m = 15;
q = 2^m;

poly = primpoly(m,'nodisplay');

primeFactors = unique(factor(2^m-1));
rng(123456);
while 1
    g = gf(randi([1,q-1]),m,poly);
    isPrimitive = true;
    for i = 1:length(primeFactors)
        if g^((q-1)/primeFactors(i)) == gf(1,m,poly)
            isPrimitive = false;
            break;
        end
    end
    if isPrimitive
        break;
    end
end

privateKey = 12;
publicKey = {g,g^privateKey,poly};

text = ['The Fourier transform decomposes a function of time (a signal)' newline ...
    'into the frequencies that make it up, in a way similar to how a' newline ...
    'musical chord can be expressed as the amplitude (or loudness) of' newline ...
    'its constituent notes.'];
disp(text);

bitsPerChar = 7;
binMsg = de2bi(int8(text),bitsPerChar,'left-msb')';
numPaddedBits = m - mod(numel(binMsg),m);
if numPaddedBits == m
    numPaddedBits = 0;
end
binMsg = [binMsg(:); zeros(numPaddedBits,1)];
textToEncrypt = bi2de(reshape(binMsg,[],m),'left-msb');

cipherText = gf(zeros(length(textToEncrypt),2),m,poly);

for i = 1:length(textToEncrypt)
    k = randi([1 2^m-2]);
    cipherText(i,:) = [publicKey{1}^k, ...
        gf(textToEncrypt(i),m,poly)*publicKey{2}^k];
end

tmp = cipherText.x;
disp(de2char(tmp(:,2),bitsPerChar,m));

decipherText = gf(zeros(size(cipherText,1),1),m,poly);
for i = 1:size(cipherText,1)
    decipherText(i) = cipherText(i,2) * cipherText(i,1)^(-privateKey);
end

disp(de2char(decipherText.x,bitsPerChar,m));

function text = de2char(msg,bitsPerChar,m)
binDecipherText = de2bi(msg,m,'left-msb');
text = char(bi2de(reshape(binDecipherText(1:end-mod(numel(binDecipherText), ...
    bitsPerChar)),bitsPerChar,[])','left-msb'))';
end