int main() {
initialize();
Path<int> p_1(5), p_2(5), p_3(5);
createPath(p_1);
createPath(p_2);
createPath(p_3);
float res_0, res_1, res_2, res_3;
res_0 = weight(p_1);
res_1 = weight(p_2);
res_2 = weight(p_1+p_3);
res_3 = weight(p_2+p_3);
__ESBMC_assume(res_0 >= res_1);
__ESBMC_assert(res_2 >= res_3, "Right-isotonicity violated!");
return 0;
}
int crypto_aead_encrypt(
unsigned char *c,unsigned long long *clen,
const unsigned char *m,unsigned long long mlen,
const unsigned char *ad,unsigned long long adlen,
const unsigned char *nsec,
const unsigned char *npub,
const unsigned char *k
)
{
/*...
... generating a ciphertext c[0],c[1],...,c[*clen-1]
... from a plaintext m[0],m[1],...,m[mlen-1]
... and associated data ad[0],ad[1],...,ad[adlen-1]
... and secret message number nsec[0],nsec[1],...
... and public message number npub[0],npub[1],...
... and secret key k[0],k[1],...
...*/
unsigned char V[StateSize]; //the state represented in Elements
//Temp variables represented as elements
unsigned char key[KeySizeElements];
unsigned char nonce[NonceSizeElements];
unsigned char tag[TagSizeElements];
unsigned char data[RateSizeElements];
unsigned char cipher[RateSizeElements];
Bytes2Element(key,k,0,KeySizeElements); //representing k as elements
Bytes2Element(nonce,npub,0,NonceSizeElements); //representing npub as elements
// V <-- p_1(O||K||N)
InitializeState(V,key,nonce);
p_1(V);
if(adlen!=0)
{
// for i=1 to u-1
if(adlen>RateSizeBytes)
{
for(unsigned long long i=0; i<adlen-RateSizeBytes; i=i+RateSizeBytes)
{
Bytes2Element(data,ad,i,RateSizeElements); // representing a block of ad as elements
// V <-- p_4 (A[i]^V_r || V_c)
for(int j=0; j<RateSizeElements; j++)
V[j]^=data[j];
p_4(V);
}
}
// V <-- A[u]^v_r || V_c
int l = adlen%RateSizeBytes;
if(l==0) { //do padding with spill over
Bytes2Element(data,ad,adlen-RateSizeBytes,RateSizeElements); // representing last block of ad as elements
for(int i=0; i<RateSizeElements; i++)
V[i]^=data[i];
V[RateSizeElements]^=16; //padding spills over to capacity
}
else { //do standard padding
unsigned char dataP[RateSizeBytes];
for(int i=0; i< l; i++)
dataP[i]=ad[adlen-l+i];
dataP[l]=128; //padding over bytes
for(int i=l+1; i<RateSizeBytes; i++)
dataP[i]=0;
Bytes2Element(data,dataP,0,RateSizeElements); // representing last padded block of ad as elements
for(int i=0; i<RateSizeElements; i++)
V[i]^=data[i];
}
// V <-- p_1(V)
p_1(V);
}
//for i=1 to w-1 (except the last block which needs padding)
if(mlen>RateSizeBytes)
{
for(unsigned long long i=0; i<mlen-RateSizeBytes; i=i+RateSizeBytes)
{
Bytes2Element(data,m,i,RateSizeElements); //representing a block of m as elements
// C[i] <-- M[i]^V_r
for(int j=0; j<RateSizeElements; j++)
cipher[j]=V[j]^data[j];
Element2Bytes(c,cipher,i,RateSizeBytes); //representing a block of c as bytes
//V <-- p_1 (C[i] || V_c)
for(int j=0; j<RateSizeElements; j++)
V[j]=cipher[j];
p_1(V);
}
}
//for i=w
int l = mlen%RateSizeBytes;
// C[i] <-- M[i]^V_r
if((l==0) && (mlen!=0)) { //do padding with spill over
Bytes2Element(data,m,mlen-RateSizeBytes,RateSizeElements); // representing last block of m as elements
for(int i=0; i<RateSizeElements; i++)
cipher[i]=V[i]^data[i];
Element2Bytes(c,cipher,mlen-RateSizeBytes,RateSizeBytes); //representing last block of c as bytes
V[RateSizeElements]^=16; //padding spills over to capacity
}
else { //do standard padding
unsigned char dataP[RateSizeBytes];
for(int i=0; i< l; i++)
dataP[i]=m[mlen-l+i];
dataP[l]=128; //padding over bytes
for(int i=l+1; i<RateSizeBytes; i++)
dataP[i]=0;
Bytes2Element(data,dataP,0,RateSizeElements); // representing last block of m as elements
for(int i=0; i<RateSizeElements; i++)
cipher[i]=V[i]^data[i];
unsigned char ct[RateSizeBytes];
Element2Bytes(ct,cipher,0,RateSizeBytes); //representing last block of c as bytes
for(int i=0; i< l; i++)
c[mlen-l+i]=ct[i]; //storing only l bytes of c
}
//V <-- p_1 (C[i] || V_c)
for(int j=0; j<RateSizeElements; j++)
V[j]=cipher[j];
p_1(V);
// T <-- (V_c)_c/2 ^ K
for(int i=0; i<TagSizeElements; i++)
tag[i]=V[RateSizeElements+i]^key[i];
Element2Bytes(c,tag,mlen,TagSizeBytes) ;
*clen=mlen+TagSizeBytes;
return 0;
}
int crypto_aead_decrypt(
unsigned char *m,unsigned long long *mlen,
unsigned char *nsec,
const unsigned char *c,unsigned long long clen,
const unsigned char *ad,unsigned long long adlen,
const unsigned char *npub,
const unsigned char *k
)
{
/*
... generating a plaintext m[0],m[1],...,m[*mlen-1]
... and secret message number nsec[0],nsec[1],...
... from a ciphertext c[0],c[1],...,c[clen-1]
... and associated data ad[0],ad[1],...,ad[adlen-1]
... and public message number npub[0],npub[1],...
... and secret key k[0],k[1],...
...
*/
unsigned char V[StateSize]; //the state represented in Elements
//Temp variables represented as elements
unsigned char key[KeySizeElements];
unsigned char nonce[NonceSizeElements];
unsigned char tag[TagSizeElements];
unsigned char data[RateSizeElements];
unsigned char cipher[RateSizeElements];
*mlen=clen-TagSizeBytes;
if(clen<TagSizeBytes) return -1; //invalid ciphertext
//a temporary array for message
unsigned char *mT = (unsigned char*) malloc(clen-TagSizeBytes);
if (mT == NULL) return -2; // memory allocation failure
Bytes2Element(key,k,0,KeySizeElements); //representing k as elements
Bytes2Element(nonce,npub,0,NonceSizeElements); //representing npub as elements
// V <-- p_1(O||K||N)
InitializeState(V,key,nonce);
p_1(V);
if(adlen!=0)
{
// for i=1 to u-1
if(adlen>RateSizeBytes)
{
for(unsigned long long i=0; i<adlen-RateSizeBytes; i=i+RateSizeBytes)
{
Bytes2Element(data,ad,i,RateSizeElements); // representing a block of ad as elements
// V <-- p_4 (A[i]^V_r || V_c)
for(int j=0; j<RateSizeElements; j++)
V[j]^=data[j];
p_4(V);
}
}
// V <-- A[u]^v_r || V_c
int l = adlen%RateSizeBytes;
if(l==0) { //do padding with spill over
Bytes2Element(data,ad,adlen-RateSizeBytes,RateSizeElements);
for(int i=0; i<RateSizeElements; i++)
V[i]^=data[i];
V[RateSizeElements]^=16; //padding spills over to capacity
}
else { //do standard padding
unsigned char dataP[RateSizeBytes];
for(int i=0; i< l; i++)
dataP[i]=ad[adlen-l+i];
dataP[l]=128; //padding over bytes
for(int i=l+1; i<RateSizeBytes; i++)
dataP[i]=0;
Bytes2Element(data,dataP,0,RateSizeElements);
for(int i=0; i<RateSizeElements; i++)
V[i]^=data[i];
}
// V <-- p_1(V)
p_1(V);
}
//for i=1 to w-1 (except the last block which needs padding)
if(clen-TagSizeBytes>RateSizeBytes)
{
for(unsigned long long i=0; i<clen-(TagSizeBytes+RateSizeBytes); i=i+RateSizeBytes)
{
Bytes2Element(cipher,c,i,RateSizeElements); //representing a block of c as elements
// M[i] <-- C[i]^V_r
for(int j=0; j<RateSizeElements; j++)
data[j]=V[j]^cipher[j];
Element2Bytes(mT,data,i,RateSizeBytes); //representing m as bytes
//V <-- p_1 (C[i] || V_c)
for(int j=0; j<RateSizeElements; j++)
V[j]=cipher[j];
p_1(V);
}
}
//for i=w
int l = clen%RateSizeBytes;
// M[w] <-- C[w]^V_r
// V <-- M[w]||10* ^ V
if((l==0) && ((clen-TagSizeBytes)!=0)) { //do padding with spill over
Bytes2Element(cipher,c,clen-(TagSizeBytes+RateSizeBytes),RateSizeElements);
for(int i=0; i<RateSizeElements; i++) {
data[i]=V[i]^cipher[i];
V[i]=cipher[i];
}
Element2Bytes(mT,data,clen-(TagSizeBytes+RateSizeBytes),RateSizeBytes); //representing last block m as bytes
V[RateSizeElements]^=16; //padding spills over to capacity
}
else { //do standard padding
unsigned char cipherP[RateSizeElements];
unsigned char mtmp[RateSizeBytes];
for(int i=0; i< RateSizeElements; i++)
cipherP[i]=V[i];
Element2Bytes(mtmp,cipherP,0,RateSizeBytes);
for(int i=0; i< l; i++)
mT[clen-TagSizeBytes-l+i]=mtmp[i]^c[clen-TagSizeBytes-l+i];
unsigned char dataP[RateSizeBytes];
for(int i=0; i< l; i++)
dataP[i]=mT[clen-TagSizeBytes-l+i];
dataP[l]=128; //padding over bytes
for(int i=l+1; i<RateSizeBytes; i++)
dataP[i]=0;
Bytes2Element(data,dataP,0,RateSizeElements);
for(int i=0; i<RateSizeElements; i++)
V[i]^=data[i];
}
//V <-- p_1 (V)
p_1(V);
// T <-- (V_c)_c/2 ^ K
for(int i=0; i<TagSizeElements; i++)
tag[i]=V[RateSizeElements+i]^key[i];
unsigned char tagT[TagSizeBytes];
Element2Bytes(tagT,tag,0,TagSizeBytes) ;
unsigned char cor=0;
for(int i=0; i<TagSizeBytes; i++) //check if tags match
cor = cor || (tagT[i]^c[clen-TagSizeBytes+i]);
if(cor==0) //if tags match release the message
for(unsigned long long i=0; i<clen-TagSizeBytes; i++)
m[i]=mT[i];
free(mT);
if(cor==0) return 0;
else return -1;
}
int crypto_aead_decrypt(
unsigned char *m,unsigned long long *mlen,
unsigned char *nsec,
const unsigned char *c,unsigned long long clen,
const unsigned char *ad,unsigned long long adlen,
const unsigned char *npub,
const unsigned char *k
)
{
/*
... generating a plaintext m[0],m[1],...,m[*mlen-1]
... and secret message number nsec[0],nsec[1],...
... from a ciphertext c[0],c[1],...,c[clen-1]
... and associated data ad[0],ad[1],...,ad[adlen-1]
... and public message number npub[0],npub[1],...
... and secret key k[0],k[1],...
...
*/
unsigned char V[StateSize]; //the state represented in Elements
//Temp variables represented as elements
unsigned char key[KeySizeElements];
unsigned char nonce[NonceSizeElements];
unsigned char tag[TagSizeElements];
unsigned char data[RateSizeElements];
unsigned char cipher[RateSizeElements];
unsigned char IV[StateSize]; //temp state represented in Elements
if((clen<(TagSizeBytes+RateSizeBytes))&&(clen!=TagSizeBytes)) return -1; //invalid ciphertext
//a temporary array for message
unsigned char *mT = (unsigned char*) malloc(clen-TagSizeBytes);
if (mT == NULL) return -2; // memory allocation failure
Bytes2Element(key,k,0,KeySizeElements); //representing k as elements
Bytes2Element(nonce,npub,0,NonceSizeElements); //representing npub as elements
// IV <-- O||K
InitializeState(IV,key);
// Treating the nonce as the first part of the associated data
for(int i=0; i<(NonceSizeElements/RateSizeElements); i++)
{
// IV <-- p_1 (N[i]^IV_r || IV_c)
for(int j=0; j<RateSizeElements; j++)
IV[j]^=nonce[RateSizeElements*i+j];
p_1(IV);
}
if(adlen!=0)
{
// for i=1 to u-1 (except the last block which needs padding)
if(adlen>RateSizeBytes)
{
for(unsigned long long i=0; i<adlen-RateSizeBytes; i=i+RateSizeBytes)
{
Bytes2Element(data,ad,i,RateSizeElements); // representing a block of ad as elements
// IV <-- p_1 (A[i]^IV_r || IV_c)
for(int j=0; j<RateSizeElements; j++)
IV[j]^=data[j];
p_1(IV);
}
}
// IV <-- A[u]^IV_r || IV_c
int l = adlen%RateSizeBytes;
if(l==0){ //do padding with spill over
Bytes2Element(data,ad,adlen-RateSizeBytes,RateSizeElements); // representing last block of ad as elements
for(int i=0; i<RateSizeElements; i++)
IV[i]^=data[i];
IV[RateSizeElements]^=16; //padding spills over to capacity
}
else{ //do standard padding
unsigned char dataP[RateSizeBytes];
for(int i=0; i< l; i++)
dataP[i]=ad[adlen-l+i];
dataP[l]=128; //padding over bytes
for(int i=l+1; i<RateSizeBytes; i++)
dataP[i]=0;
Bytes2Element(data,dataP,0,RateSizeElements); // representing last padded block of ad as elements
for(int i=0; i<RateSizeElements; i++)
IV[i]^=data[i];
}
// IV <-- p_1(IV)
p_1(IV);
}
// IV <-- IV ^ (0..01)
IV[StateSize-1]^=1;
unsigned char tagT[TagSizeBytes];
if(clen==TagSizeBytes){ //ciphertext length and hence the message length is 0
*mlen=0;
//do standard padding
unsigned char dataP[RateSizeBytes];
dataP[0]=128; //padding over bytes
for(int i=1; i<RateSizeBytes; i++)
dataP[i]=0;
Bytes2Element(data,dataP,0,RateSizeElements); // representing last block of m as elements
// V <-- p_1 (M[1]^V_r || V_c)
for(int i=0; i<RateSizeElements; i++)
IV[i]^=data[i];
p_1(IV);
// T <-- (V_c)_c/2 ^ K
for(int i=0; i<TagSizeElements; i++)
tag[i]=IV[RateSizeElements+i]^key[i];
Element2Bytes(tagT,tag,0,TagSizeBytes) ;
unsigned char cor=0;
for(int i=0; i<TagSizeBytes; i++) //check if tags match
cor = cor || (tagT[i]^c[i]);
free(mT);
if(cor==0) return 0;
else return -1;
}
else{
// V <-- p_1_inv(C[w] || K^T)
Bytes2Element(cipher,c,clen-(TagSizeBytes+RateSizeBytes),RateSizeElements);
Bytes2Element(tag,c,clen-(TagSizeBytes),TagSizeElements);
for(int i=0; i<RateSizeElements; i++)
V[i]=cipher[i];
for(int i=0; i<CapacitySize; i++)
V[RateSizeElements+i]=key[i]^tag[i];
p_1_inv(V);
if(clen==(TagSizeBytes+RateSizeBytes)){ //ciphertext is one block only hence plaintext length is less then or equal to RateSize
// V <-- V ^ IV
for(int i=0; i<StateSize; i++)
V[i] ^= IV[i];
unsigned char cor=0;
for(int i=RateSizeElements+1; i<StateSize; i++) //check if IV_c matches with V_c
cor = cor || V[i];
cor = cor || (!((V[RateSizeElements]==0) || (V[RateSizeElements]==16)));
if (cor==0)
{
for(int i=0; i<RateSizeElements; i++)
data[i]=V[i];
Element2Bytes(mT,data,0,RateSizeBytes); //representing m as bytes
if(V[RateSizeElements]==16) *mlen=(unsigned long long) RateSizeBytes;
else{
unsigned char match=0;
for(int i=0; i<RateSizeBytes; i++) {
match |= (mT[i]==128);
}
if(match==0) { free(mT); return -1; }
for(int i=RateSizeBytes-1; i>=0; i--)
if(mT[i]==128) { *mlen=(unsigned long long) i; break;}
}
for(unsigned long long i=0; i<*mlen; i++)
m[i]=mT[i];
free(mT);
return 0;
}
else { free(mT); return -1; }
}
else{
*mlen=clen-TagSizeBytes;
//for i=w (tha last block)
int l = clen%RateSizeBytes;
if (l==0){
//M[w] <-- |V_r|_l^C[w-1]
Bytes2Element(cipher,c,clen-(TagSizeBytes+2*RateSizeBytes),RateSizeElements);
for(int i=0; i<RateSizeElements; i++)
data[i]=V[i]^cipher[i];
Element2Bytes(mT,data,clen-(TagSizeBytes+RateSizeBytes),RateSizeBytes); //representing last block m as bytes
//V <-- V^M[w]10*
for(int i=0; i<(RateSizeElements); i++)
V[i]^=data[i];
V[RateSizeElements]^=16;
}
else{
//M[w] <-- |V_r|_l^C[w-1]
unsigned char cipherP[RateSizeBytes];
unsigned char mtmp[RateSizeBytes];
Element2Bytes(cipherP,V,0,RateSizeBytes); //representing last block m as bytes
for(int i=0; i<l; i++){
mT[(clen-TagSizeBytes)-l+i]=cipherP[i]^c[clen-(TagSizeBytes+RateSizeBytes+l)+i];
mtmp[i]=mT[(clen-TagSizeBytes)-l+i];
}
mtmp[l]=128;
for(int i=l+1; i<RateSizeBytes; i++)
mtmp[i]=0;
Bytes2Element(data,mtmp,0,RateSizeElements);
//V <-- V^M[w]10*
for(int i=0; i<RateSizeElements; i++)
V[i]^=data[i];
}
l = (l==0) ? RateSizeBytes : l;
//for i=w-1 to 2
for(unsigned long long i=((clen-TagSizeBytes)-l); i>RateSizeBytes; i=i-5){
// V <-- p_1_inv(V)
p_1_inv(V);
// M[i] <-- C[i-1]^V_r
unsigned char mtmp[RateSizeElements];
Bytes2Element(data,c,i-2*RateSizeBytes,RateSizeElements);
for(int j=0; j<RateSizeElements; j++)
mtmp[j]=data[j]^V[j];
Element2Bytes(mT,mtmp,i-RateSizeBytes,RateSizeBytes); //representing last block m as bytes
// V <-- C[i-1] || V_c
for(int j=0; j<RateSizeElements; j++)
V[j]=data[j];
}
//for i=1
// V <-- p_1_inv(V)
p_1_inv(V);
// M[i] <-- C[i-1]^V_r
for(int i=0; i<RateSizeElements; i++)
data[i]=IV[i]^V[i];
Element2Bytes(mT,data,0,RateSizeBytes); //representing last block m as bytes
//check if IV_c matches with V_c
for(int j=0; j<RateSizeElements; j++)
V[j]^=data[j];
unsigned char cor=0;
for(int i=RateSizeElements; i<StateSize; i++)
cor = cor || (V[i]^IV[i]);
if(cor==0) {
for(unsigned long long i=0; i<*mlen; i++)
m[i]=mT[i];
}
free(mT);
if (cor == 0) return 0;
else return -1;
}
}
}