y233);
mip->IOBASE=10;
convert(A233,A2);
ecurve2_init(m233,a233,b233,c233,A2,b,FALSE,MR_PROJECTIVE);
g=epoint_init();
if (!epoint2_set(x,y,0,g))
{
printf("This is not a point on the curve!\n");
exit(0);
}
tr1=mults2(k,g);
td=mult2_double(k,g);
tp=mult2_precomp(k,x,y,A2,b,m233,a233,b233,c233);
printf("\n");
printf("%4d bit ECDH :-\n",k);
printf(" offline, no precomputation %8.2lf ms \n",tr1);
printf(" offline, w. precomputation %8.2lf ms \n",tp);
printf(" online %8.2lf ms \n",tr1);
printf("%4d bit ECDSA :-\n",k);
printf(" signature no precomputation %8.2lf ms \n",tr1);
printf(" signature w. precomputation %8.2lf ms \n",tp);
printf(" verification %8.2lf ms \n",td);
printf("\n233 bit GF(2^m) Koblitz Elliptic Curve....\n");
k=233;
mip->IOBASE=16;
cinstr(b,KB233);
cinstr(x,Kx233);
cinstr(y,Ky233);
mip->IOBASE=10;
convert(KA233,A2);
ecurve2_init(m233,a233,b233,c233,A2,b,FALSE,MR_PROJECTIVE);
g=epoint_init();
if (!epoint2_set(x,y,0,g))
{
printf("This is not a point on the curve!\n");
exit(0);
}
tr1=mults2(k,g);
td=mult2_double(k,g);
tp=mult2_precomp(k,x,y,A2,b,m233,a233,b233,c233);
printf("\n");
printf("%4d bit ECDH :-\n",k);
printf(" offline, no precomputation %8.2lf ms \n",tr1);
printf(" offline, w. precomputation %8.2lf ms \n",tp);
printf(" online %8.2lf ms \n",tr1);
printf("%4d bit ECDSA :-\n",k);
printf(" signature no precomputation %8.2lf ms \n",tr1);
printf(" signature w. precomputation %8.2lf ms \n",tp);
printf(" verification %8.2lf ms \n",td);
printf("\n283 bit GF(2^m) Elliptic Curve....\n");
k=283;
mip->IOBASE=16;
cinstr(b,B283);
cinstr(x,x283);
cinstr(y,y283);
mip->IOBASE=10;
convert(A283,A2);
ecurve2_init(m283,a283,b283,c283,A2,b,FALSE,MR_PROJECTIVE);
g=epoint_init();
if (!epoint2_set(x,y,0,g))
{
printf("This is not a point on the curve!\n");
exit(0);
}
tr1=mults2(k,g);
td=mult2_double(k,g);
tp=mult2_precomp(k,x,y,A2,b,m283,a283,b283,c283);
printf("\n");
printf("%4d bit ECDH :-\n",k);
printf(" offline, no precomputation %8.2lf ms \n",tr1);
printf(" offline, w. precomputation %8.2lf ms \n",tp);
printf(" online %8.2lf ms \n",tr1);
printf("%4d bit ECDSA :-\n",k);
printf(" signature no precomputation %8.2lf ms \n",tr1);
printf(" signature w. precomputation %8.2lf ms \n",tp);
printf(" verification %8.2lf ms \n",td);
printf("\n283 bit GF(2^m) Koblitz Elliptic Curve....\n");
k=283;
mip->IOBASE=16;
cinstr(b,KB283);
cinstr(x,Kx283);
cinstr(y,Ky283);
mip->IOBASE=10;
convert(KA283,A2);
ecurve2_init(m283,a283,b283,c283,A2,b,FALSE,MR_PROJECTIVE);
g=epoint_init();
if (!epoint2_set(x,y,0,g))
{
printf("This is not a point on the curve!\n");
exit(0);
}
tr1=mults2(k,g);
td=mult2_double(k,g);
tp=mult2_precomp(k,x,y,A2,b,m283,a283,b283,c283);
printf("\n");
printf("%4d bit ECDH :-\n",k);
printf(" offline, no precomputation %8.2lf ms \n",tr1);
printf(" offline, w. precomputation %8.2lf ms \n",tp);
printf(" online %8.2lf ms \n",tr1);
printf("%4d bit ECDSA :-\n",k);
printf(" signature no precomputation %8.2lf ms \n",tr1);
printf(" signature w. precomputation %8.2lf ms \n",tp);
printf(" verification %8.2lf ms \n",td);
printf("\n571 bit GF(2^m) Elliptic Curve....\n");
k=571;
mip->IOBASE=16;
cinstr(b,B571);
cinstr(x,x571);
cinstr(y,y571);
mip->IOBASE=10;
convert(A571,A2);
ecurve2_init(m571,a571,b571,c571,A2,b,FALSE,MR_PROJECTIVE);
g=epoint_init();
if (!epoint2_set(x,y,0,g))
{
printf("This is not a point on the curve!\n");
exit(0);
}
tr1=mults2(k,g);
td=mult2_double(k,g);
tp=mult2_precomp(k,x,y,A2,b,m571,a571,b571,c571);
printf("\n");
printf("%4d bit ECDH :-\n",k);
printf(" offline, no precomputation %8.2lf ms \n",tr1);
printf(" offline, w. precomputation %8.2lf ms \n",tp);
printf(" online %8.2lf ms \n",tr1);
printf("%4d bit ECDSA :-\n",k);
printf(" signature no precomputation %8.2lf ms \n",tr1);
printf(" signature w. precomputation %8.2lf ms \n",tp);
printf(" verification %8.2lf ms \n",td);
printf("\n571 bit GF(2^m) Koblitz Elliptic Curve....\n");
k=571;
mip->IOBASE=16;
cinstr(b,KB571);
cinstr(x,Kx571);
cinstr(y,Ky571);
mip->IOBASE=10;
convert(KA571,A2);
ecurve2_init(m571,a571,b571,c571,A2,b,FALSE,MR_PROJECTIVE);
g=epoint_init();
if (!epoint2_set(x,y,0,g))
{
printf("This is not a point on the curve!\n");
exit(0);
}
tr1=mults2(k,g);
td=mult2_double(k,g);
tp=mult2_precomp(k,x,y,A2,b,m571,a571,b571,c571);
printf("\n");
printf("%4d bit ECDH :-\n",k);
printf(" offline, no precomputation %8.2lf ms \n",tr1);
printf(" offline, w. precomputation %8.2lf ms \n",tp);
printf(" online %8.2lf ms \n",tr1);
printf("%4d bit ECDSA :-\n",k);
printf(" signature no precomputation %8.2lf ms \n",tr1);
printf(" signature w. precomputation %8.2lf ms \n",tp);
printf(" verification %8.2lf ms \n",td);
#endif
return 0;
}
int main()
{ /* Pollard's lambda algorithm for finding discrete logs *
* which are known to be less than a certain limit LIMIT */
big x,n,t,trap,table[32];
int i,j,m;
long dm,dn,s,distance[32];
miracl *mip=mirsys(50,0);
x=mirvar(0);
n=mirvar(0);
t=mirvar(0);
trap=mirvar(0);
for (s=1L,m=1;;m++)
{ /* find table size */
distance[m-1]=s;
s*=2;
if ((2*s/m)>(LEAPS/4)) break;
}
mip->IOBASE=60; /* get large modulus */
cinstr(n,modulus);
mip->IOBASE=10;
printf("solve discrete logarithm problem - using Pollard's kangaroos\n");
printf("finds x in y=%d^x mod n, given y, for fixed n and small x\n",ALPHA);
printf("known to be less than %ld\n",LIMIT);
printf("n= ");
cotnum(n,stdout);
for (i=0;i<m;i++)
{ /* create table */
lgconv(distance[i],t);
table[i]=mirvar(0);
powltr(ALPHA,t,n,table[i]);
}
lgconv(LIMIT,t);
powltr(ALPHA,t,n,x);
printf("setting trap .... \n");
for (dn=0L,j=0;j<LEAPS;j++)
{ /* set traps beyond LIMIT using tame kangaroo */
i=subdiv(x,m,t); /* random function */
mad(x,table[i],x,n,n,x);
dn+=distance[i];
}
printf("trap set!\n");
copy(x,trap);
forever
{ /* ready to solve */
printf("Enter x= ");
cinnum(x,stdin);
if (size(x)<=0) break;
powltr(ALPHA,x,n,t);
printf("y= ");
cotnum(t,stdout);
copy(t,x);
for (dm=0L;;)
{ /* unlease wild kangaroo - boing - boing ... */
i=subdiv(x,m,t);
mad(x,table[i],x,n,n,x);
dm+=distance[i];
if (compare(x,trap)==0 || dm>LIMIT+dn) break;
}
if (dm>LIMIT+dn)
{ /* trap stepped over */
printf("trap failed\n");
continue;
}
printf("Gotcha!\n");
printf("Discrete log of y= %ld\n",LIMIT+dn-dm);
}
return 0;
}
