Find Linear Patterns in 16x16 bit S-Boxes

sbox.js

// Useful when performing linear cryptanalysis of block ciphers w/ S-Boxes
// Example S-Boxes used in the GHOST algorithm
var sb1 = [ 4, 10, 9, 2, 13, 8, 0, 14, 6, 11, 1, 12, 7, 15, 5, 3 ],
    sb2 = [ 14, 11, 4, 12, 6, 13, 15, 10, 2, 3, 8, 1, 0, 7, 5, 9 ],
    sb3 = [ 5, 8, 1, 13, 10, 3, 4, 2, 14, 15, 12, 7, 6, 0, 9, 11 ],
    sb4 = [ 7, 13, 10, 1, 0, 8, 9, 15, 14, 4, 6, 12, 11, 2, 5, 3 ],
    sb5 = [ 6, 12, 7, 1, 5, 15, 13, 8, 4, 10, 9, 14, 0, 2, 11, 2 ],
    sb6 = [ 4, 11, 10, 0, 7, 2, 1, 13, 3, 6, 8, 5, 9, 12, 15, 14 ],
    sb7 = [ 13, 11, 4, 1, 3, 15, 5, 9, 0, 10, 14, 7, 6, 8, 2, 12 ],
    sb8 = [ 1, 15, 13, 0, 5, 7, 10, 4, 9, 2, 3, 14, 6, 11, 8, 12 ];

function findRel(sbox, X, Y){

    var works = 0;

    for(var i = 0, len = sbox.length; i < len; i++){
        var x = i,
            x4 = (x & 1) ? 1 : 0,
            x3 = (x & 2) ? 1 : 0,
            x2 = (x & 4) ? 1 : 0,
            x1 = (x & 8) ? 1 : 0;

        var y = sbox[i],
            y4 = (y & 1) ? 1 : 0,
            y3 = (y & 2) ? 1 : 0,
            y2 = (y & 4) ? 1 : 0,
            y1 = (y & 8) ? 1 : 0;

        var Xres = ((X[0]*x1) ^ (X[1]*x2) ^ (X[2]*x3) ^ (X[3]*x4)),
            Yres = ((Y[0]*y1) ^ (Y[1]*y2) ^ (Y[2]*y3) ^ (Y[3]*y4));

        if(Xres == Yres)
            works++;
    }

    return works;
}

function everyRel(sbox){

    var picks = [];

    for(var i = 0, len = sbox.length; i < len; i++){
        var b = i,
            b4 = (b & 1) ? 1 : 0,
            b3 = (b & 2) ? 1 : 0,
            b2 = (b & 4) ? 1 : 0,
            b1 = (b & 8) ? 1 : 0;

        for(var j = 0; j < len; j++){
            var B = j,
                B4 = (B & 1) ? 1 : 0,
                B3 = (B & 2) ? 1 : 0,
                B2 = (B & 4) ? 1 : 0,
                B1 = (B & 8) ? 1 : 0;

            var res = findRel(sbox, [b1, b2, b3, b4], [B1, B2, B3, B4]);

            // arbitrary limits
            if((res > 10 || res < 4) && res !== 16){
                var str = "X:"+b1+""+b2+""+b3+""+b4+"\n";
                    str += "Y:"+B1+""+B2+""+B3+""+B4+"\n";
                    str += res+"\n";

                picks.push(str);
            }
        }
    }

    return picks;
}

function pprint(picks){
    for(var i = 0; i < 3; i++){
        console.log(picks[i]);
    }
}


console.log("S-box 1");
pprint(everyRel(sb1));
console.log("S-box 2");
pprint(everyRel(sb2));
console.log("S-box 3");
pprint(everyRel(sb3));
console.log("S-box 4");
pprint(everyRel(sb4));
console.log("S-box 5");
pprint(everyRel(sb5));
console.log("S-box 6");
pprint(everyRel(sb6));
console.log("S-box 7");
pprint(everyRel(sb7));
console.log("S-box 8");
pprint(everyRel(sb8));