version3/cpp/mpin256.cpp - incubator-milagro-crypto - Git at Google

 /*
 Licensed to the Apache Software Foundation (ASF) under one
 or more contributor license agreements.  See the NOTICE file
 distributed with this work for additional information
 regarding copyright ownership.  The ASF licenses this file
 to you under the Apache License, Version 2.0 (the
 "License"); you may not use this file except in compliance
 with the License.  You may obtain a copy of the License at

   http://www.apache.org/licenses/LICENSE-2.0

 Unless required by applicable law or agreed to in writing,
 software distributed under the License is distributed on an
 "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
 KIND, either express or implied.  See the License for the
 specific language governing permissions and limitations
 under the License.
 */

 /* MPIN Functions */

 /* Version 3.0 - supports Time Permits */

 #include <stdio.h>
 #include <stdlib.h>
 #include <string.h>
 #include <time.h>
 #include "mpin256_ZZZ.h"

 using namespace XXX;
 using namespace YYY;

 #define ROUNDUP(a,b) ((a)-1)/(b)+1

 namespace ZZZ {
 	static void mpin_hash(int,FP16 *, ECP *,octet *);
 	static void map(ECP *,BIG ,int );
 	static int unmap(BIG ,int *,ECP *);
 }

 /* Special mpin hashing */
 static void ZZZ::mpin_hash(int sha,FP16 *f, ECP *P,octet *w)
 {
     int i;
     BIG x,y;
     char h[64];
     hash256 sha256;
     hash512 sha512;
     char t[18*MODBYTES_XXX];  // to hold 10 BIGs
     int hlen=sha;

 	FP_redc(x,&(f->a.a.a.a));
     BIG_toBytes(&t[0],x);
 	FP_redc(x,&(f->a.a.a.b));
     BIG_toBytes(&t[MODBYTES_XXX],x);

     FP_redc(x,&(f->a.a.b.a));
     BIG_toBytes(&t[2*MODBYTES_XXX],x);
     FP_redc(x,&(f->a.a.b.b));
     BIG_toBytes(&t[3*MODBYTES_XXX],x);

     FP_redc(x,&(f->a.b.a.a));
     BIG_toBytes(&t[4*MODBYTES_XXX],x);
     FP_redc(x,&(f->a.b.a.b));
     BIG_toBytes(&t[5*MODBYTES_XXX],x);

     FP_redc(x,&(f->a.b.b.a));
     BIG_toBytes(&t[6*MODBYTES_XXX],x);
     FP_redc(x,&(f->a.b.b.b));
     BIG_toBytes(&t[7*MODBYTES_XXX],x);

 	FP_redc(x,&(f->b.a.a.a));
     BIG_toBytes(&t[8*MODBYTES_XXX],x);
 	FP_redc(x,&(f->b.a.a.b));
     BIG_toBytes(&t[9*MODBYTES_XXX],x);

     FP_redc(x,&(f->b.a.b.a));
     BIG_toBytes(&t[10*MODBYTES_XXX],x);
 	FP_redc(x,&(f->b.a.b.b));
     BIG_toBytes(&t[11*MODBYTES_XXX],x);

     FP_redc(x,&(f->b.b.a.a));
     BIG_toBytes(&t[12*MODBYTES_XXX],x);
     FP_redc(x,&(f->b.b.a.b));
     BIG_toBytes(&t[13*MODBYTES_XXX],x);

     FP_redc(x,&(f->b.b.b.a));
     BIG_toBytes(&t[14*MODBYTES_XXX],x);
     FP_redc(x,&(f->b.b.b.b));
     BIG_toBytes(&t[15*MODBYTES_XXX],x);

     ECP_get(x,y,P);
     BIG_toBytes(&t[16*MODBYTES_XXX],x);
     BIG_toBytes(&t[17*MODBYTES_XXX],y);

     OCT_empty(w);
     switch (sha)
     {
     case SHA256:
         HASH256_init(&sha256);
         for (i=0; i<18*MODBYTES_XXX; i++) HASH256_process(&sha256,t[i]);
         HASH256_hash(&sha256,h);
         break;
     case SHA384:
         HASH384_init(&sha512);
         for (i=0; i<18*MODBYTES_XXX; i++) HASH384_process(&sha512,t[i]);
         HASH384_hash(&sha512,h);
         break;
     case SHA512:
         HASH512_init(&sha512);
         for (i=0; i<18*MODBYTES_XXX; i++) HASH512_process(&sha512,t[i]);
         HASH512_hash(&sha512,h);
         break;
     }

     OCT_jbytes(w,h,AESKEY_ZZZ);
     for (i=0; i<hlen; i++) h[i]=0;
 }

 /* these next two functions help to implement elligator squared - http://eprint.iacr.org/2014/043 */
 /* maps a random u to a point on the curve */
 static void ZZZ::map(ECP *P,BIG u,int cb)
 {
     BIG x,q;

     BIG_rcopy(q,Modulus);
     BIG_copy(x,u);
     BIG_mod(x,q);

     while (!ECP_setx(P,x,cb))
 	{
         BIG_inc(x,1); BIG_norm(x);
 	}
 }

 /* returns u derived from P. Random value in range 1 to return value should then be added to u */
 static int ZZZ::unmap(BIG u,int *cb,ECP *P)
 {
     int s,r=0;
     BIG x;

     s=ECP_get(x,x,P);
     BIG_copy(u,x);
     do
     {
         BIG_dec(u,1); BIG_norm(u);
         r++;
     }
     while (!ECP_setx(P,u,s));
     ECP_setx(P,x,s);

     *cb=s;

     return r;
 }

 /* these next two functions implement elligator squared - http://eprint.iacr.org/2014/043 */
 /* Elliptic curve point E in format (0x04,x,y} is converted to form {0x0-,u,v} */
 /* Note that u and v are indistinguisible from random strings */
 int ZZZ::MPIN_ENCODING(csprng *RNG,octet *E)
 {
     int rn,m,su,sv,res=0;

     BIG q,u,v;
     ECP P,W;

     if (!ECP_fromOctet(&P,E)) res=MPIN_INVALID_POINT;
     if (res==0)
     {
         BIG_rcopy(q,Modulus);

         BIG_randomnum(u,q,RNG);

         su=RAND_byte(RNG);
         if (su<0) su=-su;
         su%=2;
         map(&W,u,su);
         ECP_sub(&P,&W); //ECP_affine(&P);

         rn=unmap(v,&sv,&P);
         m=RAND_byte(RNG);
         if (m<0) m=-m;
         m%=rn;
         BIG_inc(v,m+1);
         E->val[0]=su+2*sv;
         BIG_toBytes(&(E->val[1]),u);
         BIG_toBytes(&(E->val[PFS_ZZZ+1]),v);
     }
     return res;
 }

 int ZZZ::MPIN_DECODING(octet *D)
 {
     int su,sv;
     BIG u,v;
     ECP P,W;
     int res=0;

     if ((D->val[0]&0x04)!=0) res=MPIN_INVALID_POINT;
     if (res==0)
     {

         BIG_fromBytes(u,&(D->val[1]));
         BIG_fromBytes(v,&(D->val[PFS_ZZZ+1]));

         su=D->val[0]&1;
         sv=(D->val[0]>>1)&1;
         map(&W,u,su);
         map(&P,v,sv);
         ECP_add(&P,&W); //ECP_affine(&P);
         ECP_toOctet(D,&P,false);
     }

     return res;
 }

 /* R=R1+R2 in group G1 */
 int ZZZ::MPIN_RECOMBINE_G1(octet *R1,octet *R2,octet *R)
 {
     ECP P,T;
     int res=0;
     if (res==0)
     {
         if (!ECP_fromOctet(&P,R1)) res=MPIN_INVALID_POINT;
         if (!ECP_fromOctet(&T,R2)) res=MPIN_INVALID_POINT;
     }
     if (res==0)
     {
         ECP_add(&P,&T); //ECP_affine(&P);
         ECP_toOctet(R,&P,false);
     }
     return res;
 }

 /* W=W1+W2 in group G2 */
 int ZZZ::MPIN_RECOMBINE_G2(octet *W1,octet *W2,octet *W)
 {
     ECP8 Q,T;
     int res=0;
     if (!ECP8_fromOctet(&Q,W1)) res=MPIN_INVALID_POINT;
     if (!ECP8_fromOctet(&T,W2)) res=MPIN_INVALID_POINT;
     if (res==0)
     {
         ECP8_add(&Q,&T); //ECP8_affine(&Q);
         ECP8_toOctet(W,&Q);
     }
     return res;
 }

 /* create random secret S */
 int ZZZ::MPIN_RANDOM_GENERATE(csprng *RNG,octet* S)
 {
     BIG r,s;

     BIG_rcopy(r,CURVE_Order);
     BIG_randomnum(s,r,RNG);
 #ifdef AES_S
     BIG_mod2m(s,2*AES_S);
 #endif
     BIG_toBytes(S->val,s);
     S->len=MODBYTES_XXX;
     return 0;
 }

 /* Extract PIN from TOKEN for identity CID */
 int ZZZ::MPIN_EXTRACT_PIN(int sha,octet *CID,int pin,octet *TOKEN)
 {
 	pin%=MAXPIN;
 	return MPIN_EXTRACT_FACTOR(sha,CID,pin,PBLEN,TOKEN);
 }

 /* Extract a factor < 32 bits for identity CID */
 int ZZZ::MPIN_EXTRACT_FACTOR(int sha,octet *CID,int factor,int facbits,octet *TOKEN)
 {
     ECP P,R;
     int res=0;
     char h[MODBYTES_XXX];
     octet H= {0,sizeof(h),h};

     if (!ECP_fromOctet(&P,TOKEN))  res=MPIN_INVALID_POINT;
     if (res==0)
     {
         mhashit(sha,-1,CID,&H);
         ECP_mapit(&R,&H);

         ECP_pinmul(&R,factor,facbits);
         ECP_sub(&P,&R); //ECP_affine(&P);

         ECP_toOctet(TOKEN,&P,false);
     }
     return res;
 }

 /* Extract a factor < 32 bits for identity CID */
 int ZZZ::MPIN_RESTORE_FACTOR(int sha,octet *CID,int factor,int facbits,octet *TOKEN)
 {
     ECP P,R;
     int res=0;
     char h[MODBYTES_XXX];
     octet H= {0,sizeof(h),h};

     if (!ECP_fromOctet(&P,TOKEN))  res=MPIN_INVALID_POINT;
     if (res==0)
     {
         mhashit(sha,-1,CID,&H);
         ECP_mapit(&R,&H);

         ECP_pinmul(&R,factor,facbits);
         ECP_add(&P,&R); //ECP_affine(&P);

         ECP_toOctet(TOKEN,&P,false);
     }
     return res;
 }

 /* Implement step 2 on client side of MPin protocol - SEC=-(x+y)*SEC */
 int ZZZ::MPIN_CLIENT_2(octet *X,octet *Y,octet *SEC)
 {
     BIG px,py,r;
     ECP P;
     int res=0;
     BIG_rcopy(r,CURVE_Order);
     if (!ECP_fromOctet(&P,SEC)) res=MPIN_INVALID_POINT;
     if (res==0)
     {
         BIG_fromBytes(px,X->val);
         BIG_fromBytes(py,Y->val);
         BIG_add(px,px,py);
         BIG_mod(px,r);
         //	BIG_sub(px,r,px);
         PAIR_G1mul(&P,px);
         ECP_neg(&P);
         ECP_toOctet(SEC,&P,false);
     }
     return res;
 }

 /*
  W=x*H(G);
  if RNG == NULL then X is passed in
  if RNG != NULL the X is passed out
  if type=0 W=x*G where G is point on the curve, else W=x*M(G), where M(G) is mapping of octet G to point on the curve
 */

 int ZZZ::MPIN_GET_G1_MULTIPLE(csprng *RNG,int type,octet *X,octet *G,octet *W)
 {
     ECP P;
     BIG r,x;
     int res=0;
     if (RNG!=NULL)
     {
         BIG_rcopy(r,CURVE_Order);
         BIG_randomnum(x,r,RNG);
 #ifdef AES_S
         BIG_mod2m(x,2*AES_S);
 #endif
         X->len=MODBYTES_XXX;
         BIG_toBytes(X->val,x);
     }
     else
         BIG_fromBytes(x,X->val);

     if (type==0)
     {
         if (!ECP_fromOctet(&P,G)) res=MPIN_INVALID_POINT;
     }
     else
 	{
 		ECP_mapit(&P,G);
 	}

     if (res==0)
     {
         PAIR_G1mul(&P,x);
         ECP_toOctet(W,&P,false);
     }
     return res;
 }

 /*
  if RNG == NULL then X is passed in
  if RNG != NULL the X is passed out
  W=x*G where G is point on the curve
  if type==1 W=(x^-1)G
 */

 int ZZZ::MPIN_GET_G2_MULTIPLE(csprng *RNG,int type,octet *X,octet *G,octet *W)
 {
     ECP8 P;
     BIG r,x;
     int res=0;
     BIG_rcopy(r,CURVE_Order);
     if (RNG!=NULL)
     {
         BIG_randomnum(x,r,RNG);
 #ifdef AES_S
         BIG_mod2m(x,2*AES_S);
 #endif
         X->len=MODBYTES_XXX;
         BIG_toBytes(X->val,x);
     }
     else
     {
         BIG_fromBytes(x,X->val);
         if (type==1) BIG_invmodp(x,x,r);
     }

     if (!ECP8_fromOctet(&P,G)) res=MPIN_INVALID_POINT;

     if (res==0)
     {
         PAIR_G2mul(&P,x);
         ECP8_toOctet(W,&P);
     }
     return res;
 }


 /* Client secret CST=s*H(CID) where CID is client ID and s is master secret */
 /* CID is hashed externally */
 int ZZZ::MPIN_GET_CLIENT_SECRET(octet *S,octet *CID,octet *CST)
 {
     return MPIN_GET_G1_MULTIPLE(NULL,1,S,CID,CST);
 }

 /* Implement step 1 on client side of MPin protocol */
 int ZZZ::MPIN_CLIENT_1(int sha,int date,octet *CLIENT_ID,csprng *RNG,octet *X,int pin,octet *TOKEN,octet *SEC,octet *xID,octet *xCID,octet *PERMIT)
 {
     BIG r,x;
     ECP P,T,W;
     int res=0;
     char h[MODBYTES_XXX];
     octet H= {0,sizeof(h),h};

     BIG_rcopy(r,CURVE_Order);
     if (RNG!=NULL)
     {
         BIG_randomnum(x,r,RNG);
 #ifdef AES_S
         BIG_mod2m(x,2*AES_S);
 #endif
         X->len=MODBYTES_XXX;
         BIG_toBytes(X->val,x);
     }
     else
         BIG_fromBytes(x,X->val);

     mhashit(sha,-1,CLIENT_ID,&H);

     ECP_mapit(&P,&H);

     if (!ECP_fromOctet(&T,TOKEN)) res=MPIN_INVALID_POINT;

     if (res==0)
     {
         pin%=MAXPIN;

         ECP_copy(&W,&P);				// W=H(ID)
         ECP_pinmul(&W,pin,PBLEN);			// W=alpha.H(ID)
         ECP_add(&T,&W);					// T=Token+alpha.H(ID) = s.H(ID)

         if (date)
         {
             if (PERMIT!=NULL)
             {
                 if (!ECP_fromOctet(&W,PERMIT)) res=MPIN_INVALID_POINT;
                 ECP_add(&T,&W);					// SEC=s.H(ID)+s.H(T|ID)
             }
             mhashit(sha,date,&H,&H);

             ECP_mapit(&W,&H);
             if (xID!=NULL)
             {
                 PAIR_G1mul(&P,x);				// P=x.H(ID)
                 ECP_toOctet(xID,&P,false);  // xID
                 PAIR_G1mul(&W,x);               // W=x.H(T|ID)
                 ECP_add(&P,&W); //ECP_affine(&P);
             }
             else
             {
                 ECP_add(&P,&W); //ECP_affine(&P);
                 PAIR_G1mul(&P,x);
             }
             if (xCID!=NULL) ECP_toOctet(xCID,&P,false);  // U
         }
         else
         {
             if (xID!=NULL)
             {
                 PAIR_G1mul(&P,x);				// P=x.H(ID)
                 ECP_toOctet(xID,&P,false);  // xID
             }
         }
     }

     if (res==0)
 	{
 		//ECP_affine(&T);
         ECP_toOctet(SEC,&T,false);  // V
 	}
     return res;
 }

 /* Extract Server Secret SST=S*Q where Q is fixed generator in G2 and S is master secret */
 int ZZZ::MPIN_GET_SERVER_SECRET(octet *S,octet *SST)
 {
     BIG r,s;
     ECP8 Q;
     int res=0;

     BIG_rcopy(r,CURVE_Order);

 	ECP8_generator(&Q);

     if (res==0)
     {
         BIG_fromBytes(s,S->val);
         PAIR_G2mul(&Q,s);
         ECP8_toOctet(SST,&Q);
     }

     return res;
 }


 /* Time Permit CTT=s*H(date|H(CID)) where s is master secret */
 int ZZZ::MPIN_GET_CLIENT_PERMIT(int sha,int date,octet *S,octet *CID,octet *CTT)
 {
     BIG s;
     ECP P;
     char h[MODBYTES_XXX];
     octet H= {0,sizeof(h),h};

     mhashit(sha,date,CID,&H);

     ECP_mapit(&P,&H);

 //printf("P= "); ECP_output(&P); printf("\n");
 //exit(0);

     BIG_fromBytes(s,S->val);


 //printf("s= "); BIG_output(s); printf("\n");
     PAIR_G1mul(&P,s);
 //printf("OP= "); ECP_output(&P); printf("\n");
 //
     ECP_toOctet(CTT,&P,false);
     return 0;
 }

 // if date=0 only use HID, set HCID=NULL
 // if date and PE, use HID and HCID

 /* Outputs H(CID) and H(CID)+H(T|H(CID)) for time permits. If no time permits set HTID=NULL */
 void ZZZ::MPIN_SERVER_1(int sha,int date,octet *CID,octet *HID,octet *HTID)
 {
     char h[MODBYTES_XXX];
     octet H= {0,sizeof(h),h};
     ECP P,R;
 	BIG x;

 #ifdef USE_ANONYMOUS
     ECP_mapit(&P,CID);
 #else
     mhashit(sha,-1,CID,&H);
     ECP_mapit(&P,&H);
 #endif

     ECP_toOctet(HID,&P,false);  // new

     if (date)
     {
         //	if (HID!=NULL) ECP_toOctet(HID,&P,false);
 #ifdef USE_ANONYMOUS
         mhashit(sha,date,CID,&H);
 #else
         mhashit(sha,date,&H,&H);
 #endif
         ECP_mapit(&R,&H);
         ECP_add(&P,&R); //ECP_affine(&P);
         ECP_toOctet(HTID,&P,false);
     }
     //else ECP_toOctet(HID,&P,false);

 }

 /* Implement M-Pin on server side */
 int ZZZ::MPIN_SERVER_2(int date,octet *HID,octet *HTID,octet *Y,octet *SST,octet *xID,octet *xCID,octet *mSEC,octet *E,octet *F,octet *Pa)
 {
     BIG y;
     FP48 g;
     ECP8 Q,sQ;
     ECP P,R;
     int res=0;

 	ECP8_generator(&Q);

     // key-escrow less scheme: use Pa instead of Q in pairing computation
     // Q left for backward compatiblity
     if (Pa!=NULL)
     {
         if (!ECP8_fromOctet(&Q, Pa)) res=MPIN_INVALID_POINT;
     }


     if (res==0)
     {
         if (!ECP8_fromOctet(&sQ,SST)) res=MPIN_INVALID_POINT;
     }

     if (res==0)
     {
         if (date)
         {
             //BIG_fromBytes(px,&(xCID->val[1]));
             //BIG_fromBytes(py,&(xCID->val[PFS_ZZZ+1]));
 			if (!ECP_fromOctet(&R,xCID))  res=MPIN_INVALID_POINT;

         }
         else
         {
             //BIG_fromBytes(px,&(xID->val[1]));
             //BIG_fromBytes(py,&(xID->val[PFS_ZZZ+1]));
 			if (!ECP_fromOctet(&R,xID))  res=MPIN_INVALID_POINT;
         }
         //if (!ECP_set(&R,px,py)) res=MPIN_INVALID_POINT; // x(A+AT)
     }
     if (res==0)
     {
         BIG_fromBytes(y,Y->val);
         if (date)
         {
             if (!ECP_fromOctet(&P,HTID))  res=MPIN_INVALID_POINT;
         }
         else
         {
             if (!ECP_fromOctet(&P,HID))  res=MPIN_INVALID_POINT;
         }
     }
     if (res==0)
     {
         PAIR_G1mul(&P,y);  // y(A+AT)
         ECP_add(&P,&R); // x(A+AT)+y(A+T)
 		//ECP_affine(&P);
         if (!ECP_fromOctet(&R,mSEC))  res=MPIN_INVALID_POINT; // V
     }
     if (res==0)
     {

         PAIR_double_ate(&g,&Q,&R,&sQ,&P);
         PAIR_fexp(&g);

         if (!FP48_isunity(&g))
         {
             if (HID!=NULL && xID!=NULL && E!=NULL && F !=NULL)
             {
                 /* xID is set to NULL if there is no way to calculate PIN error */
                 FP48_toOctet(E,&g);

                 /* Note error is in the PIN, not in the time permit! Hence the need to exclude Time Permit from this check */

                 if (date)
                 {
                     if (!ECP_fromOctet(&P,HID)) res=MPIN_INVALID_POINT;
                     if (!ECP_fromOctet(&R,xID)) res=MPIN_INVALID_POINT; // U

                     if (res==0)
                     {
                         PAIR_G1mul(&P,y);  // yA
                         ECP_add(&P,&R); // yA+xA
 						//ECP_affine(&P);
                     }
                 }
                 if (res==0)
                 {
                     PAIR_ate(&g,&Q,&P);
                     PAIR_fexp(&g);
                     FP48_toOctet(F,&g);
                 }
             }
             res=MPIN_BAD_PIN;
         }
     }

     return res;
 }

 #if MAXPIN==10000
 #define MR_TS 10  /* 2^10/10 approx = sqrt(MAXPIN) */
 #define TRAP 200  /* 2*sqrt(MAXPIN) */
 #endif

 #if MAXPIN==1000000
 #define MR_TS 14
 #define TRAP 2000
 #endif

 /* Pollards kangaroos used to return PIN error */
 int ZZZ::MPIN_KANGAROO(octet *E,octet *F)
 {
     int i,j,m,s,dn,dm,steps;
     int distance[MR_TS];
     FP48 ge,gf,t,table[MR_TS];
     int res=0;
     // BIG w;

     FP48_fromOctet(&ge,E);
     FP48_fromOctet(&gf,F);

     FP48_copy(&t,&gf);

     for (s=1,m=0; m<MR_TS; m++)
     {
         distance[m]=s;
         FP48_copy(&table[m],&t);
         s*=2;
         FP48_usqr(&t,&t);
         FP48_reduce(&t);
     }

     FP48_one(&t);

     for (dn=0,j=0; j<TRAP; j++)
     {

         //BIG_copy(w,t.a.a.a);
         //FP_redc(w);
         //i=BIG_lastbits(w,20)%MR_TS;

         i=t.a.a.a.a.a.g[0]%MR_TS;

         FP48_mul(&t,&table[i]);
         FP48_reduce(&t);
         dn+=distance[i];
     }

     FP48_conj(&gf,&t);
     steps=0;
     dm=0;
     while (dm-dn<MAXPIN)
     {
         steps++;
         if (steps>4*TRAP) break;

         //BIG_copy(w,ge.a.a.a);
         //FP_redc(w);
         //i=BIG_lastbits(w,20)%MR_TS;

         i=ge.a.a.a.a.a.g[0]%MR_TS;

         FP48_mul(&ge,&table[i]);
         FP48_reduce(&ge);
         dm+=distance[i];
         if (FP48_equals(&ge,&t))
         {
             res=dm-dn;
             break;
         }
         if (FP48_equals(&ge,&gf))
         {
             res=dn-dm;
             break;
         }
     }
     if (steps>4*TRAP || dm-dn>=MAXPIN)
     {
         res=0;    /* Trap Failed  - probable invalid token */
     }

     return res;
 }

 /* Functions to support M-Pin Full */

 int ZZZ::MPIN_PRECOMPUTE(octet *TOKEN,octet *CID,octet *CP,octet *G1,octet *G2)
 {
     ECP P,T;
     ECP8 Q;
     FP48 g;
 	BIG x;
     int res=0;

     if (!ECP_fromOctet(&T,TOKEN)) res=MPIN_INVALID_POINT;

     if (res==0)
     {
         ECP_mapit(&P,CID);
         if (CP!=NULL)
         {
             if (!ECP8_fromOctet(&Q,CP)) res=MPIN_INVALID_POINT;
         }
         else
         {
 			ECP8_generator(&Q);
         }
     }
     if (res==0)
     {
         PAIR_ate(&g,&Q,&T);
         PAIR_fexp(&g);

         FP48_toOctet(G1,&g);
         if (G2!=NULL)
         {
             PAIR_ate(&g,&Q,&P);
             PAIR_fexp(&g);
             FP48_toOctet(G2,&g);
         }
     }
     return res;
 }

 /* calculate common key on client side */
 /* wCID = w.(A+AT) */
 int ZZZ::MPIN_CLIENT_KEY(int sha,octet *G1,octet *G2,int pin,octet *R,octet *X,octet *H,octet *wCID,octet *CK)
 {
     FP48 g1,g2;
 	FP16 c;//,cp,cpm1,cpm2;

     ECP W;
     int res=0;
     BIG r,z,x,h;//q,m,a,b;

     FP48_fromOctet(&g1,G1);
     FP48_fromOctet(&g2,G2);
     BIG_fromBytes(z,R->val);
     BIG_fromBytes(x,X->val);
     BIG_fromBytes(h,H->val);

     if (!ECP_fromOctet(&W,wCID)) res=MPIN_INVALID_POINT;

     if (res==0)
     {
         BIG_rcopy(r,CURVE_Order);
         BIG_add(z,z,h);    // new
         BIG_mod(z,r);

         FP48_pinpow(&g2,pin,PBLEN);
         FP48_mul(&g1,&g2);

 		PAIR_G1mul(&W,x);

 		FP48_compow(&c,&g1,z,r);
 		mpin_hash(sha,&c,&W,CK);

     }
     return res;
 }

 /* calculate common key on server side */
 /* Z=r.A - no time permits involved */

 int ZZZ::MPIN_SERVER_KEY(int sha,octet *Z,octet *SST,octet *W,octet *H,octet *HID,octet *xID,octet *xCID,octet *SK)
 {
     int res=0;
     FP48 g;
     FP16 c;
     ECP R,U,A;
     ECP8 sQ;
     BIG w,h;

     if (!ECP8_fromOctet(&sQ,SST)) res=MPIN_INVALID_POINT;
     if (!ECP_fromOctet(&R,Z)) res=MPIN_INVALID_POINT;


     if (!ECP_fromOctet(&A,HID)) res=MPIN_INVALID_POINT;

     // new
     if (xCID!=NULL)
     {
         if (!ECP_fromOctet(&U,xCID)) res=MPIN_INVALID_POINT;
     }
     else
     {
         if (!ECP_fromOctet(&U,xID)) res=MPIN_INVALID_POINT;
     }
     BIG_fromBytes(w,W->val);
     BIG_fromBytes(h,H->val);


     PAIR_ate(&g,&sQ,&A);
     PAIR_fexp(&g);

     if (res==0)
     {
         PAIR_G1mul(&A,h);
         ECP_add(&R,&A);  // new
 		//ECP_affine(&R);
         PAIR_ate(&g,&sQ,&R);
         PAIR_fexp(&g);
         PAIR_G1mul(&U,w);
         FP48_trace(&c,&g);
         mpin_hash(sha,&c,&U,SK);
     }
     return res;
 }

 /* Generate Y = H(TimeValue, xCID/xID) */
 void ZZZ::MPIN_GET_Y(int sha,int TimeValue,octet *xCID,octet *Y)
 {
     BIG q,y;
     char h[MODBYTES_XXX];
     octet H= {0,sizeof(h),h};

     mhashit(sha,TimeValue,xCID,&H);
     BIG_fromBytes(y,H.val);
     BIG_rcopy(q,CURVE_Order);
     BIG_mod(y,q);
     BIG_toBytes(Y->val,y);
     Y->len=PGS_ZZZ;
 }

 /* One pass MPIN Client */
 int ZZZ::MPIN_CLIENT(int sha,int date,octet *ID,csprng *RNG,octet *X,int pin,octet *TOKEN,octet *V,octet *U,octet *UT,octet *TP,octet *MESSAGE,int TimeValue,octet *Y)
 {
     int rtn=0;
     char m[2*PFS_ZZZ+1];
     octet M= {0,sizeof(m),m};

     octet *pID;
     if (date == 0)
         pID = U;
     else
         pID = UT;

     rtn = MPIN_CLIENT_1(sha,date,ID,RNG,X,pin,TOKEN,V,U,UT,TP);
     if (rtn != 0)
         return rtn;

     OCT_joctet(&M,pID);
    if (MESSAGE!=NULL)
    {
        OCT_joctet(&M,MESSAGE);
    }

     MPIN_GET_Y(sha,TimeValue,&M,Y);

     rtn = MPIN_CLIENT_2(X,Y,V);
     if (rtn != 0)
         return rtn;

     return 0;
 }

 /* One pass MPIN Server */
 int ZZZ::MPIN_SERVER(int sha,int date,octet *HID,octet *HTID,octet *Y,octet *sQ,octet *U,octet *UT,octet *V,octet *E,octet *F,octet *ID,octet *MESSAGE,int TimeValue, octet *Pa)
 {
     int rtn=0;
     char m[2*PFS_ZZZ+1];
     octet M= {0,sizeof(m),m};

     octet *pU;
     if (date == 0)
         pU = U;
     else
         pU = UT;

     MPIN_SERVER_1(sha,date,ID,HID,HTID);

     OCT_joctet(&M,pU);
    if (MESSAGE!=NULL)
    {
        OCT_joctet(&M,MESSAGE);
    }

     MPIN_GET_Y(sha,TimeValue,&M,Y);

     rtn = MPIN_SERVER_2(date,HID,HTID,Y,sQ,U,UT,V,E,F,Pa);
     if (rtn != 0)
         return rtn;

     return 0;
 }

 int ZZZ::MPIN_GET_DVS_KEYPAIR(csprng *R,octet *Z,octet *Pa)
 {
     BIG z,r;
     ECP8 Q;
     int res=0;

     BIG_rcopy(r,CURVE_Order);

     if (R!=NULL)
     {
         BIG_randomnum(z,r,R);
         Z->len=MODBYTES_XXX;
         BIG_toBytes(Z->val,z);
     }
     else
         BIG_fromBytes(z,Z->val);

     BIG_invmodp(z,z,r);

 	ECP8_generator(&Q);

     if (res==0)
     {
         PAIR_G2mul(&Q,z);
         ECP8_toOctet(Pa,&Q);
     }

     return res;
 }
	/*
	Licensed to the Apache Software Foundation (ASF) under one
	or more contributor license agreements. See the NOTICE file
	distributed with this work for additional information
	regarding copyright ownership. The ASF licenses this file
	to you under the Apache License, Version 2.0 (the
	"License"); you may not use this file except in compliance
	with the License. You may obtain a copy of the License at

	http://www.apache.org/licenses/LICENSE-2.0

	Unless required by applicable law or agreed to in writing,
	software distributed under the License is distributed on an
	"AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
	KIND, either express or implied. See the License for the
	specific language governing permissions and limitations
	under the License.
	*/

	/* MPIN Functions */

	/* Version 3.0 - supports Time Permits */

	#include <stdio.h>
	#include <stdlib.h>
	#include <string.h>
	#include <time.h>
	#include "mpin256_ZZZ.h"

	using namespace XXX;
	using namespace YYY;

	#define ROUNDUP(a,b) ((a)-1)/(b)+1

	namespace ZZZ {
	static void mpin_hash(int,FP16 , ECP ,octet *);
	static void map(ECP *,BIG ,int );
	static int unmap(BIG ,int ,ECP );
	}

	/* Special mpin hashing */
	static void ZZZ::mpin_hash(int sha,FP16 f, ECP P,octet *w)
	{
	int i;
	BIG x,y;
	char h[64];
	hash256 sha256;
	hash512 sha512;
	char t[18*MODBYTES_XXX]; // to hold 10 BIGs
	int hlen=sha;

	FP_redc(x,&(f->a.a.a.a));
	BIG_toBytes(&t[0],x);
	FP_redc(x,&(f->a.a.a.b));
	BIG_toBytes(&t[MODBYTES_XXX],x);

	FP_redc(x,&(f->a.a.b.a));
	BIG_toBytes(&t[2*MODBYTES_XXX],x);
	FP_redc(x,&(f->a.a.b.b));
	BIG_toBytes(&t[3*MODBYTES_XXX],x);

	FP_redc(x,&(f->a.b.a.a));
	BIG_toBytes(&t[4*MODBYTES_XXX],x);
	FP_redc(x,&(f->a.b.a.b));
	BIG_toBytes(&t[5*MODBYTES_XXX],x);

	FP_redc(x,&(f->a.b.b.a));
	BIG_toBytes(&t[6*MODBYTES_XXX],x);
	FP_redc(x,&(f->a.b.b.b));
	BIG_toBytes(&t[7*MODBYTES_XXX],x);

	FP_redc(x,&(f->b.a.a.a));
	BIG_toBytes(&t[8*MODBYTES_XXX],x);
	FP_redc(x,&(f->b.a.a.b));
	BIG_toBytes(&t[9*MODBYTES_XXX],x);

	FP_redc(x,&(f->b.a.b.a));
	BIG_toBytes(&t[10*MODBYTES_XXX],x);
	FP_redc(x,&(f->b.a.b.b));
	BIG_toBytes(&t[11*MODBYTES_XXX],x);

	FP_redc(x,&(f->b.b.a.a));
	BIG_toBytes(&t[12*MODBYTES_XXX],x);
	FP_redc(x,&(f->b.b.a.b));
	BIG_toBytes(&t[13*MODBYTES_XXX],x);

	FP_redc(x,&(f->b.b.b.a));
	BIG_toBytes(&t[14*MODBYTES_XXX],x);
	FP_redc(x,&(f->b.b.b.b));
	BIG_toBytes(&t[15*MODBYTES_XXX],x);

	ECP_get(x,y,P);
	BIG_toBytes(&t[16*MODBYTES_XXX],x);
	BIG_toBytes(&t[17*MODBYTES_XXX],y);

	OCT_empty(w);
	switch (sha)
	{
	case SHA256:
	HASH256_init(&sha256);
	for (i=0; i<18*MODBYTES_XXX; i++) HASH256_process(&sha256,t[i]);
	HASH256_hash(&sha256,h);
	break;
	case SHA384:
	HASH384_init(&sha512);
	for (i=0; i<18*MODBYTES_XXX; i++) HASH384_process(&sha512,t[i]);
	HASH384_hash(&sha512,h);
	break;
	case SHA512:
	HASH512_init(&sha512);
	for (i=0; i<18*MODBYTES_XXX; i++) HASH512_process(&sha512,t[i]);
	HASH512_hash(&sha512,h);
	break;
	}

	OCT_jbytes(w,h,AESKEY_ZZZ);
	for (i=0; i<hlen; i++) h[i]=0;
	}

	/* these next two functions help to implement elligator squared - http://eprint.iacr.org/2014/043 */
	/* maps a random u to a point on the curve */
	static void ZZZ::map(ECP *P,BIG u,int cb)
	{
	BIG x,q;

	BIG_rcopy(q,Modulus);
	BIG_copy(x,u);
	BIG_mod(x,q);

	while (!ECP_setx(P,x,cb))
	{
	BIG_inc(x,1); BIG_norm(x);
	}
	}

	/* returns u derived from P. Random value in range 1 to return value should then be added to u */
	static int ZZZ::unmap(BIG u,int cb,ECP P)
	{
	int s,r=0;
	BIG x;

	s=ECP_get(x,x,P);
	BIG_copy(u,x);
	do
	{
	BIG_dec(u,1); BIG_norm(u);
	r++;
	}
	while (!ECP_setx(P,u,s));
	ECP_setx(P,x,s);

	*cb=s;

	return r;
	}

	/* these next two functions implement elligator squared - http://eprint.iacr.org/2014/043 */
	/* Elliptic curve point E in format (0x04,x,y} is converted to form {0x0-,u,v} */
	/* Note that u and v are indistinguisible from random strings */
	int ZZZ::MPIN_ENCODING(csprng RNG,octet E)
	{
	int rn,m,su,sv,res=0;

	BIG q,u,v;
	ECP P,W;

	if (!ECP_fromOctet(&P,E)) res=MPIN_INVALID_POINT;
	if (res==0)
	{
	BIG_rcopy(q,Modulus);

	BIG_randomnum(u,q,RNG);

	su=RAND_byte(RNG);
	if (su<0) su=-su;
	su%=2;
	map(&W,u,su);
	ECP_sub(&P,&W); //ECP_affine(&P);

	rn=unmap(v,&sv,&P);
	m=RAND_byte(RNG);
	if (m<0) m=-m;
	m%=rn;
	BIG_inc(v,m+1);
	E->val[0]=su+2*sv;
	BIG_toBytes(&(E->val[1]),u);
	BIG_toBytes(&(E->val[PFS_ZZZ+1]),v);
	}
	return res;
	}

	int ZZZ::MPIN_DECODING(octet *D)
	{
	int su,sv;
	BIG u,v;
	ECP P,W;
	int res=0;

	if ((D->val[0]&0x04)!=0) res=MPIN_INVALID_POINT;
	if (res==0)
	{

	BIG_fromBytes(u,&(D->val[1]));
	BIG_fromBytes(v,&(D->val[PFS_ZZZ+1]));

	su=D->val[0]&1;
	sv=(D->val[0]>>1)&1;
	map(&W,u,su);
	map(&P,v,sv);
	ECP_add(&P,&W); //ECP_affine(&P);
	ECP_toOctet(D,&P,false);
	}

	return res;
	}

	/* R=R1+R2 in group G1 */
	int ZZZ::MPIN_RECOMBINE_G1(octet R1,octet R2,octet *R)
	{
	ECP P,T;
	int res=0;
	if (res==0)
	{
	if (!ECP_fromOctet(&P,R1)) res=MPIN_INVALID_POINT;
	if (!ECP_fromOctet(&T,R2)) res=MPIN_INVALID_POINT;
	}
	if (res==0)
	{
	ECP_add(&P,&T); //ECP_affine(&P);
	ECP_toOctet(R,&P,false);
	}
	return res;
	}

	/* W=W1+W2 in group G2 */
	int ZZZ::MPIN_RECOMBINE_G2(octet W1,octet W2,octet *W)
	{
	ECP8 Q,T;
	int res=0;
	if (!ECP8_fromOctet(&Q,W1)) res=MPIN_INVALID_POINT;
	if (!ECP8_fromOctet(&T,W2)) res=MPIN_INVALID_POINT;
	if (res==0)
	{
	ECP8_add(&Q,&T); //ECP8_affine(&Q);
	ECP8_toOctet(W,&Q);
	}
	return res;
	}

	/* create random secret S */
	int ZZZ::MPIN_RANDOM_GENERATE(csprng RNG,octet S)
	{
	BIG r,s;

	BIG_rcopy(r,CURVE_Order);
	BIG_randomnum(s,r,RNG);
	#ifdef AES_S
	BIG_mod2m(s,2*AES_S);
	#endif
	BIG_toBytes(S->val,s);
	S->len=MODBYTES_XXX;
	return 0;
	}

	/* Extract PIN from TOKEN for identity CID */
	int ZZZ::MPIN_EXTRACT_PIN(int sha,octet CID,int pin,octet TOKEN)
	{
	pin%=MAXPIN;
	return MPIN_EXTRACT_FACTOR(sha,CID,pin,PBLEN,TOKEN);
	}

	/* Extract a factor < 32 bits for identity CID */
	int ZZZ::MPIN_EXTRACT_FACTOR(int sha,octet CID,int factor,int facbits,octet TOKEN)
	{
	ECP P,R;
	int res=0;
	char h[MODBYTES_XXX];
	octet H= {0,sizeof(h),h};

	if (!ECP_fromOctet(&P,TOKEN)) res=MPIN_INVALID_POINT;
	if (res==0)
	{
	mhashit(sha,-1,CID,&H);
	ECP_mapit(&R,&H);

	ECP_pinmul(&R,factor,facbits);
	ECP_sub(&P,&R); //ECP_affine(&P);

	ECP_toOctet(TOKEN,&P,false);
	}
	return res;
	}

	/* Extract a factor < 32 bits for identity CID */
	int ZZZ::MPIN_RESTORE_FACTOR(int sha,octet CID,int factor,int facbits,octet TOKEN)
	{
	ECP P,R;
	int res=0;
	char h[MODBYTES_XXX];
	octet H= {0,sizeof(h),h};

	if (!ECP_fromOctet(&P,TOKEN)) res=MPIN_INVALID_POINT;
	if (res==0)
	{
	mhashit(sha,-1,CID,&H);
	ECP_mapit(&R,&H);

	ECP_pinmul(&R,factor,facbits);
	ECP_add(&P,&R); //ECP_affine(&P);

	ECP_toOctet(TOKEN,&P,false);
	}
	return res;
	}

	/* Implement step 2 on client side of MPin protocol - SEC=-(x+y)SEC /
	int ZZZ::MPIN_CLIENT_2(octet X,octet Y,octet *SEC)
	{
	BIG px,py,r;
	ECP P;
	int res=0;
	BIG_rcopy(r,CURVE_Order);
	if (!ECP_fromOctet(&P,SEC)) res=MPIN_INVALID_POINT;
	if (res==0)
	{
	BIG_fromBytes(px,X->val);
	BIG_fromBytes(py,Y->val);
	BIG_add(px,px,py);
	BIG_mod(px,r);
	// BIG_sub(px,r,px);
	PAIR_G1mul(&P,px);
	ECP_neg(&P);
	ECP_toOctet(SEC,&P,false);
	}
	return res;
	}

	/*
	W=x*H(G);
	if RNG == NULL then X is passed in
	if RNG != NULL the X is passed out
	if type=0 W=xG where G is point on the curve, else W=xM(G), where M(G) is mapping of octet G to point on the curve
	*/

	int ZZZ::MPIN_GET_G1_MULTIPLE(csprng RNG,int type,octet X,octet G,octet W)
	{
	ECP P;
	BIG r,x;
	int res=0;
	if (RNG!=NULL)
	{
	BIG_rcopy(r,CURVE_Order);
	BIG_randomnum(x,r,RNG);
	#ifdef AES_S
	BIG_mod2m(x,2*AES_S);
	#endif
	X->len=MODBYTES_XXX;
	BIG_toBytes(X->val,x);
	}
	else
	BIG_fromBytes(x,X->val);

	if (type==0)
	{
	if (!ECP_fromOctet(&P,G)) res=MPIN_INVALID_POINT;
	}
	else
	{
	ECP_mapit(&P,G);
	}

	if (res==0)
	{
	PAIR_G1mul(&P,x);
	ECP_toOctet(W,&P,false);
	}
	return res;
	}

	/*
	if RNG == NULL then X is passed in
	if RNG != NULL the X is passed out
	W=x*G where G is point on the curve
	if type==1 W=(x^-1)G
	*/

	int ZZZ::MPIN_GET_G2_MULTIPLE(csprng RNG,int type,octet X,octet G,octet W)
	{
	ECP8 P;
	BIG r,x;
	int res=0;
	BIG_rcopy(r,CURVE_Order);
	if (RNG!=NULL)
	{
	BIG_randomnum(x,r,RNG);
	#ifdef AES_S
	BIG_mod2m(x,2*AES_S);
	#endif
	X->len=MODBYTES_XXX;
	BIG_toBytes(X->val,x);
	}
	else
	{
	BIG_fromBytes(x,X->val);
	if (type==1) BIG_invmodp(x,x,r);
	}

	if (!ECP8_fromOctet(&P,G)) res=MPIN_INVALID_POINT;

	if (res==0)
	{
	PAIR_G2mul(&P,x);
	ECP8_toOctet(W,&P);
	}
	return res;
	}



	/* Client secret CST=sH(CID) where CID is client ID and s is master secret /
	/* CID is hashed externally */
	int ZZZ::MPIN_GET_CLIENT_SECRET(octet S,octet CID,octet *CST)
	{
	return MPIN_GET_G1_MULTIPLE(NULL,1,S,CID,CST);
	}

	/* Implement step 1 on client side of MPin protocol */
	int ZZZ::MPIN_CLIENT_1(int sha,int date,octet CLIENT_ID,csprng RNG,octet X,int pin,octet TOKEN,octet SEC,octet xID,octet xCID,octet PERMIT)
	{
	BIG r,x;
	ECP P,T,W;
	int res=0;
	char h[MODBYTES_XXX];
	octet H= {0,sizeof(h),h};

	BIG_rcopy(r,CURVE_Order);
	if (RNG!=NULL)
	{
	BIG_randomnum(x,r,RNG);
	#ifdef AES_S
	BIG_mod2m(x,2*AES_S);
	#endif
	X->len=MODBYTES_XXX;
	BIG_toBytes(X->val,x);
	}
	else
	BIG_fromBytes(x,X->val);

	mhashit(sha,-1,CLIENT_ID,&H);

	ECP_mapit(&P,&H);

	if (!ECP_fromOctet(&T,TOKEN)) res=MPIN_INVALID_POINT;

	if (res==0)
	{
	pin%=MAXPIN;

	ECP_copy(&W,&P); // W=H(ID)
	ECP_pinmul(&W,pin,PBLEN); // W=alpha.H(ID)
	ECP_add(&T,&W); // T=Token+alpha.H(ID) = s.H(ID)

	if (date)
	{
	if (PERMIT!=NULL)
	{
	if (!ECP_fromOctet(&W,PERMIT)) res=MPIN_INVALID_POINT;
	ECP_add(&T,&W); // SEC=s.H(ID)+s.H(T\|ID)
	}
	mhashit(sha,date,&H,&H);

	ECP_mapit(&W,&H);
	if (xID!=NULL)
	{
	PAIR_G1mul(&P,x); // P=x.H(ID)
	ECP_toOctet(xID,&P,false); // xID
	PAIR_G1mul(&W,x); // W=x.H(T\|ID)
	ECP_add(&P,&W); //ECP_affine(&P);
	}
	else
	{
	ECP_add(&P,&W); //ECP_affine(&P);
	PAIR_G1mul(&P,x);
	}
	if (xCID!=NULL) ECP_toOctet(xCID,&P,false); // U
	}
	else
	{
	if (xID!=NULL)
	{
	PAIR_G1mul(&P,x); // P=x.H(ID)
	ECP_toOctet(xID,&P,false); // xID
	}
	}
	}

	if (res==0)
	{
	//ECP_affine(&T);
	ECP_toOctet(SEC,&T,false); // V
	}
	return res;
	}

	/* Extract Server Secret SST=SQ where Q is fixed generator in G2 and S is master secret /
	int ZZZ::MPIN_GET_SERVER_SECRET(octet S,octet SST)
	{
	BIG r,s;
	ECP8 Q;
	int res=0;

	BIG_rcopy(r,CURVE_Order);

	ECP8_generator(&Q);

	if (res==0)
	{
	BIG_fromBytes(s,S->val);
	PAIR_G2mul(&Q,s);
	ECP8_toOctet(SST,&Q);
	}

	return res;
	}


	/* Time Permit CTT=sH(date\|H(CID)) where s is master secret /
	int ZZZ::MPIN_GET_CLIENT_PERMIT(int sha,int date,octet S,octet CID,octet *CTT)
	{
	BIG s;
	ECP P;
	char h[MODBYTES_XXX];
	octet H= {0,sizeof(h),h};

	mhashit(sha,date,CID,&H);

	ECP_mapit(&P,&H);

	//printf("P= "); ECP_output(&P); printf("\n");
	//exit(0);

	BIG_fromBytes(s,S->val);



	//printf("s= "); BIG_output(s); printf("\n");
	PAIR_G1mul(&P,s);
	//printf("OP= "); ECP_output(&P); printf("\n");
	//
	ECP_toOctet(CTT,&P,false);
	return 0;
	}

	// if date=0 only use HID, set HCID=NULL
	// if date and PE, use HID and HCID

	/* Outputs H(CID) and H(CID)+H(T\|H(CID)) for time permits. If no time permits set HTID=NULL */
	void ZZZ::MPIN_SERVER_1(int sha,int date,octet CID,octet HID,octet *HTID)
	{
	char h[MODBYTES_XXX];
	octet H= {0,sizeof(h),h};
	ECP P,R;
	BIG x;

	#ifdef USE_ANONYMOUS
	ECP_mapit(&P,CID);
	#else
	mhashit(sha,-1,CID,&H);
	ECP_mapit(&P,&H);
	#endif

	ECP_toOctet(HID,&P,false); // new

	if (date)
	{
	// if (HID!=NULL) ECP_toOctet(HID,&P,false);
	#ifdef USE_ANONYMOUS
	mhashit(sha,date,CID,&H);
	#else
	mhashit(sha,date,&H,&H);
	#endif
	ECP_mapit(&R,&H);
	ECP_add(&P,&R); //ECP_affine(&P);
	ECP_toOctet(HTID,&P,false);
	}
	//else ECP_toOctet(HID,&P,false);

	}

	/* Implement M-Pin on server side */
	int ZZZ::MPIN_SERVER_2(int date,octet HID,octet HTID,octet Y,octet SST,octet xID,octet xCID,octet mSEC,octet E,octet F,octet Pa)
	{
	BIG y;
	FP48 g;
	ECP8 Q,sQ;
	ECP P,R;
	int res=0;

	ECP8_generator(&Q);

	// key-escrow less scheme: use Pa instead of Q in pairing computation
	// Q left for backward compatiblity
	if (Pa!=NULL)
	{
	if (!ECP8_fromOctet(&Q, Pa)) res=MPIN_INVALID_POINT;
	}


	if (res==0)
	{
	if (!ECP8_fromOctet(&sQ,SST)) res=MPIN_INVALID_POINT;
	}

	if (res==0)
	{
	if (date)
	{
	//BIG_fromBytes(px,&(xCID->val[1]));
	//BIG_fromBytes(py,&(xCID->val[PFS_ZZZ+1]));
	if (!ECP_fromOctet(&R,xCID)) res=MPIN_INVALID_POINT;

	}
	else
	{
	//BIG_fromBytes(px,&(xID->val[1]));
	//BIG_fromBytes(py,&(xID->val[PFS_ZZZ+1]));
	if (!ECP_fromOctet(&R,xID)) res=MPIN_INVALID_POINT;
	}
	//if (!ECP_set(&R,px,py)) res=MPIN_INVALID_POINT; // x(A+AT)
	}
	if (res==0)
	{
	BIG_fromBytes(y,Y->val);
	if (date)
	{
	if (!ECP_fromOctet(&P,HTID)) res=MPIN_INVALID_POINT;
	}
	else
	{
	if (!ECP_fromOctet(&P,HID)) res=MPIN_INVALID_POINT;
	}
	}
	if (res==0)
	{
	PAIR_G1mul(&P,y); // y(A+AT)
	ECP_add(&P,&R); // x(A+AT)+y(A+T)
	//ECP_affine(&P);
	if (!ECP_fromOctet(&R,mSEC)) res=MPIN_INVALID_POINT; // V
	}
	if (res==0)
	{

	PAIR_double_ate(&g,&Q,&R,&sQ,&P);
	PAIR_fexp(&g);

	if (!FP48_isunity(&g))
	{
	if (HID!=NULL && xID!=NULL && E!=NULL && F !=NULL)
	{
	/* xID is set to NULL if there is no way to calculate PIN error */
	FP48_toOctet(E,&g);

	/* Note error is in the PIN, not in the time permit! Hence the need to exclude Time Permit from this check */

	if (date)
	{
	if (!ECP_fromOctet(&P,HID)) res=MPIN_INVALID_POINT;
	if (!ECP_fromOctet(&R,xID)) res=MPIN_INVALID_POINT; // U

	if (res==0)
	{
	PAIR_G1mul(&P,y); // yA
	ECP_add(&P,&R); // yA+xA
	//ECP_affine(&P);
	}
	}
	if (res==0)
	{
	PAIR_ate(&g,&Q,&P);
	PAIR_fexp(&g);
	FP48_toOctet(F,&g);
	}
	}
	res=MPIN_BAD_PIN;
	}
	}

	return res;
	}

	#if MAXPIN==10000
	#define MR_TS 10 /* 2^10/10 approx = sqrt(MAXPIN) */
	#define TRAP 200 /* 2sqrt(MAXPIN) /
	#endif

	#if MAXPIN==1000000
	#define MR_TS 14
	#define TRAP 2000
	#endif

	/* Pollards kangaroos used to return PIN error */
	int ZZZ::MPIN_KANGAROO(octet E,octet F)
	{
	int i,j,m,s,dn,dm,steps;
	int distance[MR_TS];
	FP48 ge,gf,t,table[MR_TS];
	int res=0;
	// BIG w;

	FP48_fromOctet(&ge,E);
	FP48_fromOctet(&gf,F);

	FP48_copy(&t,&gf);

	for (s=1,m=0; m<MR_TS; m++)
	{
	distance[m]=s;
	FP48_copy(&table[m],&t);
	s*=2;
	FP48_usqr(&t,&t);
	FP48_reduce(&t);
	}

	FP48_one(&t);

	for (dn=0,j=0; j<TRAP; j++)
	{

	//BIG_copy(w,t.a.a.a);
	//FP_redc(w);
	//i=BIG_lastbits(w,20)%MR_TS;

	i=t.a.a.a.a.a.g[0]%MR_TS;

	FP48_mul(&t,&table[i]);
	FP48_reduce(&t);
	dn+=distance[i];
	}

	FP48_conj(&gf,&t);
	steps=0;
	dm=0;
	while (dm-dn<MAXPIN)
	{
	steps++;
	if (steps>4*TRAP) break;

	//BIG_copy(w,ge.a.a.a);
	//FP_redc(w);
	//i=BIG_lastbits(w,20)%MR_TS;

	i=ge.a.a.a.a.a.g[0]%MR_TS;

	FP48_mul(&ge,&table[i]);
	FP48_reduce(&ge);
	dm+=distance[i];
	if (FP48_equals(&ge,&t))
	{
	res=dm-dn;
	break;
	}
	if (FP48_equals(&ge,&gf))
	{
	res=dn-dm;
	break;
	}
	}
	if (steps>4*TRAP \|\| dm-dn>=MAXPIN)
	{
	res=0; /* Trap Failed - probable invalid token */
	}

	return res;
	}

	/* Functions to support M-Pin Full */

	int ZZZ::MPIN_PRECOMPUTE(octet TOKEN,octet CID,octet CP,octet G1,octet *G2)
	{
	ECP P,T;
	ECP8 Q;
	FP48 g;
	BIG x;
	int res=0;

	if (!ECP_fromOctet(&T,TOKEN)) res=MPIN_INVALID_POINT;

	if (res==0)
	{
	ECP_mapit(&P,CID);
	if (CP!=NULL)
	{
	if (!ECP8_fromOctet(&Q,CP)) res=MPIN_INVALID_POINT;
	}
	else
	{
	ECP8_generator(&Q);
	}
	}
	if (res==0)
	{
	PAIR_ate(&g,&Q,&T);
	PAIR_fexp(&g);

	FP48_toOctet(G1,&g);
	if (G2!=NULL)
	{
	PAIR_ate(&g,&Q,&P);
	PAIR_fexp(&g);
	FP48_toOctet(G2,&g);
	}
	}
	return res;
	}

	/* calculate common key on client side */
	/* wCID = w.(A+AT) */
	int ZZZ::MPIN_CLIENT_KEY(int sha,octet G1,octet G2,int pin,octet R,octet X,octet H,octet wCID,octet *CK)
	{
	FP48 g1,g2;
	FP16 c;//,cp,cpm1,cpm2;

	ECP W;
	int res=0;
	BIG r,z,x,h;//q,m,a,b;

	FP48_fromOctet(&g1,G1);
	FP48_fromOctet(&g2,G2);
	BIG_fromBytes(z,R->val);
	BIG_fromBytes(x,X->val);
	BIG_fromBytes(h,H->val);

	if (!ECP_fromOctet(&W,wCID)) res=MPIN_INVALID_POINT;

	if (res==0)
	{
	BIG_rcopy(r,CURVE_Order);
	BIG_add(z,z,h); // new
	BIG_mod(z,r);

	FP48_pinpow(&g2,pin,PBLEN);
	FP48_mul(&g1,&g2);

	PAIR_G1mul(&W,x);

	FP48_compow(&c,&g1,z,r);
	mpin_hash(sha,&c,&W,CK);

	}
	return res;
	}

	/* calculate common key on server side */
	/* Z=r.A - no time permits involved */

	int ZZZ::MPIN_SERVER_KEY(int sha,octet Z,octet SST,octet W,octet H,octet HID,octet xID,octet xCID,octet SK)
	{
	int res=0;
	FP48 g;
	FP16 c;
	ECP R,U,A;
	ECP8 sQ;
	BIG w,h;

	if (!ECP8_fromOctet(&sQ,SST)) res=MPIN_INVALID_POINT;
	if (!ECP_fromOctet(&R,Z)) res=MPIN_INVALID_POINT;


	if (!ECP_fromOctet(&A,HID)) res=MPIN_INVALID_POINT;

	// new
	if (xCID!=NULL)
	{
	if (!ECP_fromOctet(&U,xCID)) res=MPIN_INVALID_POINT;
	}
	else
	{
	if (!ECP_fromOctet(&U,xID)) res=MPIN_INVALID_POINT;
	}
	BIG_fromBytes(w,W->val);
	BIG_fromBytes(h,H->val);


	PAIR_ate(&g,&sQ,&A);
	PAIR_fexp(&g);

	if (res==0)
	{
	PAIR_G1mul(&A,h);
	ECP_add(&R,&A); // new
	//ECP_affine(&R);
	PAIR_ate(&g,&sQ,&R);
	PAIR_fexp(&g);
	PAIR_G1mul(&U,w);
	FP48_trace(&c,&g);
	mpin_hash(sha,&c,&U,SK);
	}
	return res;
	}

	/* Generate Y = H(TimeValue, xCID/xID) */
	void ZZZ::MPIN_GET_Y(int sha,int TimeValue,octet xCID,octet Y)
	{
	BIG q,y;
	char h[MODBYTES_XXX];
	octet H= {0,sizeof(h),h};

	mhashit(sha,TimeValue,xCID,&H);
	BIG_fromBytes(y,H.val);
	BIG_rcopy(q,CURVE_Order);
	BIG_mod(y,q);
	BIG_toBytes(Y->val,y);
	Y->len=PGS_ZZZ;
	}

	/* One pass MPIN Client */
	int ZZZ::MPIN_CLIENT(int sha,int date,octet ID,csprng RNG,octet X,int pin,octet TOKEN,octet V,octet U,octet UT,octet TP,octet MESSAGE,int TimeValue,octet Y)
	{
	int rtn=0;
	char m[2*PFS_ZZZ+1];
	octet M= {0,sizeof(m),m};

	octet *pID;
	if (date == 0)
	pID = U;
	else
	pID = UT;

	rtn = MPIN_CLIENT_1(sha,date,ID,RNG,X,pin,TOKEN,V,U,UT,TP);
	if (rtn != 0)
	return rtn;

	OCT_joctet(&M,pID);
	if (MESSAGE!=NULL)
	{
	OCT_joctet(&M,MESSAGE);
	}

	MPIN_GET_Y(sha,TimeValue,&M,Y);

	rtn = MPIN_CLIENT_2(X,Y,V);
	if (rtn != 0)
	return rtn;

	return 0;
	}

	/* One pass MPIN Server */
	int ZZZ::MPIN_SERVER(int sha,int date,octet HID,octet HTID,octet Y,octet sQ,octet U,octet UT,octet V,octet E,octet F,octet ID,octet MESSAGE,int TimeValue, octet Pa)
	{
	int rtn=0;
	char m[2*PFS_ZZZ+1];
	octet M= {0,sizeof(m),m};

	octet *pU;
	if (date == 0)
	pU = U;
	else
	pU = UT;

	MPIN_SERVER_1(sha,date,ID,HID,HTID);

	OCT_joctet(&M,pU);
	if (MESSAGE!=NULL)
	{
	OCT_joctet(&M,MESSAGE);
	}

	MPIN_GET_Y(sha,TimeValue,&M,Y);

	rtn = MPIN_SERVER_2(date,HID,HTID,Y,sQ,U,UT,V,E,F,Pa);
	if (rtn != 0)
	return rtn;

	return 0;
	}

	int ZZZ::MPIN_GET_DVS_KEYPAIR(csprng R,octet Z,octet *Pa)
	{
	BIG z,r;
	ECP8 Q;
	int res=0;

	BIG_rcopy(r,CURVE_Order);

	if (R!=NULL)
	{
	BIG_randomnum(z,r,R);
	Z->len=MODBYTES_XXX;
	BIG_toBytes(Z->val,z);
	}
	else
	BIG_fromBytes(z,Z->val);

	BIG_invmodp(z,z,r);

	ECP8_generator(&Q);

	if (res==0)
	{
	PAIR_G2mul(&Q,z);
	ECP8_toOctet(Pa,&Q);
	}

	return res;
	}