NTL - how to get the integer representation of an element in GF(2^n)

Question

Is there a way to get the integer representation of that vector of coefficients? i.e. in a way that the highest degree coefficient is the MSB of that integer and the coefficient of x^0 is the LSB? when using the method BytesFromGF2X it results in a weird representation which is neither big endian nor little endian.

For example, if the element is x^23+x^20+x+1 then I would like to get the integer: 2^23+2^20+2+1.

Answer 1

Use these two methods to convert back and forth to a little endian integer representation:

FROM GF2X TO LITTLE ENDIAN INTEGER

void MyBytesFromGF2X(unsigned char* buffer, NTL::GF2X& p, int numbytes) {
    int degree = NTL::deg(p);
    memset(buffer,0,numbytes);
    for(int i=0; i<=degree; i++) {
        if(NTL::IsOne(NTL::coeff(p,i))) {
            buffer[i/8] |= 1 << i%8;
        }
    }
}

At the end buffer contains the number represented by p in a normal little-endian fashion.

If you want to get the integer, then assume that the maximum degree of p is 32 then you do the following:

USAGE

unsigned char buffer[4];
int *integer = buffer;
NTL::GF2X p;
NTL::SetCoeff(p,1,1); // set the coefficient of x^1 to 1
NTL::SetCoeff(p,30,1); // set the coefficient of x^30 to 1
MyBytesFromGF2X(buffer,p,4);
printf("%d",integer);
//result will be LE integer representation of 2^30+2^1

In order to convert back to GF2X you ca use this:

FROM LITTLE ENDIAN INTEGER TO GF2X

void MyBytesToGF2X(const unsigned char* buffer, NTL::GF2X& p, int numbytes) {
    for(int i=0; i<numbytes; i++) {
        for(int j=0; j<8; j++) {
            int bit = (buffer[i]>>j)&1;
            NTL::SetCoeff(p, i*8+j, bit);
        }
    }
}