An implementation of the ElGamal encryption system in JavaScript.

elGamal.js

var Alphabet = "!\"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\\]^_`abcdefghijklmnopqrstuvwxyz{|}~ 𮃩∆";

Alphabet = Alphabet.split("");

var Crypto = function (alpha, gen, C) {
    var p, B, encrypt, decrypt, f, g, modInv, modPow, toAlpha, to10;
    toAlpha = function (x) {
        var y, p, l, n;
        if (x === 0) {
            return "!!!!";
        }
        y = [];
        n = 4;
        n = Math.ceil(n);
        while (n--) {
            p = Math.pow(alpha.length, n);
            l = Math.floor(x / p);
            y.push(alpha[l]);
            x -= l * p;
        }
        y = y.join("");
        return y;
    };
    to10 = function (x) {
        var y, p, n;
        y = 0;
        p = 1;
        x = x.split("");
        n = x.length;
        while (n--) {
            y += alpha.indexOf(x[n]) * p;
            p *= alpha.length;
        }
        return y;
    };
    modInv = function (gen, mod) {
        var v, d, u, t, c, q;
        v = 1;
        d = gen;
        t = 1;
        c = mod % gen;
        u = Math.floor(mod / gen);
        while (d > 1) {
            q = Math.floor(d / c);
            d = d % c;
            v = v + q * u;
            if (d) {
                q = Math.floor(c / d);
                c = c % d;
                u = u + q * v;
            }
        }
        return d ? v : mod - u;
    };
    modPow = function (base, exp, mod) {
        var c, x;
        if (exp === 0) {
            return 1;
        } else if (exp < 0) {
            exp = -exp;
            base = modInv(base, mod);
        }
        c = 1;
        while (exp > 0) {
            if (exp % 2 === 0) {
                base = (base * base) % mod;
                exp /= 2;
            } else {
                c = (c * base) % mod;
                exp--;
            }
        }
        return c;
    };
    p = 91744613;
    C = parseInt(C, 10);
    if (isNaN(C)) {
        C = Math.round(Math.sqrt(Math.random() * Math.random()) * (p - 2) + 2);
    }
    B = modPow(gen, C, p);
    decrypt = function (a) {
        var d, x, y;
        x = a[1];
        y = modPow(a[0], -C, p);
        d = (x * y) % p;
        d = Math.round(d) % p;
        d %= alpha.length;
        return alpha[d - 2];
    };
    encrypt = function (key, d) {
        var k, a;
        k = Math.ceil(Math.sqrt(Math.random() * Math.random()) * 1E10);
        d = alpha.indexOf(d) + 2;
        a = [];
        a[0] = modPow(key[1], k, key[0]);
        a[1] = (d * modPow(key[2], k, key[0])) % key[0];
        return a;
    };
    f = function (message, key) {
        var n, x, y, w;
        y = [];
        message = message.split("");
        n = message.length;
        while (n--) {
            x = encrypt(key, message[n]);
            y.push(toAlpha(x[0]));
            y.push(toAlpha(x[1]));
        }
        y = y.join("");
        return y;
    };
    g = function (message) {
        var n, m, d, x;
        m = [];
        n = message.length / 8;
        while (n--) {
            x = message[8 * n + 4];
            x += message[8 * n + 5];
            x += message[8 * n + 6];
            x += message[8 * n + 7];
            m.unshift(x);
            x = message[8 * n];
            x += message[8 * n + 1];
            x += message[8 * n + 2];
            x += message[8 * n + 3];
            m.unshift(x);
        }
        x = [];
        d = [];
        n = m.length / 2;
        while (n--) {
            x[0] = m[2 * n];
            x[1] = m[2 * n + 1];
            x[0] = to10(x[0]);
            x[1] = to10(x[1]);
            d.push(decrypt(x));
        }
        message = d.join("");
        return message;
    };
    return {
        pubKey: [p, gen, B],
        priKey: C,
        decrypt: g,
        encrypt: f
    };
};

var Alice = Crypto(Alphabet, 69);
var Bob = Crypto(Alphabet, 69);
var Eve = Crypto(Alphabet, 69);

var message1 = "Hello!";
var message2 = "Dear Bob, I wanted to tell you that my Very Important Secret Number is 1234567890.";

message1 = Alice.encrypt(message1, Bob.pubKey);
message2 = Alice.encrypt(message2, Bob.pubKey);


print("Alice writes: ");
print("     " + message1);
print("     " + message2);
/*Alice writes: 
     qZqffP9O(3xw<Z{?Te&$Xw:8OR®aOB/8)Pi@0PnADt``E<En
     D_2fxid$D:!suIs?=|fDXaMXm|R:tqU3Fl1(rPp+lFXq3[crJP/U`MXpsxp@"cb?h^dM1F"TXπBUT∆\h5_®wsTbZ.J,yGn%s{',jOπ2>2`y({Y∆EwuY4\7hπFdZTu9>%N'yFizmTjAEBdDPGCETALWZOO>kM@I∆U\i<;AiW@t6ifH1M-`IcrcOwDaFOU!4d.9=rB2®ms0{π><Bdi;PfO$ƒZgUi`©PP0®.edZ9^x=k'kz7mnF`"ƒJJ_/Vd%jDF:U®&EN'$-hn[®E:L6c?&©tfE{7_V;π93N/NN+*i"\#pF"tS90j∆N_2JaY/h!n6wQ8®/IS®3'j?®^i _]SEwdM%_6∆J/==[%3>=#E.qKk/'A&y#+l[-'QUx7G`R`ZmASJ)nE%ss%(=&>iRƒ'**ƒC;]l"[email protected]>I/ZI|wk[πHGpS1I_B]DKb%aeFKzAP6:®(KW;6;4Da;D.>Rq{pLvP/$XN/;e2∆ta+V=>W:"e=!T>8)q8w*f+J,kWv@`@x®K-7`mb%9r]Xrcx(π'R&8+"{|[xj'^!)4eLF<Ngi;OufZp0(π\(6x<1Qja=Jhqπ(J,k[ZF9©{96IjF∆®3c6[p6hs8IJs"/S$O-(cLgzGJ`r{&&;#=K 3q,"cy/I$*,n\∆I9dnE7*HNb8<vj^]$35^rLmj
*/

print("Bob reads: ");
print("     " + Bob.decrypt(message1));
print("     " + Bob.decrypt(message2));
/*
    Bob reads: 
         Hello!
         Dear Bob, I wanted to tell you that my Very Important Secret Number is 1234567890.
*/


print("Eve reads: ");
print("     " + Eve.decrypt(message1));
print("     " + Eve.decrypt(message2));
/*
    Eve reads: 
         %4mG=t
         eaw~@iC3W,(\w+/3ee!`{){π<LY~VW8VSm5g+dLqyV}Z#jl%KπJD$Q$W$R+9{/gO<[wC|@)1;~fπO
*/


// This system isn't cryptographically secure for practical purposes. The value of p (91744613) is as large as JS can handle natively, but is still much too small. Please don't use it as-is for anything that actually needs to be secured. If you want to make it secure, I would suggest building functions that can handle larger numbers abstractly, or using a BigNum library; then set p to a much larger prime (hundreds of digits).

Hey. I wanted to use this code with a smaller set of alphabets. Changing the Alphabet variable creates issues: the encrypted message is no longer divisible by 8 because Math.floor(x/p) returns an index more than that within the Alphabet array. Could you explain how to fix this? Thanks.

Values used:
var Alphabet="abcdefghijklmnopqrstuvwxyz 0123456789'(!#$%^_)*+,-";
var message = "An even longer message";