DrI-T/README.md

## README.md

      
    Raw
  

              README.md
            
          
# What's our secret ?
One can safely share a secret using DH key exchange :
 pubkey(self) = g ^ privkey mod prime
 
 secret = pubkey(otherparty) ^ privkey mod prime

Cryptography can be understood with the annalogy padlock and keys.
How can we exchange a secret at plain sight ?

Indeed your public key "act" as a padlock to secure
a message, I have a key of this pad lock.
And my public key is the padlock that can be open with your private key
to reveal the exact same secret !

Your key (private key): 

Padlock (public key): 
Our shared DH secret is: 
This secret is only know to  you and me ... and can be used as a "master key"
for locks we both have access too.
As a quick verification that we have the same key, we see the same robot image
at the top right of this page.
This file can be viewed on gist.io,
and executed on bl.ocks.org.

  
## app.js

var g = bigInt(3);
var prime = bigInt('k672zw0jialf0skyp85r078stdrmlucv5fnkl85vjz6d4v3pqqb'.slice(1),36);
console.log(g,prime);

// my secret keys ...
let privkey = 'k6n4zqqme17qgl1u6gb7f2kzvmg2ii0y36';
let sk2 = bigInt(privkey.slice(1),36);
var pk2 = g.modPow(sk2,prime);
console.log('sk2: k'+sk2.toString(36))
console.log('pk2: k'+pk2.toString(36));
update({});


function update(ev) {
skelem = document.getElementsByName('private')[0];
skelem.addEventListener('change',update,false);
if (skelem.value == '') {
 skelem.value = privkey
} else {
 privkey = skelem.value || privkey;
}
// your private key ...
let sk1 = bigInt(privkey.slice(1),36);
var pk1 = g.modPow(sk1,prime);
pkelem = document.getElementsByName('public')[0];
pkelem.value = 'k'+pk1.toString(36)


// our shared secret from me to you
var sec1 = pk2.modPow(sk1,prime);
secelem = document.getElementsByName('secret')[0];
secelem.value = 'k'+sec1.toString(36)
// our shared secret from you to me
var sec2 = pk1.modPow(sk2,prime);

// encrypted bot keys ...
let bot2 = sec2.modPow(pk2,prime);
console.log('bot1:',sec1.modPow(pk2,prime).toString(16));
console.log('bot2:',bot2.toString(16));
let img = document.getElementsByTagName('img')[0];
 img.src = `https://robohash.org/${bot2.toString(36)}`
 img.title = bot2.toString(36)

 return sec1;

}


function hex2byte(hex) {
   let bytes = [];
   for(var i=0; i< hex.length-1; i+=2){
      bytes.push(parseInt(hex.substr(i, 2), 16));
   }
   let str = String.fromCharCode.apply(String, bytes);
   //console.log('hex:',byte2hex(str));
   return str;

}
function byte2hex(str) {
  let hex = ''
  for (let i=0; i < str.length; ++i) {
    let chr = str.charCodeAt(i).toString(16)
    hex += chr.length < 2 ? '0' + chr : chr
  }
  //console.log('str:',hex2byte(hex));
  return hex
}


function keyGen(base, exponent, modulus) {
 return base.modPow(exponent,modulus);
}


## bigint.js

var bigInt = function(e) {
    "use strict";

    function o(e, t) {
        this.value = e, this.sign = t, this.isSmall = !1
    }

    function u(e) {
        this.value = e, this.sign = e < 0, this.isSmall = !0
    }

    function a(e) {
        return -r < e && e < r
    }

    function f(e) {
        return e < 1e7 ? [e] : e < 1e14 ? [e % 1e7, Math.floor(e / 1e7)] : [e % 1e7, Math.floor(e / 1e7) % 1e7, Math.floor(e / 1e14)]
    }

    function l(e) {
        c(e);
        var n = e.length;
        if (n < 4 && O(e, i) < 0) switch (n) {
            case 0:
                return 0;
            case 1:
                return e[0];
            case 2:
                return e[0] + e[1] * t;
            default:
                return e[0] + (e[1] + e[2] * t) * t
        }
        return e
    }

    function c(e) {
        var t = e.length;
        while (e[--t] === 0);
        e.length = t + 1
    }

    function h(e) {
        var t = new Array(e),
            n = -1;
        while (++n < e) t[n] = 0;
        return t
    }

    function p(e) {
        return e > 0 ? Math.floor(e) : Math.ceil(e)
    }

    function d(e, n) {
        var r = e.length,
            i = n.length,
            s = new Array(r),
            o = 0,
            u = t,
            a, f;
        for (f = 0; f < i; f++) a = e[f] + n[f] + o, o = a >= u ? 1 : 0, s[f] = a - o * u;
        while (f < r) a = e[f] + o, o = a === u ? 1 : 0, s[f++] = a - o * u;
        return o > 0 && s.push(o), s
    }

    function v(e, t) {
        return e.length >= t.length ? d(e, t) : d(t, e)
    }

    function m(e, n) {
        var r = e.length,
            i = new Array(r),
            s = t,
            o, u;
        for (u = 0; u < r; u++) o = e[u] - s + n, n = Math.floor(o / s), i[u] = o - n * s, n += 1;
        while (n > 0) i[u++] = n % s, n = Math.floor(n / s);
        return i
    }

    function g(e, n) {
        var r = e.length,
            i = n.length,
            s = new Array(r),
            o = 0,
            u = t,
            a, f;
        for (a = 0; a < i; a++) f = e[a] - o - n[a], f < 0 ? (f += u, o = 1) : o = 0, s[a] = f;
        for (a = i; a < r; a++) {
            f = e[a] - o;
            if (!(f < 0)) {
                s[a++] = f;
                break
            }
            f += u, s[a] = f
        }
        for (; a < r; a++) s[a] = e[a];
        return c(s), s
    }

    function y(e, t, n) {
        var r, i;
        return O(e, t) >= 0 ? r = g(e, t) : (r = g(t, e), n = !n), r = l(r), typeof r == "number" ? (n && (r = -r), new u(r)) : new o(r, n)
    }

    function b(e, n, r) {
        var i = e.length,
            s = new Array(i),
            a = -n,
            f = t,
            c, h;
        for (c = 0; c < i; c++) h = e[c] + a, a = Math.floor(h / f), h %= f, s[c] = h < 0 ? h + f : h;
        return s = l(s), typeof s == "number" ? (r && (s = -s), new u(s)) : new o(s, r)
    }

    function w(e, n) {
        var r = e.length,
            i = n.length,
            s = r + i,
            o = h(s),
            u = t,
            a, f, l, p, d;
        for (l = 0; l < r; ++l) {
            p = e[l];
            for (var v = 0; v < i; ++v) d = n[v], a = p * d + o[l + v], f = Math.floor(a / u), o[l + v] = a - f * u, o[l + v + 1] += f
        }
        return c(o), o
    }

    function E(e, n) {
        var r = e.length,
            i = new Array(r),
            s = t,
            o = 0,
            u, a;
        for (a = 0; a < r; a++) u = e[a] * n + o, o = Math.floor(u / s), i[a] = u - o * s;
        while (o > 0) i[a++] = o % s, o = Math.floor(o / s);
        return i
    }

    function S(e, t) {
        var n = [];
        while (t-- > 0) n.push(0);
        return n.concat(e)
    }

    function x(e, t) {
        var n = Math.max(e.length, t.length);
        if (n <= 400) return w(e, t);
        n = Math.ceil(n / 2);
        var r = e.slice(n),
            i = e.slice(0, n),
            s = t.slice(n),
            o = t.slice(0, n),
            u = x(i, o),
            a = x(r, s),
            f = x(v(i, r), v(o, s));
        return v(v(u, S(g(g(f, u), a), n)), S(a, 2 * n))
    }

    function T(e, n, r) {
        return e < t ? new o(E(n, e), r) : new o(w(n, f(e)), r)
    }

    function N(e) {
        var n = e.length,
            r = h(n + n),
            i = t,
            s, o, u, a, f;
        for (u = 0; u < n; u++) {
            a = e[u];
            for (var l = 0; l < n; l++) f = e[l], s = a * f + r[u + l], o = Math.floor(s / i), r[u + l] = s - o * i, r[u + l + 1] += o
        }
        return c(r), r
    }

    function C(e, n) {
        var r = e.length,
            i = n.length,
            s = t,
            o = h(n.length),
            u = n[i - 1],
            a = Math.ceil(s / (2 * u)),
            f = E(e, a),
            c = E(n, a),
            p, d, v, m, g, y, b;
        f.length <= r && f.push(0), c.push(0), u = c[i - 1];
        for (d = r - i; d >= 0; d--) {
            p = s - 1, f[d + i] !== u && (p = Math.floor((f[d + i] * s + f[d + i - 1]) / u)), v = 0, m = 0, y = c.length;
            for (g = 0; g < y; g++) v += p * c[g], b = Math.floor(v / s), m += f[d + g] - (v - b * s), v = b, m < 0 ? (f[d + g] = m + s, m = -1) : (f[d + g] = m, m = 0);
            while (m !== 0) {
                p -= 1, v = 0;
                for (g = 0; g < y; g++) v += f[d + g] - s + c[g], v < 0 ? (f[d + g] = v + s, v = 0) : (f[d + g] = v, v = 1);
                m += v
            }
            o[d] = p
        }
        return f = L(f, a)[0], [l(o), l(f)]
    }

    function k(e, n) {
        var r = e.length,
            i = n.length,
            s = [],
            o = [],
            u = t,
            a, f, c, h, p;
        while (r) {
            o.unshift(e[--r]);
            if (O(o, n) < 0) {
                s.push(0);
                continue
            }
            f = o.length, c = o[f - 1] * u + o[f - 2], h = n[i - 1] * u + n[i - 2], f > i && (c = (c + 1) * u), a = Math.ceil(c / h);
            do {
                p = E(n, a);
                if (O(p, o) <= 0) break;
                a--
            } while (a);
            s.push(a), o = g(o, p)
        }
        return s.reverse(), [l(s), l(o)]
    }

    function L(e, n) {
        var r = e.length,
            i = h(r),
            s = t,
            o, u, a, f;
        a = 0;
        for (o = r - 1; o >= 0; --o) f = a * s + e[o], u = p(f / n), a = f - u * n, i[o] = u | 0;
        return [i, a | 0]
    }

    function A(e, n) {
        var r, i = Q(n),
            s = e.value,
            a = i.value,
            c;
        if (a === 0) throw new Error("Cannot divide by zero");
        if (e.isSmall) return i.isSmall ? [new u(p(s / a)), new u(s % a)] : [G[0], e];
        if (i.isSmall) {
            if (a === 1) return [e, G[0]];
            if (a == -1) return [e.negate(), G[0]];
            var h = Math.abs(a);
            if (h < t) {
                r = L(s, h), c = l(r[0]);
                var d = r[1];
                return e.sign && (d = -d), typeof c == "number" ? (e.sign !== i.sign && (c = -c), [new u(c), new u(d)]) : [new o(c, e.sign !== i.sign), new u(d)]
            }
            a = f(h)
        }
        var v = O(s, a);
        if (v === -1) return [G[0], e];
        if (v === 0) return [G[e.sign === i.sign ? 1 : -1], G[0]];
        s.length + a.length <= 200 ? r = C(s, a) : r = k(s, a), c = r[0];
        var m = e.sign !== i.sign,
            g = r[1],
            y = e.sign;
        return typeof c == "number" ? (m && (c = -c), c = new u(c)) : c = new o(c, m), typeof g == "number" ? (y && (g = -g), g = new u(g)) : g = new o(g, y), [c, g]
    }

    function O(e, t) {
        if (e.length !== t.length) return e.length > t.length ? 1 : -1;
        for (var n = e.length - 1; n >= 0; n--)
            if (e[n] !== t[n]) return e[n] > t[n] ? 1 : -1;
        return 0
    }

    function M(e) {
        var t = e.abs();
        if (t.isUnit()) return !1;
        if (t.equals(2) || t.equals(3) || t.equals(5)) return !0;
        if (t.isEven() || t.isDivisibleBy(3) || t.isDivisibleBy(5)) return !1;
        if (t.lesser(25)) return !0
    }

    function H(e) {
        return (typeof e == "number" || typeof e == "string") && +Math.abs(e) <= t || e instanceof o && e.value.length <= 1
    }

    function B(e, t, n) {
        t = Q(t);
        var r = e.isNegative(),
            i = t.isNegative(),
            s = r ? e.not() : e,
            o = i ? t.not() : t,
            u = [],
            a = [],
            f = !1,
            l = !1;
        while (!f || !l) s.isZero() ? (f = !0, u.push(r ? 1 : 0)) : r ? u.push(s.isEven() ? 1 : 0) : u.push(s.isEven() ? 0 : 1), o.isZero() ? (l = !0, a.push(i ? 1 : 0)) : i ? a.push(o.isEven() ? 1 : 0) : a.push(o.isEven() ? 0 : 1), s = s.over(2), o = o.over(2);
        var c = [];
        for (var h = 0; h < u.length; h++) c.push(n(u[h], a[h]));
        var p = bigInt(c.pop()).negate().times(bigInt(2).pow(c.length));
        while (c.length) p = p.add(bigInt(c.pop()).times(bigInt(2).pow(c.length)));
        return p
    }

    function I(e) {
        var n = e.value,
            r = typeof n == "number" ? n | j : n[0] + n[1] * t | F;
        return r & -r
    }

    function q(e, t) {
        return e = Q(e), t = Q(t), e.greater(t) ? e : t
    }

    function R(e, t) {
        return e = Q(e), t = Q(t), e.lesser(t) ? e : t
    }

    function U(e, t) {
        e = Q(e).abs(), t = Q(t).abs();
        if (e.equals(t)) return e;
        if (e.isZero()) return t;
        if (t.isZero()) return e;
        var n = G[1],
            r, i;
        while (e.isEven() && t.isEven()) r = Math.min(I(e), I(t)), e = e.divide(r), t = t.divide(r), n = n.multiply(r);
        while (e.isEven()) e = e.divide(I(e));
        do {
            while (t.isEven()) t = t.divide(I(t));
            e.greater(t) && (i = t, t = e, e = i), t = t.subtract(e)
        } while (!t.isZero());
        return n.isUnit() ? e : e.multiply(n)
    }

    function z(e, t) {
        return e = Q(e).abs(), t = Q(t).abs(), e.divide(U(e, t)).multiply(t)
    }

    function W(e, n) {
        e = Q(e), n = Q(n);
        var r = R(e, n),
            i = q(e, n),
            s = i.subtract(r);
        if (s.isSmall) return r.add(Math.round(Math.random() * s));
        var a = s.value.length - 1,
            f = [],
            c = !0;
        for (var h = a; h >= 0; h--) {
            var d = c ? s.value[h] : t,
                v = p(Math.random() * d);
            f.unshift(v), v < d && (c = !1)
        }
        return f = l(f), r.add(typeof f == "number" ? new u(f) : new o(f, !1))
    }

    function V(e) {
        var t = e.value;
        return typeof t == "number" && (t = [t]), t.length === 1 && t[0] <= 36 ? "0123456789abcdefghijklmnopqrstuvwxyz".charAt(t[0]) : "<" + t + ">"
    }

    function $(e, t) {
        t = bigInt(t);
        if (t.isZero()) {
            if (e.isZero()) return "0";
            throw new Error("Cannot convert nonzero numbers to base 0.")
        }
        if (t.equals(-1)) return e.isZero() ? "0" : e.isNegative() ? (new Array(1 - e)).join("10") : "1" + (new Array(+e)).join("01");
        var n = "";
        e.isNegative() && t.isPositive() && (n = "-", e = e.abs());
        if (t.equals(1)) return e.isZero() ? "0" : n + (new Array(+e + 1)).join(1);
        var r = [],
            i = e,
            s;
        while (i.isNegative() || i.compareAbs(t) >= 0) {
            s = i.divmod(t), i = s.quotient;
            var o = s.remainder;
            o.isNegative() && (o = t.minus(o).abs(), i = i.next()), r.push(V(o))
        }
        return r.push(V(i)), n + r.reverse().join("")
    }

    function J(e) {
        if (a(+e)) {
            var t = +e;
            if (t === p(t)) return new u(t);
            throw "Invalid integer: " + e
        }
        var r = e[0] === "-";
        r && (e = e.slice(1));
        var i = e.split(/e/i);
        if (i.length > 2) throw new Error("Invalid integer: " + f.join("e"));
        if (i.length === 2) {
            var s = i[1];
            s[0] === "+" && (s = s.slice(1)), s = +s;
            if (s !== p(s) || !a(s)) throw new Error("Invalid integer: " + s + " is not a valid exponent.");
            var f = i[0],
                l = f.indexOf(".");
            l >= 0 && (s -= f.length - l, f = f.slice(0, l) + f.slice(l + 1));
            if (s < 0) throw new Error("Cannot include negative exponent part for integers");
            f += (new Array(s + 1)).join("0"), e = f
        }
        var h = /^([0-9][0-9]*)$/.test(e);
        if (!h) throw new Error("Invalid integer: " + e);
        var d = [],
            v = e.length,
            m = n,
            g = v - m;
        while (v > 0) d.push(+e.slice(g, v)), g -= m, g < 0 && (g = 0), v -= m;
        return c(d), new o(d, r)
    }

    function K(e) {
        return a(e) ? new u(e) : J(e.toString())
    }

    function Q(e) {
        return typeof e == "number" ? K(e) : typeof e == "string" ? J(e) : e
    }
    var t = 1e7,
        n = 7,
        r = 9007199254740992,
        i = f(r),
        s = Math.log(r);
    o.prototype.add = function(e) {
        var t, n = Q(e);
        if (this.sign !== n.sign) return this.subtract(n.negate());
        var r = this.value,
            i = n.value;
        return n.isSmall ? new o(m(r, Math.abs(i)), this.sign) : new o(v(r, i), this.sign)
    }, o.prototype.plus = o.prototype.add, u.prototype.add = function(e) {
        var t = Q(e),
            n = this.value;
        if (n < 0 !== t.sign) return this.subtract(t.negate());
        var r = t.value;
        if (t.isSmall) {
            if (a(n + r)) return new u(n + r);
            r = f(Math.abs(r))
        }
        return new o(m(r, Math.abs(n)), n < 0)
    }, u.prototype.plus = u.prototype.add, o.prototype.subtract = function(e) {
        var t = Q(e);
        if (this.sign !== t.sign) return this.add(t.negate());
        var n = this.value,
            r = t.value;
        return t.isSmall ? b(n, Math.abs(r), this.sign) : y(n, r, this.sign)
    }, o.prototype.minus = o.prototype.subtract, u.prototype.subtract = function(e) {
        var t = Q(e),
            n = this.value;
        if (n < 0 !== t.sign) return this.add(t.negate());
        var r = t.value;
        return t.isSmall ? new u(n - r) : b(r, Math.abs(n), n >= 0)
    }, u.prototype.minus = u.prototype.subtract, o.prototype.negate = function() {
        return new o(this.value, !this.sign)
    }, u.prototype.negate = function() {
        var e = this.sign,
            t = new u(-this.value);
        return t.sign = !e, t
    }, o.prototype.abs = function() {
        return new o(this.value, !1)
    }, u.prototype.abs = function() {
        return new u(Math.abs(this.value))
    }, o.prototype.multiply = function(e) {
        var n, r = Q(e),
            i = this.value,
            s = r.value,
            u = this.sign !== r.sign,
            a;
        if (r.isSmall) {
            if (s === 0) return G[0];
            if (s === 1) return this;
            if (s === -1) return this.negate();
            a = Math.abs(s);
            if (a < t) return new o(E(i, a), u);
            s = f(a)
        }
        return i.length + s.length > 4e3 ? new o(x(i, s), u) : new o(w(i, s), u)
    }, o.prototype.times = o.prototype.multiply, u.prototype._multiplyBySmall = function(e) {
        return a(e.value * this.value) ? new u(e.value * this.value) : T(Math.abs(e.value), f(Math.abs(this.value)), this.sign !== e.sign)
    }, o.prototype._multiplyBySmall = function(e) {
        return e.value === 0 ? G[0] : e.value === 1 ? this : e.value === -1 ? this.negate() : T(Math.abs(e.value), this.value, this.sign !== e.sign)
    }, u.prototype.multiply = function(e) {
        return Q(e)._multiplyBySmall(this)
    }, u.prototype.times = u.prototype.multiply, o.prototype.square = function() {
        return new o(N(this.value), !1)
    }, u.prototype.square = function() {
        var e = this.value * this.value;
        return a(e) ? new u(e) : new o(N(f(Math.abs(this.value))), !1)
    }, o.prototype.divmod = function(e) {
        var t = A(this, e);
        return {
            quotient: t[0],
            remainder: t[1]
        }
    }, u.prototype.divmod = o.prototype.divmod, o.prototype.divide = function(e) {
        return A(this, e)[0]
    }, u.prototype.over = u.prototype.divide = o.prototype.over = o.prototype.divide, o.prototype.mod = function(e) {
        return A(this, e)[1]
    }, u.prototype.remainder = u.prototype.mod = o.prototype.remainder = o.prototype.mod, o.prototype.pow = function(e) {
        var t = Q(e),
            n = this.value,
            r = t.value,
            i, s, o;
        if (r === 0) return G[1];
        if (n === 0) return G[0];
        if (n === 1) return G[1];
        if (n === -1) return t.isEven() ? G[1] : G[-1];
        if (t.sign) return G[0];
        if (!t.isSmall) throw new Error("The exponent " + t.toString() + " is too large.");
        if (this.isSmall && a(i = Math.pow(n, r))) return new u(p(i));
        s = this, o = G[1];
        for (;;) {
            r & !0 && (o = o.times(s), --r);
            if (r === 0) break;
            r /= 2, s = s.square()
        }
        return o
    }, u.prototype.pow = o.prototype.pow, o.prototype.modPow = function(e, t) {
        e = Q(e), t = Q(t);
        if (t.isZero()) throw new Error("Cannot take modPow with modulus 0");
        var n = G[1],
            r = this.mod(t);
        if (r.isZero()) return G[0];
        while (e.isPositive()) e.isOdd() && (n = n.multiply(r).mod(t)), e = e.divide(2), r = r.square().mod(t);
        return n
    }, u.prototype.modPow = o.prototype.modPow, o.prototype.compareAbs = function(e) {
        var t = Q(e),
            n = this.value,
            r = t.value;
        return t.isSmall ? 1 : O(n, r)
    }, u.prototype.compareAbs = function(e) {
        var t = Q(e),
            n = Math.abs(this.value),
            r = t.value;
        return t.isSmall ? (r = Math.abs(r), n === r ? 0 : n > r ? 1 : -1) : -1
    }, o.prototype.compare = function(e) {
        if (e === Infinity) return -1;
        if (e === -Infinity) return 1;
        var t = Q(e),
            n = this.value,
            r = t.value;
        return this.sign !== t.sign ? t.sign ? 1 : -1 : t.isSmall ? this.sign ? -1 : 1 : O(n, r) * (this.sign ? -1 : 1)
    }, o.prototype.compareTo = o.prototype.compare, u.prototype.compare = function(e) {
        if (e === Infinity) return -1;
        if (e === -Infinity) return 1;
        var t = Q(e),
            n = this.value,
            r = t.value;
        return t.isSmall ? n == r ? 0 : n > r ? 1 : -1 : n < 0 !== t.sign ? n < 0 ? -1 : 1 : n < 0 ? 1 : -1
    }, u.prototype.compareTo = u.prototype.compare, o.prototype.equals = function(e) {
        return this.compare(e) === 0
    }, u.prototype.eq = u.prototype.equals = o.prototype.eq = o.prototype.equals, o.prototype.notEquals = function(e) {
        return this.compare(e) !== 0
    }, u.prototype.neq = u.prototype.notEquals = o.prototype.neq = o.prototype.notEquals, o.prototype.greater = function(e) {
        return this.compare(e) > 0
    }, u.prototype.gt = u.prototype.greater = o.prototype.gt = o.prototype.greater, o.prototype.lesser = function(e) {
        return this.compare(e) < 0
    }, u.prototype.lt = u.prototype.lesser = o.prototype.lt = o.prototype.lesser, o.prototype.greaterOrEquals = function(e) {
        return this.compare(e) >= 0
    }, u.prototype.geq = u.prototype.greaterOrEquals = o.prototype.geq = o.prototype.greaterOrEquals, o.prototype.lesserOrEquals = function(e) {
        return this.compare(e) <= 0
    }, u.prototype.leq = u.prototype.lesserOrEquals = o.prototype.leq = o.prototype.lesserOrEquals, o.prototype.isEven = function() {
        return (this.value[0] & 1) === 0
    }, u.prototype.isEven = function() {
        return (this.value & 1) === 0
    }, o.prototype.isOdd = function() {
        return (this.value[0] & 1) === 1
    }, u.prototype.isOdd = function() {
        return (this.value & 1) === 1
    }, o.prototype.isPositive = function() {
        return !this.sign
    }, u.prototype.isPositive = function() {
        return this.value > 0
    }, o.prototype.isNegative = function() {
        return this.sign
    }, u.prototype.isNegative = function() {
        return this.value < 0
    }, o.prototype.isUnit = function() {
        return !1
    }, u.prototype.isUnit = function() {
        return Math.abs(this.value) === 1
    }, o.prototype.isZero = function() {
        return !1
    }, u.prototype.isZero = function() {
        return this.value === 0
    }, o.prototype.isDivisibleBy = function(e) {
        var t = Q(e),
            n = t.value;
        return n === 0 ? !1 : n === 1 ? !0 : n === 2 ? this.isEven() : this.mod(t).equals(G[0])
    }, u.prototype.isDivisibleBy = o.prototype.isDivisibleBy, o.prototype.isPrime = function() {
        var t = M(this);
        if (t !== e) return t;
        var n = this.abs(),
            r = n.prev(),
            i = [2, 3, 5, 7, 11, 13, 17, 19],
            s = r,
            o, u, a, f;
        while (s.isEven()) s = s.divide(2);
        for (a = 0; a < i.length; a++) {
            f = bigInt(i[a]).modPow(s, n);
            if (f.equals(G[1]) || f.equals(r)) continue;
            for (u = !0, o = s; u && o.lesser(r); o = o.multiply(2)) f = f.square().mod(n), f.equals(r) && (u = !1);
            if (u) return !1
        }
        return !0
    }, u.prototype.isPrime = o.prototype.isPrime, o.prototype.isProbablePrime = function(t) {
        var n = M(this);
        if (n !== e) return n;
        var r = this.abs(),
            i = t === e ? 5 : t;
        for (var s = 0; s < i; s++) {
            var o = bigInt.randBetween(2, r.minus(2));
            if (!o.modPow(r.prev(), r).isUnit()) return !1
        }
        return !0
    }, u.prototype.isProbablePrime = o.prototype.isProbablePrime, o.prototype.next = function() {
        var e = this.value;
        return this.sign ? b(e, 1, this.sign) : new o(m(e, 1), this.sign)
    }, u.prototype.next = function() {
        var e = this.value;
        return e + 1 < r ? new u(e + 1) : new o(i, !1)
    }, o.prototype.prev = function() {
        var e = this.value;
        return this.sign ? new o(m(e, 1), !0) : b(e, 1, this.sign)
    }, u.prototype.prev = function() {
        var e = this.value;
        return e - 1 > -r ? new u(e - 1) : new o(i, !0)
    };
    var _ = [1];
    while (_[_.length - 1] <= t) _.push(2 * _[_.length - 1]);
    var D = _.length,
        P = _[D - 1];
    o.prototype.shiftLeft = function(e) {
        if (!H(e)) return e.isNegative() ? this.shiftRight(e.abs()) : this.times(G[2].pow(e));
        e = +e;
        if (e < 0) return this.shiftRight(-e);
        var t = this;
        while (e >= D) t = t.multiply(P), e -= D - 1;
        return t.multiply(_[e])
    }, u.prototype.shiftLeft = o.prototype.shiftLeft, o.prototype.shiftRight = function(e) {
        var t;
        if (!H(e)) return e.isNegative() ? this.shiftLeft(e.abs()) : (t = this.divmod(G[2].pow(e)), t.remainder.isNegative() ? t.quotient.prev() : t.quotient);
        e = +e;
        if (e < 0) return this.shiftLeft(-e);
        var n = this;
        while (e >= D) {
            if (n.isZero()) return n;
            t = A(n, P), n = t[1].isNegative() ? t[0].prev() : t[0], e -= D - 1
        }
        return t = A(n, _[e]), t[1].isNegative() ? t[0].prev() : t[0]
    }, u.prototype.shiftRight = o.prototype.shiftRight, o.prototype.not = function() {
        return this.negate().prev()
    }, u.prototype.not = o.prototype.not, o.prototype.and = function(e) {
        return B(this, e, function(e, t) {
            return e & t
        })
    }, u.prototype.and = o.prototype.and, o.prototype.or = function(e) {
        return B(this, e, function(e, t) {
            return e | t
        })
    }, u.prototype.or = o.prototype.or, o.prototype.xor = function(e) {
        return B(this, e, function(e, t) {
            return e ^ t
        })
    }, u.prototype.xor = o.prototype.xor;
    var j = 1 << 30,
        F = (t & -t) * (t & -t) | j,
        X = function(e, t) {
            var n = G[0],
                r = G[1],
                i = e.length;
            if (2 <= t && t <= 36 && i <= s / Math.log(t)) return new u(parseInt(e, t));
            t = Q(t);
            var o = [],
                a, f = e[0] === "-";
            for (a = f ? 1 : 0; a < e.length; a++) {
                var l = e[a].toLowerCase(),
                    c = l.charCodeAt(0);
                if (48 <= c && c <= 57) o.push(Q(l));
                else if (97 <= c && c <= 122) o.push(Q(l.charCodeAt(0) - 87));
                else {
                    if (l !== "<") throw new Error(l + " is not a valid character");
                    var h = a;
                    do a++; while (e[a] !== ">");
                    o.push(Q(e.slice(h + 1, a)))
                }
            }
            o.reverse();
            for (a = 0; a < o.length; a++) n = n.add(o[a].times(r)), r = r.times(t);
            return f ? n.negate() : n
        };
    o.prototype.toString = function(t) {
        t === e && (t = 10);
        if (t !== 10) return $(this, t);
        var n = this.value,
            r = n.length,
            i = String(n[--r]),
            s = "0000000",
            o;
        while (--r >= 0) o = String(n[r]), i += s.slice(o.length) + o;
        var u = this.sign ? "-" : "";
        return u + i
    }, u.prototype.toString = function(t) {
        return t === e && (t = 10), t != 10 ? $(this, t) : String(this.value)
    }, o.prototype.valueOf = function() {
        return +this.toString()
    }, o.prototype.toJSNumber = o.prototype.valueOf, u.prototype.valueOf = function() {
        return this.value
    }, u.prototype.toJSNumber = u.prototype.valueOf;
    var G = function(e, t) {
        return typeof e == "undefined" ? G[0] : typeof t != "undefined" ? +t === 10 ? Q(e) : X(e, t) : Q(e)
    };
    for (var Y = 0; Y < 1e3; Y++) G[Y] = new u(Y), Y > 0 && (G[-Y] = new u(-Y));
    return G.one = G[1], G.zero = G[0], G.minusOne = G[-1], G.max = q, G.min = R, G.gcd = U, G.lcm = z, G.isInstance = function(e) {
        return e instanceof o || e instanceof u
    }, G.randBetween = W, G
}();
typeof module != "undefined" && module.hasOwnProperty("exports") && (module.exports = bigInt);

## build.sh
#

pandoc --template index.htm README.md -o index.html

## index.htm
<!DOCTYPE html><meta charset="utf8">
<link rel=stylesheet href=style.css>
<div id=container>
$body$
</div>

<script src="bigint.js"></script>
<script src="app.js"></script>

## index.html
<!DOCTYPE html><meta charset="utf8">
<link rel=stylesheet href=style.css>
<div id=container>
<p><img style="float: right; display:block"> # What’s our secret ?</p>
<p>One can safely share a secret using DH key exchange :</p>
<pre><code> pubkey(self) = g ^ privkey mod prime

 secret = pubkey(otherparty) ^ privkey mod prime</code></pre>
<p>Cryptography can be understood with the annalogy padlock and keys. How can we exchange a secret at plain sight ?</p>
<!--If you give me your public key (the padlock use to secure our secret),
we will be 2 in the whole world to know the secret image of the \*bot below.
-->
<p>Indeed your public key “act” as a padlock to secure a message, I have a key of this pad lock.</p>
<p>And my public key is the padlock that can be open with your private key to reveal the exact same secret !</p>
<p><br clear=all>Your key (private key): <input name="private"> <br>Padlock (public key): <input name=public disabled></p>
<p>Our shared DH secret is: <input name=secret disabled></p>
<p>This secret is only know to you and me … and can be used as a “master key” for locks we both have access too.</p>
<p>As a quick verification that we have the same key, we see the same robot image at the top right of this page.</p>
<p>This file can be viewed on <a href="https://gist.io/@DrI-T/43f6be1ca8c83c0a25687dac2564a7f1">gist.io</a>, and executed on <a href="https://bl.ocks.org/DrI-T/43f6be1ca8c83c0a25687dac2564a7f1">bl.ocks.org</a>.</p>
</div>

<script src="bigint.js"></script>
<script src="app.js"></script>

## style.css
input {
 width: calc(60% - 16px);
}
input[disabled] {
 border: 0px;
 background-color: transparent;
}

	var g = bigInt(3);
	var prime = bigInt('k672zw0jialf0skyp85r078stdrmlucv5fnkl85vjz6d4v3pqqb'.slice(1),36);
	console.log(g,prime);

	// my secret keys ...
	let privkey = 'k6n4zqqme17qgl1u6gb7f2kzvmg2ii0y36';
	let sk2 = bigInt(privkey.slice(1),36);
	var pk2 = g.modPow(sk2,prime);
	console.log('sk2: k'+sk2.toString(36))
	console.log('pk2: k'+pk2.toString(36));
	update({});


	function update(ev) {
	skelem = document.getElementsByName('private')[0];
	skelem.addEventListener('change',update,false);
	if (skelem.value == '') {
	skelem.value = privkey
	} else {
	privkey = skelem.value \|\| privkey;
	}
	// your private key ...
	let sk1 = bigInt(privkey.slice(1),36);
	var pk1 = g.modPow(sk1,prime);
	pkelem = document.getElementsByName('public')[0];
	pkelem.value = 'k'+pk1.toString(36)


	// our shared secret from me to you
	var sec1 = pk2.modPow(sk1,prime);
	secelem = document.getElementsByName('secret')[0];
	secelem.value = 'k'+sec1.toString(36)
	// our shared secret from you to me
	var sec2 = pk1.modPow(sk2,prime);

	// encrypted bot keys ...
	let bot2 = sec2.modPow(pk2,prime);
	console.log('bot1:',sec1.modPow(pk2,prime).toString(16));
	console.log('bot2:',bot2.toString(16));
	let img = document.getElementsByTagName('img')[0];
	img.src = `https://robohash.org/${bot2.toString(36)}`
	img.title = bot2.toString(36)

	return sec1;

	}


	function hex2byte(hex) {
	let bytes = [];
	for(var i=0; i< hex.length-1; i+=2){
	bytes.push(parseInt(hex.substr(i, 2), 16));
	}
	let str = String.fromCharCode.apply(String, bytes);
	//console.log('hex:',byte2hex(str));
	return str;

	}
	function byte2hex(str) {
	let hex = ''
	for (let i=0; i < str.length; ++i) {
	let chr = str.charCodeAt(i).toString(16)
	hex += chr.length < 2 ? '0' + chr : chr
	}
	//console.log('str:',hex2byte(hex));
	return hex
	}





	function keyGen(base, exponent, modulus) {
	return base.modPow(exponent,modulus);
	}

	var bigInt = function(e) {
	"use strict";

	function o(e, t) {
	this.value = e, this.sign = t, this.isSmall = !1
	}

	function u(e) {
	this.value = e, this.sign = e < 0, this.isSmall = !0
	}

	function a(e) {
	return -r < e && e < r
	}

	function f(e) {
	return e < 1e7 ? [e] : e < 1e14 ? [e % 1e7, Math.floor(e / 1e7)] : [e % 1e7, Math.floor(e / 1e7) % 1e7, Math.floor(e / 1e14)]
	}

	function l(e) {
	c(e);
	var n = e.length;
	if (n < 4 && O(e, i) < 0) switch (n) {
	case 0:
	return 0;
	case 1:
	return e[0];
	case 2:
	return e[0] + e[1] * t;
	default:
	return e[0] + (e[1] + e[2] * t) * t
	}
	return e
	}

	function c(e) {
	var t = e.length;
	while (e[--t] === 0);
	e.length = t + 1
	}

	function h(e) {
	var t = new Array(e),
	n = -1;
	while (++n < e) t[n] = 0;
	return t
	}

	function p(e) {
	return e > 0 ? Math.floor(e) : Math.ceil(e)
	}

	function d(e, n) {
	var r = e.length,
	i = n.length,
	s = new Array(r),
	o = 0,
	u = t,
	a, f;
	for (f = 0; f < i; f++) a = e[f] + n[f] + o, o = a >= u ? 1 : 0, s[f] = a - o * u;
	while (f < r) a = e[f] + o, o = a === u ? 1 : 0, s[f++] = a - o * u;
	return o > 0 && s.push(o), s
	}

	function v(e, t) {
	return e.length >= t.length ? d(e, t) : d(t, e)
	}

	function m(e, n) {
	var r = e.length,
	i = new Array(r),
	s = t,
	o, u;
	for (u = 0; u < r; u++) o = e[u] - s + n, n = Math.floor(o / s), i[u] = o - n * s, n += 1;
	while (n > 0) i[u++] = n % s, n = Math.floor(n / s);
	return i
	}

	function g(e, n) {
	var r = e.length,
	i = n.length,
	s = new Array(r),
	o = 0,
	u = t,
	a, f;
	for (a = 0; a < i; a++) f = e[a] - o - n[a], f < 0 ? (f += u, o = 1) : o = 0, s[a] = f;
	for (a = i; a < r; a++) {
	f = e[a] - o;
	if (!(f < 0)) {
	s[a++] = f;
	break
	}
	f += u, s[a] = f
	}
	for (; a < r; a++) s[a] = e[a];
	return c(s), s
	}

	function y(e, t, n) {
	var r, i;
	return O(e, t) >= 0 ? r = g(e, t) : (r = g(t, e), n = !n), r = l(r), typeof r == "number" ? (n && (r = -r), new u(r)) : new o(r, n)
	}

	function b(e, n, r) {
	var i = e.length,
	s = new Array(i),
	a = -n,
	f = t,
	c, h;
	for (c = 0; c < i; c++) h = e[c] + a, a = Math.floor(h / f), h %= f, s[c] = h < 0 ? h + f : h;
	return s = l(s), typeof s == "number" ? (r && (s = -s), new u(s)) : new o(s, r)
	}

	function w(e, n) {
	var r = e.length,
	i = n.length,
	s = r + i,
	o = h(s),
	u = t,
	a, f, l, p, d;
	for (l = 0; l < r; ++l) {
	p = e[l];
	for (var v = 0; v < i; ++v) d = n[v], a = p * d + o[l + v], f = Math.floor(a / u), o[l + v] = a - f * u, o[l + v + 1] += f
	}
	return c(o), o
	}

	function E(e, n) {
	var r = e.length,
	i = new Array(r),
	s = t,
	o = 0,
	u, a;
	for (a = 0; a < r; a++) u = e[a] * n + o, o = Math.floor(u / s), i[a] = u - o * s;
	while (o > 0) i[a++] = o % s, o = Math.floor(o / s);
	return i
	}

	function S(e, t) {
	var n = [];
	while (t-- > 0) n.push(0);
	return n.concat(e)
	}

	function x(e, t) {
	var n = Math.max(e.length, t.length);
	if (n <= 400) return w(e, t);
	n = Math.ceil(n / 2);
	var r = e.slice(n),
	i = e.slice(0, n),
	s = t.slice(n),
	o = t.slice(0, n),
	u = x(i, o),
	a = x(r, s),
	f = x(v(i, r), v(o, s));
	return v(v(u, S(g(g(f, u), a), n)), S(a, 2 * n))
	}

	function T(e, n, r) {
	return e < t ? new o(E(n, e), r) : new o(w(n, f(e)), r)
	}

	function N(e) {
	var n = e.length,
	r = h(n + n),
	i = t,
	s, o, u, a, f;
	for (u = 0; u < n; u++) {
	a = e[u];
	for (var l = 0; l < n; l++) f = e[l], s = a * f + r[u + l], o = Math.floor(s / i), r[u + l] = s - o * i, r[u + l + 1] += o
	}
	return c(r), r
	}

	function C(e, n) {
	var r = e.length,
	i = n.length,
	s = t,
	o = h(n.length),
	u = n[i - 1],
	a = Math.ceil(s / (2 * u)),
	f = E(e, a),
	c = E(n, a),
	p, d, v, m, g, y, b;
	f.length <= r && f.push(0), c.push(0), u = c[i - 1];
	for (d = r - i; d >= 0; d--) {
	p = s - 1, f[d + i] !== u && (p = Math.floor((f[d + i] * s + f[d + i - 1]) / u)), v = 0, m = 0, y = c.length;
	for (g = 0; g < y; g++) v += p * c[g], b = Math.floor(v / s), m += f[d + g] - (v - b * s), v = b, m < 0 ? (f[d + g] = m + s, m = -1) : (f[d + g] = m, m = 0);
	while (m !== 0) {
	p -= 1, v = 0;
	for (g = 0; g < y; g++) v += f[d + g] - s + c[g], v < 0 ? (f[d + g] = v + s, v = 0) : (f[d + g] = v, v = 1);
	m += v
	}
	o[d] = p
	}
	return f = L(f, a)[0], [l(o), l(f)]
	}

	function k(e, n) {
	var r = e.length,
	i = n.length,
	s = [],
	o = [],
	u = t,
	a, f, c, h, p;
	while (r) {
	o.unshift(e[--r]);
	if (O(o, n) < 0) {
	s.push(0);
	continue
	}
	f = o.length, c = o[f - 1] * u + o[f - 2], h = n[i - 1] * u + n[i - 2], f > i && (c = (c + 1) * u), a = Math.ceil(c / h);
	do {
	p = E(n, a);
	if (O(p, o) <= 0) break;
	a--
	} while (a);
	s.push(a), o = g(o, p)
	}
	return s.reverse(), [l(s), l(o)]
	}

	function L(e, n) {
	var r = e.length,
	i = h(r),
	s = t,
	o, u, a, f;
	a = 0;
	for (o = r - 1; o >= 0; --o) f = a * s + e[o], u = p(f / n), a = f - u * n, i[o] = u \| 0;
	return [i, a \| 0]
	}

	function A(e, n) {
	var r, i = Q(n),
	s = e.value,
	a = i.value,
	c;
	if (a === 0) throw new Error("Cannot divide by zero");
	if (e.isSmall) return i.isSmall ? [new u(p(s / a)), new u(s % a)] : [G[0], e];
	if (i.isSmall) {
	if (a === 1) return [e, G[0]];
	if (a == -1) return [e.negate(), G[0]];
	var h = Math.abs(a);
	if (h < t) {
	r = L(s, h), c = l(r[0]);
	var d = r[1];
	return e.sign && (d = -d), typeof c == "number" ? (e.sign !== i.sign && (c = -c), [new u(c), new u(d)]) : [new o(c, e.sign !== i.sign), new u(d)]
	}
	a = f(h)
	}
	var v = O(s, a);
	if (v === -1) return [G[0], e];
	if (v === 0) return [G[e.sign === i.sign ? 1 : -1], G[0]];
	s.length + a.length <= 200 ? r = C(s, a) : r = k(s, a), c = r[0];
	var m = e.sign !== i.sign,
	g = r[1],
	y = e.sign;
	return typeof c == "number" ? (m && (c = -c), c = new u(c)) : c = new o(c, m), typeof g == "number" ? (y && (g = -g), g = new u(g)) : g = new o(g, y), [c, g]
	}

	function O(e, t) {
	if (e.length !== t.length) return e.length > t.length ? 1 : -1;
	for (var n = e.length - 1; n >= 0; n--)
	if (e[n] !== t[n]) return e[n] > t[n] ? 1 : -1;
	return 0
	}

	function M(e) {
	var t = e.abs();
	if (t.isUnit()) return !1;
	if (t.equals(2) \|\| t.equals(3) \|\| t.equals(5)) return !0;
	if (t.isEven() \|\| t.isDivisibleBy(3) \|\| t.isDivisibleBy(5)) return !1;
	if (t.lesser(25)) return !0
	}

	function H(e) {
	return (typeof e == "number" \|\| typeof e == "string") && +Math.abs(e) <= t \|\| e instanceof o && e.value.length <= 1
	}

	function B(e, t, n) {
	t = Q(t);
	var r = e.isNegative(),
	i = t.isNegative(),
	s = r ? e.not() : e,
	o = i ? t.not() : t,
	u = [],
	a = [],
	f = !1,
	l = !1;
	while (!f \|\| !l) s.isZero() ? (f = !0, u.push(r ? 1 : 0)) : r ? u.push(s.isEven() ? 1 : 0) : u.push(s.isEven() ? 0 : 1), o.isZero() ? (l = !0, a.push(i ? 1 : 0)) : i ? a.push(o.isEven() ? 1 : 0) : a.push(o.isEven() ? 0 : 1), s = s.over(2), o = o.over(2);
	var c = [];
	for (var h = 0; h < u.length; h++) c.push(n(u[h], a[h]));
	var p = bigInt(c.pop()).negate().times(bigInt(2).pow(c.length));
	while (c.length) p = p.add(bigInt(c.pop()).times(bigInt(2).pow(c.length)));
	return p
	}

	function I(e) {
	var n = e.value,
	r = typeof n == "number" ? n \| j : n[0] + n[1] * t \| F;
	return r & -r
	}

	function q(e, t) {
	return e = Q(e), t = Q(t), e.greater(t) ? e : t
	}

	function R(e, t) {
	return e = Q(e), t = Q(t), e.lesser(t) ? e : t
	}

	function U(e, t) {
	e = Q(e).abs(), t = Q(t).abs();
	if (e.equals(t)) return e;
	if (e.isZero()) return t;
	if (t.isZero()) return e;
	var n = G[1],
	r, i;
	while (e.isEven() && t.isEven()) r = Math.min(I(e), I(t)), e = e.divide(r), t = t.divide(r), n = n.multiply(r);
	while (e.isEven()) e = e.divide(I(e));
	do {
	while (t.isEven()) t = t.divide(I(t));
	e.greater(t) && (i = t, t = e, e = i), t = t.subtract(e)
	} while (!t.isZero());
	return n.isUnit() ? e : e.multiply(n)
	}

	function z(e, t) {
	return e = Q(e).abs(), t = Q(t).abs(), e.divide(U(e, t)).multiply(t)
	}

	function W(e, n) {
	e = Q(e), n = Q(n);
	var r = R(e, n),
	i = q(e, n),
	s = i.subtract(r);
	if (s.isSmall) return r.add(Math.round(Math.random() * s));
	var a = s.value.length - 1,
	f = [],
	c = !0;
	for (var h = a; h >= 0; h--) {
	var d = c ? s.value[h] : t,
	v = p(Math.random() * d);
	f.unshift(v), v < d && (c = !1)
	}
	return f = l(f), r.add(typeof f == "number" ? new u(f) : new o(f, !1))
	}

	function V(e) {
	var t = e.value;
	return typeof t == "number" && (t = [t]), t.length === 1 && t[0] <= 36 ? "0123456789abcdefghijklmnopqrstuvwxyz".charAt(t[0]) : "<" + t + ">"
	}

	function $(e, t) {
	t = bigInt(t);
	if (t.isZero()) {
	if (e.isZero()) return "0";
	throw new Error("Cannot convert nonzero numbers to base 0.")
	}
	if (t.equals(-1)) return e.isZero() ? "0" : e.isNegative() ? (new Array(1 - e)).join("10") : "1" + (new Array(+e)).join("01");
	var n = "";
	e.isNegative() && t.isPositive() && (n = "-", e = e.abs());
	if (t.equals(1)) return e.isZero() ? "0" : n + (new Array(+e + 1)).join(1);
	var r = [],
	i = e,
	s;
	while (i.isNegative() \|\| i.compareAbs(t) >= 0) {
	s = i.divmod(t), i = s.quotient;
	var o = s.remainder;
	o.isNegative() && (o = t.minus(o).abs(), i = i.next()), r.push(V(o))
	}
	return r.push(V(i)), n + r.reverse().join("")
	}

	function J(e) {
	if (a(+e)) {
	var t = +e;
	if (t === p(t)) return new u(t);
	throw "Invalid integer: " + e
	}
	var r = e[0] === "-";
	r && (e = e.slice(1));
	var i = e.split(/e/i);
	if (i.length > 2) throw new Error("Invalid integer: " + f.join("e"));
	if (i.length === 2) {
	var s = i[1];
	s[0] === "+" && (s = s.slice(1)), s = +s;
	if (s !== p(s) \|\| !a(s)) throw new Error("Invalid integer: " + s + " is not a valid exponent.");
	var f = i[0],
	l = f.indexOf(".");
	l >= 0 && (s -= f.length - l, f = f.slice(0, l) + f.slice(l + 1));
	if (s < 0) throw new Error("Cannot include negative exponent part for integers");
	f += (new Array(s + 1)).join("0"), e = f
	}
	var h = /^([0-9][0-9]*)$/.test(e);
	if (!h) throw new Error("Invalid integer: " + e);
	var d = [],
	v = e.length,
	m = n,
	g = v - m;
	while (v > 0) d.push(+e.slice(g, v)), g -= m, g < 0 && (g = 0), v -= m;
	return c(d), new o(d, r)
	}

	function K(e) {
	return a(e) ? new u(e) : J(e.toString())
	}

	function Q(e) {
	return typeof e == "number" ? K(e) : typeof e == "string" ? J(e) : e
	}
	var t = 1e7,
	n = 7,
	r = 9007199254740992,
	i = f(r),
	s = Math.log(r);
	o.prototype.add = function(e) {
	var t, n = Q(e);
	if (this.sign !== n.sign) return this.subtract(n.negate());
	var r = this.value,
	i = n.value;
	return n.isSmall ? new o(m(r, Math.abs(i)), this.sign) : new o(v(r, i), this.sign)
	}, o.prototype.plus = o.prototype.add, u.prototype.add = function(e) {
	var t = Q(e),
	n = this.value;
	if (n < 0 !== t.sign) return this.subtract(t.negate());
	var r = t.value;
	if (t.isSmall) {
	if (a(n + r)) return new u(n + r);
	r = f(Math.abs(r))
	}
	return new o(m(r, Math.abs(n)), n < 0)
	}, u.prototype.plus = u.prototype.add, o.prototype.subtract = function(e) {
	var t = Q(e);
	if (this.sign !== t.sign) return this.add(t.negate());
	var n = this.value,
	r = t.value;
	return t.isSmall ? b(n, Math.abs(r), this.sign) : y(n, r, this.sign)
	}, o.prototype.minus = o.prototype.subtract, u.prototype.subtract = function(e) {
	var t = Q(e),
	n = this.value;
	if (n < 0 !== t.sign) return this.add(t.negate());
	var r = t.value;
	return t.isSmall ? new u(n - r) : b(r, Math.abs(n), n >= 0)
	}, u.prototype.minus = u.prototype.subtract, o.prototype.negate = function() {
	return new o(this.value, !this.sign)
	}, u.prototype.negate = function() {
	var e = this.sign,
	t = new u(-this.value);
	return t.sign = !e, t
	}, o.prototype.abs = function() {
	return new o(this.value, !1)
	}, u.prototype.abs = function() {
	return new u(Math.abs(this.value))
	}, o.prototype.multiply = function(e) {
	var n, r = Q(e),
	i = this.value,
	s = r.value,
	u = this.sign !== r.sign,
	a;
	if (r.isSmall) {
	if (s === 0) return G[0];
	if (s === 1) return this;
	if (s === -1) return this.negate();
	a = Math.abs(s);
	if (a < t) return new o(E(i, a), u);
	s = f(a)
	}
	return i.length + s.length > 4e3 ? new o(x(i, s), u) : new o(w(i, s), u)
	}, o.prototype.times = o.prototype.multiply, u.prototype._multiplyBySmall = function(e) {
	return a(e.value * this.value) ? new u(e.value * this.value) : T(Math.abs(e.value), f(Math.abs(this.value)), this.sign !== e.sign)
	}, o.prototype._multiplyBySmall = function(e) {
	return e.value === 0 ? G[0] : e.value === 1 ? this : e.value === -1 ? this.negate() : T(Math.abs(e.value), this.value, this.sign !== e.sign)
	}, u.prototype.multiply = function(e) {
	return Q(e)._multiplyBySmall(this)
	}, u.prototype.times = u.prototype.multiply, o.prototype.square = function() {
	return new o(N(this.value), !1)
	}, u.prototype.square = function() {
	var e = this.value * this.value;
	return a(e) ? new u(e) : new o(N(f(Math.abs(this.value))), !1)
	}, o.prototype.divmod = function(e) {
	var t = A(this, e);
	return {
	quotient: t[0],
	remainder: t[1]
	}
	}, u.prototype.divmod = o.prototype.divmod, o.prototype.divide = function(e) {
	return A(this, e)[0]
	}, u.prototype.over = u.prototype.divide = o.prototype.over = o.prototype.divide, o.prototype.mod = function(e) {
	return A(this, e)[1]
	}, u.prototype.remainder = u.prototype.mod = o.prototype.remainder = o.prototype.mod, o.prototype.pow = function(e) {
	var t = Q(e),
	n = this.value,
	r = t.value,
	i, s, o;
	if (r === 0) return G[1];
	if (n === 0) return G[0];
	if (n === 1) return G[1];
	if (n === -1) return t.isEven() ? G[1] : G[-1];
	if (t.sign) return G[0];
	if (!t.isSmall) throw new Error("The exponent " + t.toString() + " is too large.");
	if (this.isSmall && a(i = Math.pow(n, r))) return new u(p(i));
	s = this, o = G[1];
	for (;;) {
	r & !0 && (o = o.times(s), --r);
	if (r === 0) break;
	r /= 2, s = s.square()
	}
	return o
	}, u.prototype.pow = o.prototype.pow, o.prototype.modPow = function(e, t) {
	e = Q(e), t = Q(t);
	if (t.isZero()) throw new Error("Cannot take modPow with modulus 0");
	var n = G[1],
	r = this.mod(t);
	if (r.isZero()) return G[0];
	while (e.isPositive()) e.isOdd() && (n = n.multiply(r).mod(t)), e = e.divide(2), r = r.square().mod(t);
	return n
	}, u.prototype.modPow = o.prototype.modPow, o.prototype.compareAbs = function(e) {
	var t = Q(e),
	n = this.value,
	r = t.value;
	return t.isSmall ? 1 : O(n, r)
	}, u.prototype.compareAbs = function(e) {
	var t = Q(e),
	n = Math.abs(this.value),
	r = t.value;
	return t.isSmall ? (r = Math.abs(r), n === r ? 0 : n > r ? 1 : -1) : -1
	}, o.prototype.compare = function(e) {
	if (e === Infinity) return -1;
	if (e === -Infinity) return 1;
	var t = Q(e),
	n = this.value,
	r = t.value;
	return this.sign !== t.sign ? t.sign ? 1 : -1 : t.isSmall ? this.sign ? -1 : 1 : O(n, r) * (this.sign ? -1 : 1)
	}, o.prototype.compareTo = o.prototype.compare, u.prototype.compare = function(e) {
	if (e === Infinity) return -1;
	if (e === -Infinity) return 1;
	var t = Q(e),
	n = this.value,
	r = t.value;
	return t.isSmall ? n == r ? 0 : n > r ? 1 : -1 : n < 0 !== t.sign ? n < 0 ? -1 : 1 : n < 0 ? 1 : -1
	}, u.prototype.compareTo = u.prototype.compare, o.prototype.equals = function(e) {
	return this.compare(e) === 0
	}, u.prototype.eq = u.prototype.equals = o.prototype.eq = o.prototype.equals, o.prototype.notEquals = function(e) {
	return this.compare(e) !== 0
	}, u.prototype.neq = u.prototype.notEquals = o.prototype.neq = o.prototype.notEquals, o.prototype.greater = function(e) {
	return this.compare(e) > 0
	}, u.prototype.gt = u.prototype.greater = o.prototype.gt = o.prototype.greater, o.prototype.lesser = function(e) {
	return this.compare(e) < 0
	}, u.prototype.lt = u.prototype.lesser = o.prototype.lt = o.prototype.lesser, o.prototype.greaterOrEquals = function(e) {
	return this.compare(e) >= 0
	}, u.prototype.geq = u.prototype.greaterOrEquals = o.prototype.geq = o.prototype.greaterOrEquals, o.prototype.lesserOrEquals = function(e) {
	return this.compare(e) <= 0
	}, u.prototype.leq = u.prototype.lesserOrEquals = o.prototype.leq = o.prototype.lesserOrEquals, o.prototype.isEven = function() {
	return (this.value[0] & 1) === 0
	}, u.prototype.isEven = function() {
	return (this.value & 1) === 0
	}, o.prototype.isOdd = function() {
	return (this.value[0] & 1) === 1
	}, u.prototype.isOdd = function() {
	return (this.value & 1) === 1
	}, o.prototype.isPositive = function() {
	return !this.sign
	}, u.prototype.isPositive = function() {
	return this.value > 0
	}, o.prototype.isNegative = function() {
	return this.sign
	}, u.prototype.isNegative = function() {
	return this.value < 0
	}, o.prototype.isUnit = function() {
	return !1
	}, u.prototype.isUnit = function() {
	return Math.abs(this.value) === 1
	}, o.prototype.isZero = function() {
	return !1
	}, u.prototype.isZero = function() {
	return this.value === 0
	}, o.prototype.isDivisibleBy = function(e) {
	var t = Q(e),
	n = t.value;
	return n === 0 ? !1 : n === 1 ? !0 : n === 2 ? this.isEven() : this.mod(t).equals(G[0])
	}, u.prototype.isDivisibleBy = o.prototype.isDivisibleBy, o.prototype.isPrime = function() {
	var t = M(this);
	if (t !== e) return t;
	var n = this.abs(),
	r = n.prev(),
	i = [2, 3, 5, 7, 11, 13, 17, 19],
	s = r,
	o, u, a, f;
	while (s.isEven()) s = s.divide(2);
	for (a = 0; a < i.length; a++) {
	f = bigInt(i[a]).modPow(s, n);
	if (f.equals(G[1]) \|\| f.equals(r)) continue;
	for (u = !0, o = s; u && o.lesser(r); o = o.multiply(2)) f = f.square().mod(n), f.equals(r) && (u = !1);
	if (u) return !1
	}
	return !0
	}, u.prototype.isPrime = o.prototype.isPrime, o.prototype.isProbablePrime = function(t) {
	var n = M(this);
	if (n !== e) return n;
	var r = this.abs(),
	i = t === e ? 5 : t;
	for (var s = 0; s < i; s++) {
	var o = bigInt.randBetween(2, r.minus(2));
	if (!o.modPow(r.prev(), r).isUnit()) return !1
	}
	return !0
	}, u.prototype.isProbablePrime = o.prototype.isProbablePrime, o.prototype.next = function() {
	var e = this.value;
	return this.sign ? b(e, 1, this.sign) : new o(m(e, 1), this.sign)
	}, u.prototype.next = function() {
	var e = this.value;
	return e + 1 < r ? new u(e + 1) : new o(i, !1)
	}, o.prototype.prev = function() {
	var e = this.value;
	return this.sign ? new o(m(e, 1), !0) : b(e, 1, this.sign)
	}, u.prototype.prev = function() {
	var e = this.value;
	return e - 1 > -r ? new u(e - 1) : new o(i, !0)
	};
	var _ = [1];
	while (_[_.length - 1] <= t) _.push(2 * _[_.length - 1]);
	var D = _.length,
	P = _[D - 1];
	o.prototype.shiftLeft = function(e) {
	if (!H(e)) return e.isNegative() ? this.shiftRight(e.abs()) : this.times(G[2].pow(e));
	e = +e;
	if (e < 0) return this.shiftRight(-e);
	var t = this;
	while (e >= D) t = t.multiply(P), e -= D - 1;
	return t.multiply(_[e])
	}, u.prototype.shiftLeft = o.prototype.shiftLeft, o.prototype.shiftRight = function(e) {
	var t;
	if (!H(e)) return e.isNegative() ? this.shiftLeft(e.abs()) : (t = this.divmod(G[2].pow(e)), t.remainder.isNegative() ? t.quotient.prev() : t.quotient);
	e = +e;
	if (e < 0) return this.shiftLeft(-e);
	var n = this;
	while (e >= D) {
	if (n.isZero()) return n;
	t = A(n, P), n = t[1].isNegative() ? t[0].prev() : t[0], e -= D - 1
	}
	return t = A(n, _[e]), t[1].isNegative() ? t[0].prev() : t[0]
	}, u.prototype.shiftRight = o.prototype.shiftRight, o.prototype.not = function() {
	return this.negate().prev()
	}, u.prototype.not = o.prototype.not, o.prototype.and = function(e) {
	return B(this, e, function(e, t) {
	return e & t
	})
	}, u.prototype.and = o.prototype.and, o.prototype.or = function(e) {
	return B(this, e, function(e, t) {
	return e \| t
	})
	}, u.prototype.or = o.prototype.or, o.prototype.xor = function(e) {
	return B(this, e, function(e, t) {
	return e ^ t
	})
	}, u.prototype.xor = o.prototype.xor;
	var j = 1 << 30,
	F = (t & -t) * (t & -t) \| j,
	X = function(e, t) {
	var n = G[0],
	r = G[1],
	i = e.length;
	if (2 <= t && t <= 36 && i <= s / Math.log(t)) return new u(parseInt(e, t));
	t = Q(t);
	var o = [],
	a, f = e[0] === "-";
	for (a = f ? 1 : 0; a < e.length; a++) {
	var l = e[a].toLowerCase(),
	c = l.charCodeAt(0);
	if (48 <= c && c <= 57) o.push(Q(l));
	else if (97 <= c && c <= 122) o.push(Q(l.charCodeAt(0) - 87));
	else {
	if (l !== "<") throw new Error(l + " is not a valid character");
	var h = a;
	do a++; while (e[a] !== ">");
	o.push(Q(e.slice(h + 1, a)))
	}
	}
	o.reverse();
	for (a = 0; a < o.length; a++) n = n.add(o[a].times(r)), r = r.times(t);
	return f ? n.negate() : n
	};
	o.prototype.toString = function(t) {
	t === e && (t = 10);
	if (t !== 10) return $(this, t);
	var n = this.value,
	r = n.length,
	i = String(n[--r]),
	s = "0000000",
	o;
	while (--r >= 0) o = String(n[r]), i += s.slice(o.length) + o;
	var u = this.sign ? "-" : "";
	return u + i
	}, u.prototype.toString = function(t) {
	return t === e && (t = 10), t != 10 ? $(this, t) : String(this.value)
	}, o.prototype.valueOf = function() {
	return +this.toString()
	}, o.prototype.toJSNumber = o.prototype.valueOf, u.prototype.valueOf = function() {
	return this.value
	}, u.prototype.toJSNumber = u.prototype.valueOf;
	var G = function(e, t) {
	return typeof e == "undefined" ? G[0] : typeof t != "undefined" ? +t === 10 ? Q(e) : X(e, t) : Q(e)
	};
	for (var Y = 0; Y < 1e3; Y++) G[Y] = new u(Y), Y > 0 && (G[-Y] = new u(-Y));
	return G.one = G[1], G.zero = G[0], G.minusOne = G[-1], G.max = q, G.min = R, G.gcd = U, G.lcm = z, G.isInstance = function(e) {
	return e instanceof o \|\| e instanceof u
	}, G.randBetween = W, G
	}();
	typeof module != "undefined" && module.hasOwnProperty("exports") && (module.exports = bigInt);
	<!DOCTYPE html><meta charset="utf8">
	<link rel=stylesheet href=style.css>
	<div id=container>
	$body$
	</div>

	<script src="bigint.js"></script>
	<script src="app.js"></script>
	input {
	width: calc(60% - 16px);
	}
	input[disabled] {
	border: 0px;
	background-color: transparent;
	}