KGC_TEST/miracl/source/curve/pairing/ssp_pair.cpp

897 lines
17 KiB
C++

/***************************************************************************
*
Copyright 2013 CertiVox UK Ltd. *
*
This file is part of CertiVox MIRACL Crypto SDK. *
*
The CertiVox MIRACL Crypto SDK provides developers with an *
extensive and efficient set of cryptographic functions. *
For further information about its features and functionalities please *
refer to http://www.certivox.com *
*
* The CertiVox MIRACL Crypto SDK is free software: you can *
redistribute it and/or modify it under the terms of the *
GNU Affero General Public License as published by the *
Free Software Foundation, either version 3 of the License, *
or (at your option) any later version. *
*
* The CertiVox MIRACL Crypto SDK is distributed in the hope *
that it will be useful, but WITHOUT ANY WARRANTY; without even the *
implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. *
See the GNU Affero General Public License for more details. *
*
* You should have received a copy of the GNU Affero General Public *
License along with CertiVox MIRACL Crypto SDK. *
If not, see <http://www.gnu.org/licenses/>. *
*
You can be released from the requirements of the license by purchasing *
a commercial license. Buying such a license is mandatory as soon as you *
develop commercial activities involving the CertiVox MIRACL Crypto SDK *
without disclosing the source code of your own applications, or shipping *
the CertiVox MIRACL Crypto SDK with a closed source product. *
*
***************************************************************************/
/*
* ssp_pair.cpp
*
* Supersingular curve, Tate pairing embedding degree 2, ideal for security level AES-80
*
* Provides high level interface to pairing functions
*
* GT=pairing(G1,G1)
*
* This is calculated on a Pairing Friendly Curve (PFC), which must first be defined.
*
* G1 is a point over the base field
* GT is a finite field point over the 2nd extension, where 2 is the embedding degree.
*/
#define MR_PAIRING_SSP
#include "pairing_1.h"
// Supersingular curve parameters, A,B and n, where p=2nq-1
// AES_SECURITY=80 bit curve
static char param_80[]="B83DFB800C851836F9B95087F2642EF80B01601D46BA7CC14978EB4F6225BA7558E3D487FA3639FFE4C36332";
// AES_SECURITY=128 bit curve
static char param_128[]="83093742908D4D529CEF06C72191A05D5E6073FE861E637D7747C3E52FBB92DAA5DDF3EF1C61F5F70B256802481A36CAFE995FE33CD54014B846751364C0D3B8327D9E45366EA08F1B3446AC23C9D4B656886731A8D05618CFA1A3B202A2445ABA0E77C5F4F00CA1239975A05377084F256DEAA07D21C4CF2A4279BC117603ACB7B10228C3AB8F8C1742D674395701BB02071A88683041D9C4231E8EE982B8DA";
void read_only_error(void)
{
cout << "Attempt to write to read-only object" << endl;
exit(0);
}
// Using SHA256 as basic hash algorithm
//
// Hash function
//
#define HASH_LEN 32
Big H1(char *string)
{ // Hash a zero-terminated string to a number < modulus
Big h,p;
char s[HASH_LEN];
int i,j;
sha256 sh;
shs256_init(&sh);
for (i=0;;i++)
{
if (string[i]==0) break;
shs256_process(&sh,string[i]);
}
shs256_hash(&sh,s);
p=get_modulus();
h=1; j=0; i=1;
forever
{
h*=256;
if (j==HASH_LEN) {h+=i++; j=0;}
else h+=s[j++];
if (h>=p) break;
}
h%=p;
return h;
}
void PFC::start_hash(void)
{
shs256_init(&SH);
}
Big PFC::finish_hash_to_group(void)
{
Big hash;
char s[HASH_LEN];
shs256_hash(&SH,s);
hash=from_binary(HASH_LEN,s);
return hash%(*ord);
}
void PFC::add_to_hash(const GT& x)
{ // compress it and add
ZZn2 u=x.g;
Big a;
int m;
u.get(a);
while (a>0)
{
m=a%256;
shs256_process(&SH,m);
a/=256;
}
}
void PFC::add_to_hash(const G1& x)
{
Big a,X,Y;
int i,m;
x.g.get(X,Y);
a=X;
while (a>0)
{
m=a%256;
shs256_process(&SH,m);
a/=256;
}
a=Y;
while (a>0)
{
m=a%256;
shs256_process(&SH,m);
a/=256;
}
}
void PFC::add_to_hash(const Big& x)
{
int m;
Big a=x;
while (a>0)
{
m=a%256;
shs256_process(&SH,m);
a/=256;
}
}
Big H2(ZZn2 y)
{ // Hash and compress an Fp2 to a big number
sha256 sh;
Big a,h;
char s[HASH_LEN];
int m;
shs256_init(&sh);
y.get(a);
while (a>0)
{
m=a%256;
shs256_process(&sh,m);
a/=256;
}
shs256_hash(&sh,s);
h=from_binary(HASH_LEN,s);
return h;
}
#ifndef MR_AFFINE_ONLY
void force(ZZn& x,ZZn& y,ZZn& z,ECn& A)
{ // A=(x,y,z)
copy(getbig(x),A.get_point()->X);
copy(getbig(y),A.get_point()->Y);
copy(getbig(z),A.get_point()->Z);
A.get_point()->marker=MR_EPOINT_GENERAL;
}
void extract(ECn &A, ZZn& x,ZZn& y,ZZn& z)
{ // (x,y,z) <- A
big t;
x=(A.get_point())->X;
y=(A.get_point())->Y;
t=(A.get_point())->Z;
if (A.get_status()!=MR_EPOINT_GENERAL) z=1;
else z=t;
}
#endif
void force(ZZn& x,ZZn& y,ECn& A)
{ // A=(x,y)
copy(getbig(x),A.get_point()->X);
copy(getbig(y),A.get_point()->Y);
A.get_point()->marker=MR_EPOINT_NORMALIZED;
}
void extract(ECn& A,ZZn& x,ZZn& y)
{ // (x,y) <- A
if (A.iszero())
{
x=0; y=0;
return;
}
x=(A.get_point())->X;
y=(A.get_point())->Y;
}
void extractZ(ECn& A,ZZn& z)
{
big t;
t=(A.get_point())->Z;
if (A.get_status()!=MR_EPOINT_GENERAL) z=1;
else z=t;
}
//
// Line from A to destination C. Let A=(x,y)
// Line Y-slope.X-c=0, through A, so intercept c=y-slope.x
// Line Y-slope.X-y+slope.x = (Y-y)-slope.(X-x) = 0
// Now evaluate at Q -> return (Qy-y)-slope.(Qx-x)
//
ZZn2 line(ECn& A,ECn& C,ECn& B,int type,ZZn& slope,ZZn& ex1,ZZn& ex2,ZZn& Px,ZZn& Py)
{
ZZn2 w;
ZZn x,y,z3;
extractZ(C,z3);
if (type==MR_ADD)
{
extract(B,x,y);
w.set(slope*(x+Px)-z3*y,z3*Py);
}
if (type==MR_DOUBLE)
{
extract(A,x,y);
w.set(-(slope*ex2)*Px-slope*x+ex1,-(z3*ex2)*Py);
}
/*
extract(A,x,y,z);
x*=z; t=z; z*=z; z*=t; // 9 ZZn muls
n*=z; n+=x; n*=slope;
d*=z; w.set(-y,d);
extractZ(C,z3);
w*=z3; w+=n;
*/
// w.set(Px*z*z*z*slope+slope*x*z-y*z3,Py*z*z*z*z3);
return w;
}
//
// Add A=A+B (or A=A+A)
// Return line function value
//
ZZn2 g(ECn& A,ECn& B,ZZn& Px,ZZn& Py)
{
int type;
ZZn lam,extra1,extra2;
ZZn2 u;
ECn P=A;
big ptr,ex1,ex2;
type=A.add(B,&ptr,&ex1,&ex2);
if (!type) return (ZZn2)1;
lam=ptr;
extra1=ex1;
extra2=ex2;
return line(P,A,B,type,lam,extra1,extra2,Px,Py);
}
// if multiples of G1 can be precalculated, its a lot faster!
ZZn2 gp(ZZn* ptable,int &j,ZZn& Px,ZZn& Py)
{
ZZn2 w;
w.set(ptable[j]*Px+ptable[j+1],Py);
j+=2;
return w;
}
//
// Spill precomputation on pairing to byte array
//
int PFC::spill(G1& w,char *& bytes)
{
int i,j,n=2*(bits(*ord-1)-2+ham(*ord));
int bytes_per_big=(MIRACL/8)*(get_mip()->nib-1);
int len=n*bytes_per_big;
Big x;
if (w.ptable==NULL) return 0;
bytes=new char[len];
for (i=j=0;i<n;i++)
{
x=w.ptable[i];
to_binary(x,bytes_per_big,&bytes[j],TRUE);
j+=bytes_per_big;
}
delete [] w.ptable;
w.ptable=NULL;
return len;
}
//
// Restore precomputation on pairing to byte array
//
void PFC::restore(char * bytes,G1& w)
{
int i,j,n=2*(bits(*ord-1)-2+ham(*ord));
int bytes_per_big=(MIRACL/8)*(get_mip()->nib-1);
int len=n*bytes_per_big;
Big x;
if (w.ptable!=NULL) return;
w.ptable=new ZZn[n];
for (i=j=0;i<n;i++)
{
x=from_binary(bytes_per_big,&bytes[j]);
w.ptable[i]=x;
j+=bytes_per_big;
}
for (i=0;i<len;i++) bytes[i]=0;
delete [] bytes;
}
// precompute G1 table for pairing
int PFC::precomp_for_pairing(G1& w)
{
int i,j,nb,len;
ECn A,Q,B;
ZZn lam,x,y;
big ptr;
Big iters=*ord-1;
A=w.g;
normalise(A);
B=A;
nb=bits(iters);
j=0;
len=2*(nb-2+ham(*ord));
w.ptable=new ZZn[len];
get_mip()->coord=MR_AFFINE;
for (i=nb-2;i>=0;i--)
{
Q=A;
// Evaluate line from A to A+B
A.add(A,&ptr);
lam=ptr;
extract(Q,x,y);
w.ptable[j++]=lam; w.ptable[j++]=lam*x-y;
if (bit(iters,i)==1)
{
Q=A;
A.add(B,&ptr);
lam=ptr;
extract(Q,x,y);
w.ptable[j++]=lam; w.ptable[j++]=lam*x-y;
}
}
get_mip()->coord=MR_PROJECTIVE;
return len;
}
GT PFC::multi_miller(int n,G1** QQ,G1** PP)
{
GT z;
ZZn *Px,*Py;
int i,j,*k,nb;
ECn *Q,*A;
ECn P;
ZZn2 res;
Big iters=*ord-1;
Px=new ZZn[n];
Py=new ZZn[n];
Q=new ECn[n];
A=new ECn[n];
k=new int[n];
nb=bits(iters);
res=1;
for (j=0;j<n;j++)
{
k[j]=0;
P=PP[j]->g; normalise(P); Q[j]=QQ[j]->g; normalise(Q[j]);
extract(P,Px[j],Py[j]);
}
for (j=0;j<n;j++) A[j]=Q[j];
for (i=nb-2;i>=0;i--)
{
res*=res;
for (j=0;j<n;j++)
{
if (QQ[j]->ptable==NULL)
res*=g(A[j],A[j],Px[j],Py[j]);
else
res*=gp(QQ[j]->ptable,k[j],Px[j],Py[j]);
}
if (bit(iters,i)==1)
for (j=0;j<n;j++)
{
if (QQ[j]->ptable==NULL)
res*=g(A[j],Q[j],Px[j],Py[j]);
else
res*=gp(QQ[j]->ptable,k[j],Px[j],Py[j]);
}
if (res.iszero()) return 0;
}
delete [] k;
delete [] A;
delete [] Q;
delete [] Py;
delete [] Px;
z.g=res;
return z;
}
//
// Tate Pairing G1 x G1 -> GT
//
// P and Q are points of order q in G1.
//
GT PFC::miller_loop(const G1& QQ,const G1& PP)
{
GT z;
int i,j,n,nb,nbw,nzs;
ECn A,Q;
ECn P;
ZZn Px,Py;
BOOL precomp;
ZZn2 res;
Big iters=*ord-1; // can omit last addition
P=PP.g; Q=QQ.g;
precomp=FALSE;
if (QQ.ptable!=NULL) precomp=TRUE;
normalise(P);
normalise(Q);
extract(P,Px,Py);
//Px=-Px;
res=1;
A=Q; // reset A
nb=bits(iters);
j=0;
for (i=nb-2;i>=0;i--)
{
res*=res;
if (precomp) res*=gp(QQ.ptable,j,Px,Py);
else res*=g(A,A,Px,Py);
if (bit(iters,i)==1)
{
if (precomp) res*=gp(QQ.ptable,j,Px,Py);
else res*=g(A,Q,Px,Py);
}
}
z.g=res;
return z;
}
GT PFC::final_exp(const GT& z)
{
GT y;
Big p;
ZZn2 res;
res=z.g;
p=get_modulus(); // get p
res=conj(res)/res;
res=pow(res,(p+1)/(*ord)); // raise to power of (p^2-1)/q
y.g=res;
return y;
}
PFC::PFC(int s, csprng *rng)
{
int mod_bits,words;
if (s!=80 && s!=128)
{
cout << "No suitable curve available" << endl;
exit(0);
}
if (s==80) mod_bits=512;
if (s==128) mod_bits=1536;
if (mod_bits%MIRACL==0)
words=(mod_bits/MIRACL);
else
words=(mod_bits/MIRACL)+1;
#ifdef MR_SIMPLE_BASE
miracl *mip=mirsys((MIRACL/4)*words,16);
#else
miracl *mip=mirsys(words,0);
mip->IOBASE=16;
#endif
mod=new Big;
cof=new Big;
ord=new Big;
Big A=-3;
Big B=0;
if (s==80)
{
*cof=param_80;
*ord=pow((Big)2,159)+pow((Big)2,17)+1;
}
if (s==128)
{
*cof=param_128;
*ord=pow((Big)2,255)+pow((Big)2,41)+1;
}
S=s;
*mod=2*(*cof)*(*ord)-1;
ecurve(A,B,*mod,MR_PROJECTIVE);
RNG=rng;
}
G1 PFC::mult(const G1& w,const Big& k)
{
G1 z;
if (w.mtable!=NULL)
{ // we have precomputed values
Big e=k;
if (k<0) e=-e;
int i,j,t=w.mtbits; //MR_ROUNDUP(2*S,WINDOW_SIZE);
j=recode(e,t,WINDOW_SIZE,t-1);
z.g=w.mtable[j];
for (i=t-2;i>=0;i--)
{
j=recode(e,t,WINDOW_SIZE,i);
z.g+=z.g;
if (j>0) z.g+=w.mtable[j];
}
if (k<0) z.g=-z.g;
}
else
{
z.g=w.g;
z.g*=k;
}
return z;
}
GT PFC::power(const GT& w,const Big& k)
{
GT z;
Big e=k;
if (k<0) e=-e;
if (w.etable!=NULL)
{ // precomputation is available
int i,j,t=w.etbits; //MR_ROUNDUP(2*S,WINDOW_SIZE);
j=recode(e,t,WINDOW_SIZE,t-1);
z.g=w.etable[j];
for (i=t-2;i>=0;i--)
{
j=recode(e,t,WINDOW_SIZE,i);
z.g*=z.g;
if (j>0) z.g*=w.etable[j];
}
}
else
{
z.g=powu(w.g,e);
}
if (k<0) z.g=conj(z.g);
return z;
}
// random group member
void PFC::random(Big& w)
{
if (RNG==NULL) w=rand(*ord);
else w=strong_rand(RNG,*ord);
}
// random AES key
void PFC::rankey(Big& k)
{
if (RNG==NULL) k=rand(S,2);
else k=strong_rand(RNG,S,2);
}
// Can be done deterministicly
void PFC::hash_and_map(G1& w,char *ID)
{
Big x0=H1(ID);
if (is_on_curve(x0)) w.g.set(x0);
else w.g.set(-x0);
w.g*=(*cof);
}
void PFC::random(G1& w)
{
Big x0;
if (RNG==NULL) x0=rand(get_modulus());
else x0=strong_rand(RNG,get_modulus());
while (!w.g.set(x0,x0)) x0+=1;
w.g*=(*cof);
}
Big PFC::hash_to_aes_key(const GT& w)
{
Big m=pow((Big)2,S);
return H2(w.g)%m;
}
Big PFC::hash_to_group(char *ID)
{
Big m=H1(ID);
return m%(*ord);
}
GT operator*(const GT& x,const GT& y)
{
GT z=x;
z.g*=y.g;
return z;
}
GT operator/(const GT& x,const GT& y)
{
GT z=x;
z.g*=conj(y.g); // elements in GT are unitary
return z;
}
//
// spill precomputation on GT to byte array
//
int GT::spill(char *& bytes)
{
int i,j,n=(1<<WINDOW_SIZE);
int bytes_per_big=(MIRACL/8)*(get_mip()->nib-1);
int len=n*2*bytes_per_big+1;
Big x,y;
if (etable==NULL) return 0;
bytes=new char[len];
for (i=j=0;i<n;i++)
{
etable[i].get(x,y);
to_binary(x,bytes_per_big,&bytes[j],TRUE);
j+=bytes_per_big;
to_binary(y,bytes_per_big,&bytes[j],TRUE);
j+=bytes_per_big;
}
bytes[j]=etbits;
delete [] etable;
etable=NULL;
return len;
}
//
// restore precomputation for GT from byte array
//
void GT::restore(char *bytes)
{
int i,j,n=(1<<WINDOW_SIZE);
int bytes_per_big=(MIRACL/8)*(get_mip()->nib-1);
// int len=n*2*bytes_per_big;
Big x,y;
if (etable!=NULL) return;
etable=new ZZn2[1<<WINDOW_SIZE];
for (i=j=0;i<n;i++)
{
x=from_binary(bytes_per_big,&bytes[j]);
j+=bytes_per_big;
y=from_binary(bytes_per_big,&bytes[j]);
j+=bytes_per_big;
etable[i].set(x,y);
}
etbits=bytes[j];
delete [] bytes;
}
//
// spill precomputation on G1 to byte array
//
int G1::spill(char *& bytes)
{
int i,j,n=(1<<WINDOW_SIZE);
int bytes_per_big=(MIRACL/8)*(get_mip()->nib-1);
int len=n*2*bytes_per_big+1;
Big x,y;
if (mtable==NULL) return 0;
bytes=new char[len];
for (i=j=0;i<n;i++)
{
mtable[i].get(x,y);
to_binary(x,bytes_per_big,&bytes[j],TRUE);
j+=bytes_per_big;
to_binary(y,bytes_per_big,&bytes[j],TRUE);
j+=bytes_per_big;
}
bytes[j]=mtbits;
delete [] mtable;
mtable=NULL;
return len;
}
//
// restore precomputation for G1 from byte array
//
void G1::restore(char *bytes)
{
int i,j,n=(1<<WINDOW_SIZE);
int bytes_per_big=(MIRACL/8)*(get_mip()->nib-1);
// int len=n*2*bytes_per_big;
Big x,y;
if (mtable!=NULL) return;
mtable=new ECn[1<<WINDOW_SIZE];
for (i=j=0;i<n;i++)
{
x=from_binary(bytes_per_big,&bytes[j]);
j+=bytes_per_big;
y=from_binary(bytes_per_big,&bytes[j]);
j+=bytes_per_big;
mtable[i].set(x,y);
}
mtbits=bytes[j];
delete [] bytes;
}
G1 operator+(const G1& x,const G1& y)
{
G1 z=x;
z.g+=y.g;
return z;
}
G1 operator-(const G1& x)
{
G1 z=x;
z.g=-z.g;
return z;
}
BOOL PFC::member(const GT& z)
{
ZZn2 r=z.g;
if (pow(r,*ord)!=(ZZn2)1) return FALSE;
return TRUE;
}
GT PFC::pairing(const G1& x,const G1& y)
{
GT z;
z=miller_loop(x,y);
z=final_exp(z);
return z;
}
GT PFC::multi_pairing(int n,G1 **y,G1 **x)
{
GT z;
z=multi_miller(n,y,x);
z=final_exp(z);
return z;
}
int PFC::precomp_for_mult(G1& w,BOOL small)
{
ECn v=w.g;
int i,j,k,bp,is,t;
if (small) t=MR_ROUNDUP(2*S,WINDOW_SIZE);
else t=MR_ROUNDUP(bits(*ord),WINDOW_SIZE);
w.mtable=new ECn[1<<WINDOW_SIZE];
w.mtable[1]=v;
w.mtbits=t;
for (j=0;j<t;j++)
v+=v;
k=1;
for (i=2;i<(1<<WINDOW_SIZE);i++)
{
if (i==(1<<k))
{
k++;
normalise(v);
w.mtable[i]=v;
for (j=0;j<t;j++)
v+=v;
continue;
}
bp=1;
for (j=0;j<k;j++)
{
if (i&bp)
{
is=1<<j;
w.mtable[i]+=w.mtable[is];
}
bp<<=1;
}
normalise(w.mtable[i]);
}
return (1<<WINDOW_SIZE);
}
int PFC::precomp_for_power(GT& w,BOOL small)
{
ZZn2 v=w.g;
int i,j,k,bp,is,t;
if (small) t=MR_ROUNDUP(2*S,WINDOW_SIZE);
else t=MR_ROUNDUP(bits(*ord),WINDOW_SIZE);
w.etable=new ZZn2[1<<WINDOW_SIZE];
w.etable[0]=1;
w.etable[1]=v;
w.etbits=t;
for (j=0;j<t;j++)
v*=v;
k=1;
for (i=2;i<(1<<WINDOW_SIZE);i++)
{
if (i==(1<<k))
{
k++;
w.etable[i]=v;
for (j=0;j<t;j++)
v*=v;
continue;
}
bp=1;
w.etable[i]=1;
for (j=0;j<k;j++)
{
if (i&bp)
{
is=1<<j;
w.etable[i]*=w.etable[is];
}
bp<<=1;
}
}
return (1<<WINDOW_SIZE);
}