1612 lines
42 KiB
JavaScript
1612 lines
42 KiB
JavaScript
// Copyright (c) 2005 Tom Wu
|
|
// All Rights Reserved.
|
|
// See "LICENSE" for details.
|
|
|
|
// Basic JavaScript BN library - subset useful for RSA encryption.
|
|
|
|
// Bits per digit
|
|
var dbits;
|
|
|
|
// JavaScript engine analysis
|
|
var canary = 0xdeadbeefcafe;
|
|
var j_lm = (canary & 0xffffff) == 0xefcafe;
|
|
|
|
// (public) Constructor
|
|
export function BigInteger(a, b, c) {
|
|
if (a != null)
|
|
if ("number" == typeof a) this.fromNumber(a, b, c);
|
|
else if (b == null && "string" != typeof a) this.fromString(a, 256);
|
|
else this.fromString(a, b);
|
|
}
|
|
|
|
// return new, unset BigInteger
|
|
function nbi() {
|
|
return new BigInteger(null);
|
|
}
|
|
|
|
// am: Compute w_j += (x*this_i), propagate carries,
|
|
// c is initial carry, returns final carry.
|
|
// c < 3*dvalue, x < 2*dvalue, this_i < dvalue
|
|
// We need to select the fastest one that works in this environment.
|
|
|
|
// am1: use a single mult and divide to get the high bits,
|
|
// max digit bits should be 26 because
|
|
// max internal value = 2*dvalue^2-2*dvalue (< 2^53)
|
|
function am1(i, x, w, j, c, n) {
|
|
while (--n >= 0) {
|
|
var v = x * this[i++] + w[j] + c;
|
|
c = Math.floor(v / 0x4000000);
|
|
w[j++] = v & 0x3ffffff;
|
|
}
|
|
return c;
|
|
}
|
|
// am2 avoids a big mult-and-extract completely.
|
|
// Max digit bits should be <= 30 because we do bitwise ops
|
|
// on values up to 2*hdvalue^2-hdvalue-1 (< 2^31)
|
|
function am2(i, x, w, j, c, n) {
|
|
var xl = x & 0x7fff,
|
|
xh = x >> 15;
|
|
while (--n >= 0) {
|
|
var l = this[i] & 0x7fff;
|
|
var h = this[i++] >> 15;
|
|
var m = xh * l + h * xl;
|
|
l = xl * l + ((m & 0x7fff) << 15) + w[j] + (c & 0x3fffffff);
|
|
c = (l >>> 30) + (m >>> 15) + xh * h + (c >>> 30);
|
|
w[j++] = l & 0x3fffffff;
|
|
}
|
|
return c;
|
|
}
|
|
// Alternately, set max digit bits to 28 since some
|
|
// browsers slow down when dealing with 32-bit numbers.
|
|
function am3(i, x, w, j, c, n) {
|
|
var xl = x & 0x3fff,
|
|
xh = x >> 14;
|
|
while (--n >= 0) {
|
|
var l = this[i] & 0x3fff;
|
|
var h = this[i++] >> 14;
|
|
var m = xh * l + h * xl;
|
|
l = xl * l + ((m & 0x3fff) << 14) + w[j] + c;
|
|
c = (l >> 28) + (m >> 14) + xh * h;
|
|
w[j++] = l & 0xfffffff;
|
|
}
|
|
return c;
|
|
}
|
|
var inBrowser = typeof navigator !== "undefined";
|
|
if (inBrowser && j_lm && navigator.appName == "Microsoft Internet Explorer") {
|
|
BigInteger.prototype.am = am2;
|
|
dbits = 30;
|
|
} else if (inBrowser && j_lm && navigator.appName != "Netscape") {
|
|
BigInteger.prototype.am = am1;
|
|
dbits = 26;
|
|
} else {
|
|
// Mozilla/Netscape seems to prefer am3
|
|
BigInteger.prototype.am = am3;
|
|
dbits = 28;
|
|
}
|
|
|
|
BigInteger.prototype.DB = dbits;
|
|
BigInteger.prototype.DM = (1 << dbits) - 1;
|
|
BigInteger.prototype.DV = 1 << dbits;
|
|
|
|
var BI_FP = 52;
|
|
BigInteger.prototype.FV = Math.pow(2, BI_FP);
|
|
BigInteger.prototype.F1 = BI_FP - dbits;
|
|
BigInteger.prototype.F2 = 2 * dbits - BI_FP;
|
|
|
|
// Digit conversions
|
|
var BI_RM = "0123456789abcdefghijklmnopqrstuvwxyz";
|
|
var BI_RC = new Array();
|
|
var rr, vv;
|
|
rr = "0".charCodeAt(0);
|
|
for (vv = 0; vv <= 9; ++vv) BI_RC[rr++] = vv;
|
|
rr = "a".charCodeAt(0);
|
|
for (vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;
|
|
rr = "A".charCodeAt(0);
|
|
for (vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;
|
|
|
|
function int2char(n) {
|
|
return BI_RM.charAt(n);
|
|
}
|
|
function intAt(s, i) {
|
|
var c = BI_RC[s.charCodeAt(i)];
|
|
return c == null ? -1 : c;
|
|
}
|
|
|
|
// (protected) copy this to r
|
|
function bnpCopyTo(r) {
|
|
for (var i = this.t - 1; i >= 0; --i) r[i] = this[i];
|
|
r.t = this.t;
|
|
r.s = this.s;
|
|
}
|
|
|
|
// (protected) set from integer value x, -DV <= x < DV
|
|
function bnpFromInt(x) {
|
|
this.t = 1;
|
|
this.s = x < 0 ? -1 : 0;
|
|
if (x > 0) this[0] = x;
|
|
else if (x < -1) this[0] = x + this.DV;
|
|
else this.t = 0;
|
|
}
|
|
|
|
// return bigint initialized to value
|
|
function nbv(i) {
|
|
var r = nbi();
|
|
r.fromInt(i);
|
|
return r;
|
|
}
|
|
|
|
// (protected) set from string and radix
|
|
function bnpFromString(s, b) {
|
|
var k;
|
|
if (b == 16) k = 4;
|
|
else if (b == 8) k = 3;
|
|
else if (b == 256) k = 8;
|
|
// byte array
|
|
else if (b == 2) k = 1;
|
|
else if (b == 32) k = 5;
|
|
else if (b == 4) k = 2;
|
|
else {
|
|
this.fromRadix(s, b);
|
|
return;
|
|
}
|
|
this.t = 0;
|
|
this.s = 0;
|
|
var i = s.length,
|
|
mi = false,
|
|
sh = 0;
|
|
while (--i >= 0) {
|
|
var x = k == 8 ? s[i] & 0xff : intAt(s, i);
|
|
if (x < 0) {
|
|
if (s.charAt(i) == "-") mi = true;
|
|
continue;
|
|
}
|
|
mi = false;
|
|
if (sh == 0) this[this.t++] = x;
|
|
else if (sh + k > this.DB) {
|
|
this[this.t - 1] |= (x & ((1 << (this.DB - sh)) - 1)) << sh;
|
|
this[this.t++] = x >> (this.DB - sh);
|
|
} else this[this.t - 1] |= x << sh;
|
|
sh += k;
|
|
if (sh >= this.DB) sh -= this.DB;
|
|
}
|
|
if (k == 8 && (s[0] & 0x80) != 0) {
|
|
this.s = -1;
|
|
if (sh > 0) this[this.t - 1] |= ((1 << (this.DB - sh)) - 1) << sh;
|
|
}
|
|
this.clamp();
|
|
if (mi) BigInteger.ZERO.subTo(this, this);
|
|
}
|
|
|
|
// (protected) clamp off excess high words
|
|
function bnpClamp() {
|
|
var c = this.s & this.DM;
|
|
while (this.t > 0 && this[this.t - 1] == c) --this.t;
|
|
}
|
|
|
|
// (public) return string representation in given radix
|
|
function bnToString(b) {
|
|
if (this.s < 0) return "-" + this.negate().toString(b);
|
|
var k;
|
|
if (b == 16) k = 4;
|
|
else if (b == 8) k = 3;
|
|
else if (b == 2) k = 1;
|
|
else if (b == 32) k = 5;
|
|
else if (b == 4) k = 2;
|
|
else return this.toRadix(b);
|
|
var km = (1 << k) - 1,
|
|
d,
|
|
m = false,
|
|
r = "",
|
|
i = this.t;
|
|
var p = this.DB - ((i * this.DB) % k);
|
|
if (i-- > 0) {
|
|
if (p < this.DB && (d = this[i] >> p) > 0) {
|
|
m = true;
|
|
r = int2char(d);
|
|
}
|
|
while (i >= 0) {
|
|
if (p < k) {
|
|
d = (this[i] & ((1 << p) - 1)) << (k - p);
|
|
d |= this[--i] >> (p += this.DB - k);
|
|
} else {
|
|
d = (this[i] >> (p -= k)) & km;
|
|
if (p <= 0) {
|
|
p += this.DB;
|
|
--i;
|
|
}
|
|
}
|
|
if (d > 0) m = true;
|
|
if (m) r += int2char(d);
|
|
}
|
|
}
|
|
return m ? r : "0";
|
|
}
|
|
|
|
// (public) -this
|
|
function bnNegate() {
|
|
var r = nbi();
|
|
BigInteger.ZERO.subTo(this, r);
|
|
return r;
|
|
}
|
|
|
|
// (public) |this|
|
|
function bnAbs() {
|
|
return this.s < 0 ? this.negate() : this;
|
|
}
|
|
|
|
// (public) return + if this > a, - if this < a, 0 if equal
|
|
function bnCompareTo(a) {
|
|
var r = this.s - a.s;
|
|
if (r != 0) return r;
|
|
var i = this.t;
|
|
r = i - a.t;
|
|
if (r != 0) return this.s < 0 ? -r : r;
|
|
while (--i >= 0) if ((r = this[i] - a[i]) != 0) return r;
|
|
return 0;
|
|
}
|
|
|
|
// returns bit length of the integer x
|
|
function nbits(x) {
|
|
var r = 1,
|
|
t;
|
|
if ((t = x >>> 16) != 0) {
|
|
x = t;
|
|
r += 16;
|
|
}
|
|
if ((t = x >> 8) != 0) {
|
|
x = t;
|
|
r += 8;
|
|
}
|
|
if ((t = x >> 4) != 0) {
|
|
x = t;
|
|
r += 4;
|
|
}
|
|
if ((t = x >> 2) != 0) {
|
|
x = t;
|
|
r += 2;
|
|
}
|
|
if ((t = x >> 1) != 0) {
|
|
x = t;
|
|
r += 1;
|
|
}
|
|
return r;
|
|
}
|
|
|
|
// (public) return the number of bits in "this"
|
|
function bnBitLength() {
|
|
if (this.t <= 0) return 0;
|
|
return this.DB * (this.t - 1) + nbits(this[this.t - 1] ^ (this.s & this.DM));
|
|
}
|
|
|
|
// (protected) r = this << n*DB
|
|
function bnpDLShiftTo(n, r) {
|
|
var i;
|
|
for (i = this.t - 1; i >= 0; --i) r[i + n] = this[i];
|
|
for (i = n - 1; i >= 0; --i) r[i] = 0;
|
|
r.t = this.t + n;
|
|
r.s = this.s;
|
|
}
|
|
|
|
// (protected) r = this >> n*DB
|
|
function bnpDRShiftTo(n, r) {
|
|
for (var i = n; i < this.t; ++i) r[i - n] = this[i];
|
|
r.t = Math.max(this.t - n, 0);
|
|
r.s = this.s;
|
|
}
|
|
|
|
// (protected) r = this << n
|
|
function bnpLShiftTo(n, r) {
|
|
var bs = n % this.DB;
|
|
var cbs = this.DB - bs;
|
|
var bm = (1 << cbs) - 1;
|
|
var ds = Math.floor(n / this.DB),
|
|
c = (this.s << bs) & this.DM,
|
|
i;
|
|
for (i = this.t - 1; i >= 0; --i) {
|
|
r[i + ds + 1] = (this[i] >> cbs) | c;
|
|
c = (this[i] & bm) << bs;
|
|
}
|
|
for (i = ds - 1; i >= 0; --i) r[i] = 0;
|
|
r[ds] = c;
|
|
r.t = this.t + ds + 1;
|
|
r.s = this.s;
|
|
r.clamp();
|
|
}
|
|
|
|
// (protected) r = this >> n
|
|
function bnpRShiftTo(n, r) {
|
|
r.s = this.s;
|
|
var ds = Math.floor(n / this.DB);
|
|
if (ds >= this.t) {
|
|
r.t = 0;
|
|
return;
|
|
}
|
|
var bs = n % this.DB;
|
|
var cbs = this.DB - bs;
|
|
var bm = (1 << bs) - 1;
|
|
r[0] = this[ds] >> bs;
|
|
for (var i = ds + 1; i < this.t; ++i) {
|
|
r[i - ds - 1] |= (this[i] & bm) << cbs;
|
|
r[i - ds] = this[i] >> bs;
|
|
}
|
|
if (bs > 0) r[this.t - ds - 1] |= (this.s & bm) << cbs;
|
|
r.t = this.t - ds;
|
|
r.clamp();
|
|
}
|
|
|
|
// (protected) r = this - a
|
|
function bnpSubTo(a, r) {
|
|
var i = 0,
|
|
c = 0,
|
|
m = Math.min(a.t, this.t);
|
|
while (i < m) {
|
|
c += this[i] - a[i];
|
|
r[i++] = c & this.DM;
|
|
c >>= this.DB;
|
|
}
|
|
if (a.t < this.t) {
|
|
c -= a.s;
|
|
while (i < this.t) {
|
|
c += this[i];
|
|
r[i++] = c & this.DM;
|
|
c >>= this.DB;
|
|
}
|
|
c += this.s;
|
|
} else {
|
|
c += this.s;
|
|
while (i < a.t) {
|
|
c -= a[i];
|
|
r[i++] = c & this.DM;
|
|
c >>= this.DB;
|
|
}
|
|
c -= a.s;
|
|
}
|
|
r.s = c < 0 ? -1 : 0;
|
|
if (c < -1) r[i++] = this.DV + c;
|
|
else if (c > 0) r[i++] = c;
|
|
r.t = i;
|
|
r.clamp();
|
|
}
|
|
|
|
// (protected) r = this * a, r != this,a (HAC 14.12)
|
|
// "this" should be the larger one if appropriate.
|
|
function bnpMultiplyTo(a, r) {
|
|
var x = this.abs(),
|
|
y = a.abs();
|
|
var i = x.t;
|
|
r.t = i + y.t;
|
|
while (--i >= 0) r[i] = 0;
|
|
for (i = 0; i < y.t; ++i) r[i + x.t] = x.am(0, y[i], r, i, 0, x.t);
|
|
r.s = 0;
|
|
r.clamp();
|
|
if (this.s != a.s) BigInteger.ZERO.subTo(r, r);
|
|
}
|
|
|
|
// (protected) r = this^2, r != this (HAC 14.16)
|
|
function bnpSquareTo(r) {
|
|
var x = this.abs();
|
|
var i = (r.t = 2 * x.t);
|
|
while (--i >= 0) r[i] = 0;
|
|
for (i = 0; i < x.t - 1; ++i) {
|
|
var c = x.am(i, x[i], r, 2 * i, 0, 1);
|
|
if ((r[i + x.t] += x.am(i + 1, 2 * x[i], r, 2 * i + 1, c, x.t - i - 1)) >= x.DV) {
|
|
r[i + x.t] -= x.DV;
|
|
r[i + x.t + 1] = 1;
|
|
}
|
|
}
|
|
if (r.t > 0) r[r.t - 1] += x.am(i, x[i], r, 2 * i, 0, 1);
|
|
r.s = 0;
|
|
r.clamp();
|
|
}
|
|
|
|
// (protected) divide this by m, quotient and remainder to q, r (HAC 14.20)
|
|
// r != q, this != m. q or r may be null.
|
|
function bnpDivRemTo(m, q, r) {
|
|
var pm = m.abs();
|
|
if (pm.t <= 0) return;
|
|
var pt = this.abs();
|
|
if (pt.t < pm.t) {
|
|
if (q != null) q.fromInt(0);
|
|
if (r != null) this.copyTo(r);
|
|
return;
|
|
}
|
|
if (r == null) r = nbi();
|
|
var y = nbi(),
|
|
ts = this.s,
|
|
ms = m.s;
|
|
var nsh = this.DB - nbits(pm[pm.t - 1]); // normalize modulus
|
|
if (nsh > 0) {
|
|
pm.lShiftTo(nsh, y);
|
|
pt.lShiftTo(nsh, r);
|
|
} else {
|
|
pm.copyTo(y);
|
|
pt.copyTo(r);
|
|
}
|
|
var ys = y.t;
|
|
var y0 = y[ys - 1];
|
|
if (y0 == 0) return;
|
|
var yt = y0 * (1 << this.F1) + (ys > 1 ? y[ys - 2] >> this.F2 : 0);
|
|
var d1 = this.FV / yt,
|
|
d2 = (1 << this.F1) / yt,
|
|
e = 1 << this.F2;
|
|
var i = r.t,
|
|
j = i - ys,
|
|
t = q == null ? nbi() : q;
|
|
y.dlShiftTo(j, t);
|
|
if (r.compareTo(t) >= 0) {
|
|
r[r.t++] = 1;
|
|
r.subTo(t, r);
|
|
}
|
|
BigInteger.ONE.dlShiftTo(ys, t);
|
|
t.subTo(y, y); // "negative" y so we can replace sub with am later
|
|
while (y.t < ys) y[y.t++] = 0;
|
|
while (--j >= 0) {
|
|
// Estimate quotient digit
|
|
var qd = r[--i] == y0 ? this.DM : Math.floor(r[i] * d1 + (r[i - 1] + e) * d2);
|
|
if ((r[i] += y.am(0, qd, r, j, 0, ys)) < qd) {
|
|
// Try it out
|
|
y.dlShiftTo(j, t);
|
|
r.subTo(t, r);
|
|
while (r[i] < --qd) r.subTo(t, r);
|
|
}
|
|
}
|
|
if (q != null) {
|
|
r.drShiftTo(ys, q);
|
|
if (ts != ms) BigInteger.ZERO.subTo(q, q);
|
|
}
|
|
r.t = ys;
|
|
r.clamp();
|
|
if (nsh > 0) r.rShiftTo(nsh, r); // Denormalize remainder
|
|
if (ts < 0) BigInteger.ZERO.subTo(r, r);
|
|
}
|
|
|
|
// (public) this mod a
|
|
function bnMod(a) {
|
|
var r = nbi();
|
|
this.abs().divRemTo(a, null, r);
|
|
if (this.s < 0 && r.compareTo(BigInteger.ZERO) > 0) a.subTo(r, r);
|
|
return r;
|
|
}
|
|
|
|
// Modular reduction using "classic" algorithm
|
|
function Classic(m) {
|
|
this.m = m;
|
|
}
|
|
function cConvert(x) {
|
|
if (x.s < 0 || x.compareTo(this.m) >= 0) return x.mod(this.m);
|
|
else return x;
|
|
}
|
|
function cRevert(x) {
|
|
return x;
|
|
}
|
|
function cReduce(x) {
|
|
x.divRemTo(this.m, null, x);
|
|
}
|
|
function cMulTo(x, y, r) {
|
|
x.multiplyTo(y, r);
|
|
this.reduce(r);
|
|
}
|
|
function cSqrTo(x, r) {
|
|
x.squareTo(r);
|
|
this.reduce(r);
|
|
}
|
|
|
|
Classic.prototype.convert = cConvert;
|
|
Classic.prototype.revert = cRevert;
|
|
Classic.prototype.reduce = cReduce;
|
|
Classic.prototype.mulTo = cMulTo;
|
|
Classic.prototype.sqrTo = cSqrTo;
|
|
|
|
// (protected) return "-1/this % 2^DB"; useful for Mont. reduction
|
|
// justification:
|
|
// xy == 1 (mod m)
|
|
// xy = 1+km
|
|
// xy(2-xy) = (1+km)(1-km)
|
|
// x[y(2-xy)] = 1-k^2m^2
|
|
// x[y(2-xy)] == 1 (mod m^2)
|
|
// if y is 1/x mod m, then y(2-xy) is 1/x mod m^2
|
|
// should reduce x and y(2-xy) by m^2 at each step to keep size bounded.
|
|
// JS multiply "overflows" differently from C/C++, so care is needed here.
|
|
function bnpInvDigit() {
|
|
if (this.t < 1) return 0;
|
|
var x = this[0];
|
|
if ((x & 1) == 0) return 0;
|
|
var y = x & 3; // y == 1/x mod 2^2
|
|
y = (y * (2 - (x & 0xf) * y)) & 0xf; // y == 1/x mod 2^4
|
|
y = (y * (2 - (x & 0xff) * y)) & 0xff; // y == 1/x mod 2^8
|
|
y = (y * (2 - (((x & 0xffff) * y) & 0xffff))) & 0xffff; // y == 1/x mod 2^16
|
|
// last step - calculate inverse mod DV directly;
|
|
// assumes 16 < DB <= 32 and assumes ability to handle 48-bit ints
|
|
y = (y * (2 - ((x * y) % this.DV))) % this.DV; // y == 1/x mod 2^dbits
|
|
// we really want the negative inverse, and -DV < y < DV
|
|
return y > 0 ? this.DV - y : -y;
|
|
}
|
|
|
|
// Montgomery reduction
|
|
function Montgomery(m) {
|
|
this.m = m;
|
|
this.mp = m.invDigit();
|
|
this.mpl = this.mp & 0x7fff;
|
|
this.mph = this.mp >> 15;
|
|
this.um = (1 << (m.DB - 15)) - 1;
|
|
this.mt2 = 2 * m.t;
|
|
}
|
|
|
|
// xR mod m
|
|
function montConvert(x) {
|
|
var r = nbi();
|
|
x.abs().dlShiftTo(this.m.t, r);
|
|
r.divRemTo(this.m, null, r);
|
|
if (x.s < 0 && r.compareTo(BigInteger.ZERO) > 0) this.m.subTo(r, r);
|
|
return r;
|
|
}
|
|
|
|
// x/R mod m
|
|
function montRevert(x) {
|
|
var r = nbi();
|
|
x.copyTo(r);
|
|
this.reduce(r);
|
|
return r;
|
|
}
|
|
|
|
// x = x/R mod m (HAC 14.32)
|
|
function montReduce(x) {
|
|
while (
|
|
x.t <= this.mt2 // pad x so am has enough room later
|
|
)
|
|
x[x.t++] = 0;
|
|
for (var i = 0; i < this.m.t; ++i) {
|
|
// faster way of calculating u0 = x[i]*mp mod DV
|
|
var j = x[i] & 0x7fff;
|
|
var u0 = (j * this.mpl + (((j * this.mph + (x[i] >> 15) * this.mpl) & this.um) << 15)) & x.DM;
|
|
// use am to combine the multiply-shift-add into one call
|
|
j = i + this.m.t;
|
|
x[j] += this.m.am(0, u0, x, i, 0, this.m.t);
|
|
// propagate carry
|
|
while (x[j] >= x.DV) {
|
|
x[j] -= x.DV;
|
|
x[++j]++;
|
|
}
|
|
}
|
|
x.clamp();
|
|
x.drShiftTo(this.m.t, x);
|
|
if (x.compareTo(this.m) >= 0) x.subTo(this.m, x);
|
|
}
|
|
|
|
// r = "x^2/R mod m"; x != r
|
|
function montSqrTo(x, r) {
|
|
x.squareTo(r);
|
|
this.reduce(r);
|
|
}
|
|
|
|
// r = "xy/R mod m"; x,y != r
|
|
function montMulTo(x, y, r) {
|
|
x.multiplyTo(y, r);
|
|
this.reduce(r);
|
|
}
|
|
|
|
Montgomery.prototype.convert = montConvert;
|
|
Montgomery.prototype.revert = montRevert;
|
|
Montgomery.prototype.reduce = montReduce;
|
|
Montgomery.prototype.mulTo = montMulTo;
|
|
Montgomery.prototype.sqrTo = montSqrTo;
|
|
|
|
// (protected) true iff this is even
|
|
function bnpIsEven() {
|
|
return (this.t > 0 ? this[0] & 1 : this.s) == 0;
|
|
}
|
|
|
|
// (protected) this^e, e < 2^32, doing sqr and mul with "r" (HAC 14.79)
|
|
function bnpExp(e, z) {
|
|
if (e > 0xffffffff || e < 1) return BigInteger.ONE;
|
|
var r = nbi(),
|
|
r2 = nbi(),
|
|
g = z.convert(this),
|
|
i = nbits(e) - 1;
|
|
g.copyTo(r);
|
|
while (--i >= 0) {
|
|
z.sqrTo(r, r2);
|
|
if ((e & (1 << i)) > 0) z.mulTo(r2, g, r);
|
|
else {
|
|
var t = r;
|
|
r = r2;
|
|
r2 = t;
|
|
}
|
|
}
|
|
return z.revert(r);
|
|
}
|
|
|
|
// (public) this^e % m, 0 <= e < 2^32
|
|
function bnModPowInt(e, m) {
|
|
var z;
|
|
if (e < 256 || m.isEven()) z = new Classic(m);
|
|
else z = new Montgomery(m);
|
|
return this.exp(e, z);
|
|
}
|
|
|
|
// protected
|
|
BigInteger.prototype.copyTo = bnpCopyTo;
|
|
BigInteger.prototype.fromInt = bnpFromInt;
|
|
BigInteger.prototype.fromString = bnpFromString;
|
|
BigInteger.prototype.clamp = bnpClamp;
|
|
BigInteger.prototype.dlShiftTo = bnpDLShiftTo;
|
|
BigInteger.prototype.drShiftTo = bnpDRShiftTo;
|
|
BigInteger.prototype.lShiftTo = bnpLShiftTo;
|
|
BigInteger.prototype.rShiftTo = bnpRShiftTo;
|
|
BigInteger.prototype.subTo = bnpSubTo;
|
|
BigInteger.prototype.multiplyTo = bnpMultiplyTo;
|
|
BigInteger.prototype.squareTo = bnpSquareTo;
|
|
BigInteger.prototype.divRemTo = bnpDivRemTo;
|
|
BigInteger.prototype.invDigit = bnpInvDigit;
|
|
BigInteger.prototype.isEven = bnpIsEven;
|
|
BigInteger.prototype.exp = bnpExp;
|
|
|
|
// public
|
|
BigInteger.prototype.toString = bnToString;
|
|
BigInteger.prototype.negate = bnNegate;
|
|
BigInteger.prototype.abs = bnAbs;
|
|
BigInteger.prototype.compareTo = bnCompareTo;
|
|
BigInteger.prototype.bitLength = bnBitLength;
|
|
BigInteger.prototype.mod = bnMod;
|
|
BigInteger.prototype.modPowInt = bnModPowInt;
|
|
|
|
// "constants"
|
|
BigInteger.ZERO = nbv(0);
|
|
BigInteger.ONE = nbv(1);
|
|
|
|
// Copyright (c) 2005-2009 Tom Wu
|
|
// All Rights Reserved.
|
|
// See "LICENSE" for details.
|
|
|
|
// Extended JavaScript BN functions, required for RSA private ops.
|
|
|
|
// Version 1.1: new BigInteger("0", 10) returns "proper" zero
|
|
// Version 1.2: square() API, isProbablePrime fix
|
|
|
|
// (public)
|
|
function bnClone() {
|
|
var r = nbi();
|
|
this.copyTo(r);
|
|
return r;
|
|
}
|
|
|
|
// (public) return value as integer
|
|
function bnIntValue() {
|
|
if (this.s < 0) {
|
|
if (this.t == 1) return this[0] - this.DV;
|
|
else if (this.t == 0) return -1;
|
|
} else if (this.t == 1) return this[0];
|
|
else if (this.t == 0) return 0;
|
|
// assumes 16 < DB < 32
|
|
return ((this[1] & ((1 << (32 - this.DB)) - 1)) << this.DB) | this[0];
|
|
}
|
|
|
|
// (public) return value as byte
|
|
function bnByteValue() {
|
|
return this.t == 0 ? this.s : (this[0] << 24) >> 24;
|
|
}
|
|
|
|
// (public) return value as short (assumes DB>=16)
|
|
function bnShortValue() {
|
|
return this.t == 0 ? this.s : (this[0] << 16) >> 16;
|
|
}
|
|
|
|
// (protected) return x s.t. r^x < DV
|
|
function bnpChunkSize(r) {
|
|
return Math.floor((Math.LN2 * this.DB) / Math.log(r));
|
|
}
|
|
|
|
// (public) 0 if this == 0, 1 if this > 0
|
|
function bnSigNum() {
|
|
if (this.s < 0) return -1;
|
|
else if (this.t <= 0 || (this.t == 1 && this[0] <= 0)) return 0;
|
|
else return 1;
|
|
}
|
|
|
|
// (protected) convert to radix string
|
|
function bnpToRadix(b) {
|
|
if (b == null) b = 10;
|
|
if (this.signum() == 0 || b < 2 || b > 36) return "0";
|
|
var cs = this.chunkSize(b);
|
|
var a = Math.pow(b, cs);
|
|
var d = nbv(a),
|
|
y = nbi(),
|
|
z = nbi(),
|
|
r = "";
|
|
this.divRemTo(d, y, z);
|
|
while (y.signum() > 0) {
|
|
r = (a + z.intValue()).toString(b).substr(1) + r;
|
|
y.divRemTo(d, y, z);
|
|
}
|
|
return z.intValue().toString(b) + r;
|
|
}
|
|
|
|
// (protected) convert from radix string
|
|
function bnpFromRadix(s, b) {
|
|
this.fromInt(0);
|
|
if (b == null) b = 10;
|
|
var cs = this.chunkSize(b);
|
|
var d = Math.pow(b, cs),
|
|
mi = false,
|
|
j = 0,
|
|
w = 0;
|
|
for (var i = 0; i < s.length; ++i) {
|
|
var x = intAt(s, i);
|
|
if (x < 0) {
|
|
if (s.charAt(i) == "-" && this.signum() == 0) mi = true;
|
|
continue;
|
|
}
|
|
w = b * w + x;
|
|
if (++j >= cs) {
|
|
this.dMultiply(d);
|
|
this.dAddOffset(w, 0);
|
|
j = 0;
|
|
w = 0;
|
|
}
|
|
}
|
|
if (j > 0) {
|
|
this.dMultiply(Math.pow(b, j));
|
|
this.dAddOffset(w, 0);
|
|
}
|
|
if (mi) BigInteger.ZERO.subTo(this, this);
|
|
}
|
|
|
|
// (protected) alternate constructor
|
|
function bnpFromNumber(a, b, c) {
|
|
if ("number" == typeof b) {
|
|
// new BigInteger(int,int,RNG)
|
|
if (a < 2) this.fromInt(1);
|
|
else {
|
|
this.fromNumber(a, c);
|
|
if (!this.testBit(a - 1))
|
|
// force MSB set
|
|
this.bitwiseTo(BigInteger.ONE.shiftLeft(a - 1), op_or, this);
|
|
if (this.isEven()) this.dAddOffset(1, 0); // force odd
|
|
while (!this.isProbablePrime(b)) {
|
|
this.dAddOffset(2, 0);
|
|
if (this.bitLength() > a) this.subTo(BigInteger.ONE.shiftLeft(a - 1), this);
|
|
}
|
|
}
|
|
} else {
|
|
// new BigInteger(int,RNG)
|
|
var x = new Array(),
|
|
t = a & 7;
|
|
x.length = (a >> 3) + 1;
|
|
b.nextBytes(x);
|
|
if (t > 0) x[0] &= (1 << t) - 1;
|
|
else x[0] = 0;
|
|
this.fromString(x, 256);
|
|
}
|
|
}
|
|
|
|
// (public) convert to bigendian byte array
|
|
function bnToByteArray() {
|
|
var i = this.t,
|
|
r = new Array();
|
|
r[0] = this.s;
|
|
var p = this.DB - ((i * this.DB) % 8),
|
|
d,
|
|
k = 0;
|
|
if (i-- > 0) {
|
|
if (p < this.DB && (d = this[i] >> p) != (this.s & this.DM) >> p) r[k++] = d | (this.s << (this.DB - p));
|
|
while (i >= 0) {
|
|
if (p < 8) {
|
|
d = (this[i] & ((1 << p) - 1)) << (8 - p);
|
|
d |= this[--i] >> (p += this.DB - 8);
|
|
} else {
|
|
d = (this[i] >> (p -= 8)) & 0xff;
|
|
if (p <= 0) {
|
|
p += this.DB;
|
|
--i;
|
|
}
|
|
}
|
|
if ((d & 0x80) != 0) d |= -256;
|
|
if (k == 0 && (this.s & 0x80) != (d & 0x80)) ++k;
|
|
if (k > 0 || d != this.s) r[k++] = d;
|
|
}
|
|
}
|
|
return r;
|
|
}
|
|
|
|
function bnEquals(a) {
|
|
return this.compareTo(a) == 0;
|
|
}
|
|
function bnMin(a) {
|
|
return this.compareTo(a) < 0 ? this : a;
|
|
}
|
|
function bnMax(a) {
|
|
return this.compareTo(a) > 0 ? this : a;
|
|
}
|
|
|
|
// (protected) r = this op a (bitwise)
|
|
function bnpBitwiseTo(a, op, r) {
|
|
var i,
|
|
f,
|
|
m = Math.min(a.t, this.t);
|
|
for (i = 0; i < m; ++i) r[i] = op(this[i], a[i]);
|
|
if (a.t < this.t) {
|
|
f = a.s & this.DM;
|
|
for (i = m; i < this.t; ++i) r[i] = op(this[i], f);
|
|
r.t = this.t;
|
|
} else {
|
|
f = this.s & this.DM;
|
|
for (i = m; i < a.t; ++i) r[i] = op(f, a[i]);
|
|
r.t = a.t;
|
|
}
|
|
r.s = op(this.s, a.s);
|
|
r.clamp();
|
|
}
|
|
|
|
// (public) this & a
|
|
function op_and(x, y) {
|
|
return x & y;
|
|
}
|
|
function bnAnd(a) {
|
|
var r = nbi();
|
|
this.bitwiseTo(a, op_and, r);
|
|
return r;
|
|
}
|
|
|
|
// (public) this | a
|
|
function op_or(x, y) {
|
|
return x | y;
|
|
}
|
|
function bnOr(a) {
|
|
var r = nbi();
|
|
this.bitwiseTo(a, op_or, r);
|
|
return r;
|
|
}
|
|
|
|
// (public) this ^ a
|
|
function op_xor(x, y) {
|
|
return x ^ y;
|
|
}
|
|
function bnXor(a) {
|
|
var r = nbi();
|
|
this.bitwiseTo(a, op_xor, r);
|
|
return r;
|
|
}
|
|
|
|
// (public) this & ~a
|
|
function op_andnot(x, y) {
|
|
return x & ~y;
|
|
}
|
|
function bnAndNot(a) {
|
|
var r = nbi();
|
|
this.bitwiseTo(a, op_andnot, r);
|
|
return r;
|
|
}
|
|
|
|
// (public) ~this
|
|
function bnNot() {
|
|
var r = nbi();
|
|
for (var i = 0; i < this.t; ++i) r[i] = this.DM & ~this[i];
|
|
r.t = this.t;
|
|
r.s = ~this.s;
|
|
return r;
|
|
}
|
|
|
|
// (public) this << n
|
|
function bnShiftLeft(n) {
|
|
var r = nbi();
|
|
if (n < 0) this.rShiftTo(-n, r);
|
|
else this.lShiftTo(n, r);
|
|
return r;
|
|
}
|
|
|
|
// (public) this >> n
|
|
function bnShiftRight(n) {
|
|
var r = nbi();
|
|
if (n < 0) this.lShiftTo(-n, r);
|
|
else this.rShiftTo(n, r);
|
|
return r;
|
|
}
|
|
|
|
// return index of lowest 1-bit in x, x < 2^31
|
|
function lbit(x) {
|
|
if (x == 0) return -1;
|
|
var r = 0;
|
|
if ((x & 0xffff) == 0) {
|
|
x >>= 16;
|
|
r += 16;
|
|
}
|
|
if ((x & 0xff) == 0) {
|
|
x >>= 8;
|
|
r += 8;
|
|
}
|
|
if ((x & 0xf) == 0) {
|
|
x >>= 4;
|
|
r += 4;
|
|
}
|
|
if ((x & 3) == 0) {
|
|
x >>= 2;
|
|
r += 2;
|
|
}
|
|
if ((x & 1) == 0) ++r;
|
|
return r;
|
|
}
|
|
|
|
// (public) returns index of lowest 1-bit (or -1 if none)
|
|
function bnGetLowestSetBit() {
|
|
for (var i = 0; i < this.t; ++i) if (this[i] != 0) return i * this.DB + lbit(this[i]);
|
|
if (this.s < 0) return this.t * this.DB;
|
|
return -1;
|
|
}
|
|
|
|
// return number of 1 bits in x
|
|
function cbit(x) {
|
|
var r = 0;
|
|
while (x != 0) {
|
|
x &= x - 1;
|
|
++r;
|
|
}
|
|
return r;
|
|
}
|
|
|
|
// (public) return number of set bits
|
|
function bnBitCount() {
|
|
var r = 0,
|
|
x = this.s & this.DM;
|
|
for (var i = 0; i < this.t; ++i) r += cbit(this[i] ^ x);
|
|
return r;
|
|
}
|
|
|
|
// (public) true iff nth bit is set
|
|
function bnTestBit(n) {
|
|
var j = Math.floor(n / this.DB);
|
|
if (j >= this.t) return this.s != 0;
|
|
return (this[j] & (1 << n % this.DB)) != 0;
|
|
}
|
|
|
|
// (protected) this op (1<<n)
|
|
function bnpChangeBit(n, op) {
|
|
var r = BigInteger.ONE.shiftLeft(n);
|
|
this.bitwiseTo(r, op, r);
|
|
return r;
|
|
}
|
|
|
|
// (public) this | (1<<n)
|
|
function bnSetBit(n) {
|
|
return this.changeBit(n, op_or);
|
|
}
|
|
|
|
// (public) this & ~(1<<n)
|
|
function bnClearBit(n) {
|
|
return this.changeBit(n, op_andnot);
|
|
}
|
|
|
|
// (public) this ^ (1<<n)
|
|
function bnFlipBit(n) {
|
|
return this.changeBit(n, op_xor);
|
|
}
|
|
|
|
// (protected) r = this + a
|
|
function bnpAddTo(a, r) {
|
|
var i = 0,
|
|
c = 0,
|
|
m = Math.min(a.t, this.t);
|
|
while (i < m) {
|
|
c += this[i] + a[i];
|
|
r[i++] = c & this.DM;
|
|
c >>= this.DB;
|
|
}
|
|
if (a.t < this.t) {
|
|
c += a.s;
|
|
while (i < this.t) {
|
|
c += this[i];
|
|
r[i++] = c & this.DM;
|
|
c >>= this.DB;
|
|
}
|
|
c += this.s;
|
|
} else {
|
|
c += this.s;
|
|
while (i < a.t) {
|
|
c += a[i];
|
|
r[i++] = c & this.DM;
|
|
c >>= this.DB;
|
|
}
|
|
c += a.s;
|
|
}
|
|
r.s = c < 0 ? -1 : 0;
|
|
if (c > 0) r[i++] = c;
|
|
else if (c < -1) r[i++] = this.DV + c;
|
|
r.t = i;
|
|
r.clamp();
|
|
}
|
|
|
|
// (public) this + a
|
|
function bnAdd(a) {
|
|
var r = nbi();
|
|
this.addTo(a, r);
|
|
return r;
|
|
}
|
|
|
|
// (public) this - a
|
|
function bnSubtract(a) {
|
|
var r = nbi();
|
|
this.subTo(a, r);
|
|
return r;
|
|
}
|
|
|
|
// (public) this * a
|
|
function bnMultiply(a) {
|
|
var r = nbi();
|
|
this.multiplyTo(a, r);
|
|
return r;
|
|
}
|
|
|
|
// (public) this^2
|
|
function bnSquare() {
|
|
var r = nbi();
|
|
this.squareTo(r);
|
|
return r;
|
|
}
|
|
|
|
// (public) this / a
|
|
function bnDivide(a) {
|
|
var r = nbi();
|
|
this.divRemTo(a, r, null);
|
|
return r;
|
|
}
|
|
|
|
// (public) this % a
|
|
function bnRemainder(a) {
|
|
var r = nbi();
|
|
this.divRemTo(a, null, r);
|
|
return r;
|
|
}
|
|
|
|
// (public) [this/a,this%a]
|
|
function bnDivideAndRemainder(a) {
|
|
var q = nbi(),
|
|
r = nbi();
|
|
this.divRemTo(a, q, r);
|
|
return new Array(q, r);
|
|
}
|
|
|
|
// (protected) this *= n, this >= 0, 1 < n < DV
|
|
function bnpDMultiply(n) {
|
|
this[this.t] = this.am(0, n - 1, this, 0, 0, this.t);
|
|
++this.t;
|
|
this.clamp();
|
|
}
|
|
|
|
// (protected) this += n << w words, this >= 0
|
|
function bnpDAddOffset(n, w) {
|
|
if (n == 0) return;
|
|
while (this.t <= w) this[this.t++] = 0;
|
|
this[w] += n;
|
|
while (this[w] >= this.DV) {
|
|
this[w] -= this.DV;
|
|
if (++w >= this.t) this[this.t++] = 0;
|
|
++this[w];
|
|
}
|
|
}
|
|
|
|
// A "null" reducer
|
|
function NullExp() {}
|
|
function nNop(x) {
|
|
return x;
|
|
}
|
|
function nMulTo(x, y, r) {
|
|
x.multiplyTo(y, r);
|
|
}
|
|
function nSqrTo(x, r) {
|
|
x.squareTo(r);
|
|
}
|
|
|
|
NullExp.prototype.convert = nNop;
|
|
NullExp.prototype.revert = nNop;
|
|
NullExp.prototype.mulTo = nMulTo;
|
|
NullExp.prototype.sqrTo = nSqrTo;
|
|
|
|
// (public) this^e
|
|
function bnPow(e) {
|
|
return this.exp(e, new NullExp());
|
|
}
|
|
|
|
// (protected) r = lower n words of "this * a", a.t <= n
|
|
// "this" should be the larger one if appropriate.
|
|
function bnpMultiplyLowerTo(a, n, r) {
|
|
var i = Math.min(this.t + a.t, n);
|
|
r.s = 0; // assumes a,this >= 0
|
|
r.t = i;
|
|
while (i > 0) r[--i] = 0;
|
|
var j;
|
|
for (j = r.t - this.t; i < j; ++i) r[i + this.t] = this.am(0, a[i], r, i, 0, this.t);
|
|
for (j = Math.min(a.t, n); i < j; ++i) this.am(0, a[i], r, i, 0, n - i);
|
|
r.clamp();
|
|
}
|
|
|
|
// (protected) r = "this * a" without lower n words, n > 0
|
|
// "this" should be the larger one if appropriate.
|
|
function bnpMultiplyUpperTo(a, n, r) {
|
|
--n;
|
|
var i = (r.t = this.t + a.t - n);
|
|
r.s = 0; // assumes a,this >= 0
|
|
while (--i >= 0) r[i] = 0;
|
|
for (i = Math.max(n - this.t, 0); i < a.t; ++i) r[this.t + i - n] = this.am(n - i, a[i], r, 0, 0, this.t + i - n);
|
|
r.clamp();
|
|
r.drShiftTo(1, r);
|
|
}
|
|
|
|
// Barrett modular reduction
|
|
function Barrett(m) {
|
|
// setup Barrett
|
|
this.r2 = nbi();
|
|
this.q3 = nbi();
|
|
BigInteger.ONE.dlShiftTo(2 * m.t, this.r2);
|
|
this.mu = this.r2.divide(m);
|
|
this.m = m;
|
|
}
|
|
|
|
function barrettConvert(x) {
|
|
if (x.s < 0 || x.t > 2 * this.m.t) return x.mod(this.m);
|
|
else if (x.compareTo(this.m) < 0) return x;
|
|
else {
|
|
var r = nbi();
|
|
x.copyTo(r);
|
|
this.reduce(r);
|
|
return r;
|
|
}
|
|
}
|
|
|
|
function barrettRevert(x) {
|
|
return x;
|
|
}
|
|
|
|
// x = x mod m (HAC 14.42)
|
|
function barrettReduce(x) {
|
|
x.drShiftTo(this.m.t - 1, this.r2);
|
|
if (x.t > this.m.t + 1) {
|
|
x.t = this.m.t + 1;
|
|
x.clamp();
|
|
}
|
|
this.mu.multiplyUpperTo(this.r2, this.m.t + 1, this.q3);
|
|
this.m.multiplyLowerTo(this.q3, this.m.t + 1, this.r2);
|
|
while (x.compareTo(this.r2) < 0) x.dAddOffset(1, this.m.t + 1);
|
|
x.subTo(this.r2, x);
|
|
while (x.compareTo(this.m) >= 0) x.subTo(this.m, x);
|
|
}
|
|
|
|
// r = x^2 mod m; x != r
|
|
function barrettSqrTo(x, r) {
|
|
x.squareTo(r);
|
|
this.reduce(r);
|
|
}
|
|
|
|
// r = x*y mod m; x,y != r
|
|
function barrettMulTo(x, y, r) {
|
|
x.multiplyTo(y, r);
|
|
this.reduce(r);
|
|
}
|
|
|
|
Barrett.prototype.convert = barrettConvert;
|
|
Barrett.prototype.revert = barrettRevert;
|
|
Barrett.prototype.reduce = barrettReduce;
|
|
Barrett.prototype.mulTo = barrettMulTo;
|
|
Barrett.prototype.sqrTo = barrettSqrTo;
|
|
|
|
// (public) this^e % m (HAC 14.85)
|
|
function bnModPow(e, m) {
|
|
var i = e.bitLength(),
|
|
k,
|
|
r = nbv(1),
|
|
z;
|
|
if (i <= 0) return r;
|
|
else if (i < 18) k = 1;
|
|
else if (i < 48) k = 3;
|
|
else if (i < 144) k = 4;
|
|
else if (i < 768) k = 5;
|
|
else k = 6;
|
|
if (i < 8) z = new Classic(m);
|
|
else if (m.isEven()) z = new Barrett(m);
|
|
else z = new Montgomery(m);
|
|
|
|
// precomputation
|
|
var g = new Array(),
|
|
n = 3,
|
|
k1 = k - 1,
|
|
km = (1 << k) - 1;
|
|
g[1] = z.convert(this);
|
|
if (k > 1) {
|
|
var g2 = nbi();
|
|
z.sqrTo(g[1], g2);
|
|
while (n <= km) {
|
|
g[n] = nbi();
|
|
z.mulTo(g2, g[n - 2], g[n]);
|
|
n += 2;
|
|
}
|
|
}
|
|
|
|
var j = e.t - 1,
|
|
w,
|
|
is1 = true,
|
|
r2 = nbi(),
|
|
t;
|
|
i = nbits(e[j]) - 1;
|
|
while (j >= 0) {
|
|
if (i >= k1) w = (e[j] >> (i - k1)) & km;
|
|
else {
|
|
w = (e[j] & ((1 << (i + 1)) - 1)) << (k1 - i);
|
|
if (j > 0) w |= e[j - 1] >> (this.DB + i - k1);
|
|
}
|
|
|
|
n = k;
|
|
while ((w & 1) == 0) {
|
|
w >>= 1;
|
|
--n;
|
|
}
|
|
if ((i -= n) < 0) {
|
|
i += this.DB;
|
|
--j;
|
|
}
|
|
if (is1) {
|
|
// ret == 1, don't bother squaring or multiplying it
|
|
g[w].copyTo(r);
|
|
is1 = false;
|
|
} else {
|
|
while (n > 1) {
|
|
z.sqrTo(r, r2);
|
|
z.sqrTo(r2, r);
|
|
n -= 2;
|
|
}
|
|
if (n > 0) z.sqrTo(r, r2);
|
|
else {
|
|
t = r;
|
|
r = r2;
|
|
r2 = t;
|
|
}
|
|
z.mulTo(r2, g[w], r);
|
|
}
|
|
|
|
while (j >= 0 && (e[j] & (1 << i)) == 0) {
|
|
z.sqrTo(r, r2);
|
|
t = r;
|
|
r = r2;
|
|
r2 = t;
|
|
if (--i < 0) {
|
|
i = this.DB - 1;
|
|
--j;
|
|
}
|
|
}
|
|
}
|
|
return z.revert(r);
|
|
}
|
|
|
|
// (public) gcd(this,a) (HAC 14.54)
|
|
function bnGCD(a) {
|
|
var x = this.s < 0 ? this.negate() : this.clone();
|
|
var y = a.s < 0 ? a.negate() : a.clone();
|
|
if (x.compareTo(y) < 0) {
|
|
var t = x;
|
|
x = y;
|
|
y = t;
|
|
}
|
|
var i = x.getLowestSetBit(),
|
|
g = y.getLowestSetBit();
|
|
if (g < 0) return x;
|
|
if (i < g) g = i;
|
|
if (g > 0) {
|
|
x.rShiftTo(g, x);
|
|
y.rShiftTo(g, y);
|
|
}
|
|
while (x.signum() > 0) {
|
|
if ((i = x.getLowestSetBit()) > 0) x.rShiftTo(i, x);
|
|
if ((i = y.getLowestSetBit()) > 0) y.rShiftTo(i, y);
|
|
if (x.compareTo(y) >= 0) {
|
|
x.subTo(y, x);
|
|
x.rShiftTo(1, x);
|
|
} else {
|
|
y.subTo(x, y);
|
|
y.rShiftTo(1, y);
|
|
}
|
|
}
|
|
if (g > 0) y.lShiftTo(g, y);
|
|
return y;
|
|
}
|
|
|
|
// (protected) this % n, n < 2^26
|
|
function bnpModInt(n) {
|
|
if (n <= 0) return 0;
|
|
var d = this.DV % n,
|
|
r = this.s < 0 ? n - 1 : 0;
|
|
if (this.t > 0)
|
|
if (d == 0) r = this[0] % n;
|
|
else for (var i = this.t - 1; i >= 0; --i) r = (d * r + this[i]) % n;
|
|
return r;
|
|
}
|
|
|
|
// (public) 1/this % m (HAC 14.61)
|
|
function bnModInverse(m) {
|
|
var ac = m.isEven();
|
|
if ((this.isEven() && ac) || m.signum() == 0) return BigInteger.ZERO;
|
|
var u = m.clone(),
|
|
v = this.clone();
|
|
var a = nbv(1),
|
|
b = nbv(0),
|
|
c = nbv(0),
|
|
d = nbv(1);
|
|
while (u.signum() != 0) {
|
|
while (u.isEven()) {
|
|
u.rShiftTo(1, u);
|
|
if (ac) {
|
|
if (!a.isEven() || !b.isEven()) {
|
|
a.addTo(this, a);
|
|
b.subTo(m, b);
|
|
}
|
|
a.rShiftTo(1, a);
|
|
} else if (!b.isEven()) b.subTo(m, b);
|
|
b.rShiftTo(1, b);
|
|
}
|
|
while (v.isEven()) {
|
|
v.rShiftTo(1, v);
|
|
if (ac) {
|
|
if (!c.isEven() || !d.isEven()) {
|
|
c.addTo(this, c);
|
|
d.subTo(m, d);
|
|
}
|
|
c.rShiftTo(1, c);
|
|
} else if (!d.isEven()) d.subTo(m, d);
|
|
d.rShiftTo(1, d);
|
|
}
|
|
if (u.compareTo(v) >= 0) {
|
|
u.subTo(v, u);
|
|
if (ac) a.subTo(c, a);
|
|
b.subTo(d, b);
|
|
} else {
|
|
v.subTo(u, v);
|
|
if (ac) c.subTo(a, c);
|
|
d.subTo(b, d);
|
|
}
|
|
}
|
|
if (v.compareTo(BigInteger.ONE) != 0) return BigInteger.ZERO;
|
|
if (d.compareTo(m) >= 0) return d.subtract(m);
|
|
if (d.signum() < 0) d.addTo(m, d);
|
|
else return d;
|
|
if (d.signum() < 0) return d.add(m);
|
|
else return d;
|
|
}
|
|
|
|
var lowprimes = [
|
|
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109,
|
|
113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239,
|
|
241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379,
|
|
383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521,
|
|
523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661,
|
|
673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827,
|
|
829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991,
|
|
997,
|
|
];
|
|
var lplim = (1 << 26) / lowprimes[lowprimes.length - 1];
|
|
|
|
// (public) test primality with certainty >= 1-.5^t
|
|
function bnIsProbablePrime(t) {
|
|
var i,
|
|
x = this.abs();
|
|
if (x.t == 1 && x[0] <= lowprimes[lowprimes.length - 1]) {
|
|
for (i = 0; i < lowprimes.length; ++i) if (x[0] == lowprimes[i]) return true;
|
|
return false;
|
|
}
|
|
if (x.isEven()) return false;
|
|
i = 1;
|
|
while (i < lowprimes.length) {
|
|
var m = lowprimes[i],
|
|
j = i + 1;
|
|
while (j < lowprimes.length && m < lplim) m *= lowprimes[j++];
|
|
m = x.modInt(m);
|
|
while (i < j) if (m % lowprimes[i++] == 0) return false;
|
|
}
|
|
return x.millerRabin(t);
|
|
}
|
|
|
|
// (protected) true if probably prime (HAC 4.24, Miller-Rabin)
|
|
function bnpMillerRabin(t) {
|
|
var n1 = this.subtract(BigInteger.ONE);
|
|
var k = n1.getLowestSetBit();
|
|
if (k <= 0) return false;
|
|
var r = n1.shiftRight(k);
|
|
t = (t + 1) >> 1;
|
|
if (t > lowprimes.length) t = lowprimes.length;
|
|
var a = nbi();
|
|
for (var i = 0; i < t; ++i) {
|
|
//Pick bases at random, instead of starting at 2
|
|
a.fromInt(lowprimes[Math.floor(Math.random() * lowprimes.length)]);
|
|
var y = a.modPow(r, this);
|
|
if (y.compareTo(BigInteger.ONE) != 0 && y.compareTo(n1) != 0) {
|
|
var j = 1;
|
|
while (j++ < k && y.compareTo(n1) != 0) {
|
|
y = y.modPowInt(2, this);
|
|
if (y.compareTo(BigInteger.ONE) == 0) return false;
|
|
}
|
|
if (y.compareTo(n1) != 0) return false;
|
|
}
|
|
}
|
|
return true;
|
|
}
|
|
|
|
// protected
|
|
BigInteger.prototype.chunkSize = bnpChunkSize;
|
|
BigInteger.prototype.toRadix = bnpToRadix;
|
|
BigInteger.prototype.fromRadix = bnpFromRadix;
|
|
BigInteger.prototype.fromNumber = bnpFromNumber;
|
|
BigInteger.prototype.bitwiseTo = bnpBitwiseTo;
|
|
BigInteger.prototype.changeBit = bnpChangeBit;
|
|
BigInteger.prototype.addTo = bnpAddTo;
|
|
BigInteger.prototype.dMultiply = bnpDMultiply;
|
|
BigInteger.prototype.dAddOffset = bnpDAddOffset;
|
|
BigInteger.prototype.multiplyLowerTo = bnpMultiplyLowerTo;
|
|
BigInteger.prototype.multiplyUpperTo = bnpMultiplyUpperTo;
|
|
BigInteger.prototype.modInt = bnpModInt;
|
|
BigInteger.prototype.millerRabin = bnpMillerRabin;
|
|
|
|
// public
|
|
BigInteger.prototype.clone = bnClone;
|
|
BigInteger.prototype.intValue = bnIntValue;
|
|
BigInteger.prototype.byteValue = bnByteValue;
|
|
BigInteger.prototype.shortValue = bnShortValue;
|
|
BigInteger.prototype.signum = bnSigNum;
|
|
BigInteger.prototype.toByteArray = bnToByteArray;
|
|
BigInteger.prototype.equals = bnEquals;
|
|
BigInteger.prototype.min = bnMin;
|
|
BigInteger.prototype.max = bnMax;
|
|
BigInteger.prototype.and = bnAnd;
|
|
BigInteger.prototype.or = bnOr;
|
|
BigInteger.prototype.xor = bnXor;
|
|
BigInteger.prototype.andNot = bnAndNot;
|
|
BigInteger.prototype.not = bnNot;
|
|
BigInteger.prototype.shiftLeft = bnShiftLeft;
|
|
BigInteger.prototype.shiftRight = bnShiftRight;
|
|
BigInteger.prototype.getLowestSetBit = bnGetLowestSetBit;
|
|
BigInteger.prototype.bitCount = bnBitCount;
|
|
BigInteger.prototype.testBit = bnTestBit;
|
|
BigInteger.prototype.setBit = bnSetBit;
|
|
BigInteger.prototype.clearBit = bnClearBit;
|
|
BigInteger.prototype.flipBit = bnFlipBit;
|
|
BigInteger.prototype.add = bnAdd;
|
|
BigInteger.prototype.subtract = bnSubtract;
|
|
BigInteger.prototype.multiply = bnMultiply;
|
|
BigInteger.prototype.divide = bnDivide;
|
|
BigInteger.prototype.remainder = bnRemainder;
|
|
BigInteger.prototype.divideAndRemainder = bnDivideAndRemainder;
|
|
BigInteger.prototype.modPow = bnModPow;
|
|
BigInteger.prototype.modInverse = bnModInverse;
|
|
BigInteger.prototype.pow = bnPow;
|
|
BigInteger.prototype.gcd = bnGCD;
|
|
BigInteger.prototype.isProbablePrime = bnIsProbablePrime;
|
|
|
|
// JSBN-specific extension
|
|
BigInteger.prototype.square = bnSquare;
|
|
|
|
// Expose the Barrett function
|
|
BigInteger.prototype.Barrett = Barrett;
|
|
|
|
// BigInteger interfaces not implemented in jsbn:
|
|
|
|
// BigInteger(int signum, byte[] magnitude)
|
|
// double doubleValue()
|
|
// float floatValue()
|
|
// int hashCode()
|
|
// long longValue()
|
|
// static BigInteger valueOf(long val)
|
|
|
|
// Random number generator - requires a PRNG backend, e.g. prng4.js
|
|
|
|
// For best results, put code like
|
|
// <body onClick='rng_seed_time();' onKeyPress='rng_seed_time();'>
|
|
// in your main HTML document.
|
|
|
|
var rng_state;
|
|
var rng_pool;
|
|
var rng_pptr;
|
|
|
|
// Mix in a 32-bit integer into the pool
|
|
function rng_seed_int(x) {
|
|
rng_pool[rng_pptr++] ^= x & 255;
|
|
rng_pool[rng_pptr++] ^= (x >> 8) & 255;
|
|
rng_pool[rng_pptr++] ^= (x >> 16) & 255;
|
|
rng_pool[rng_pptr++] ^= (x >> 24) & 255;
|
|
if (rng_pptr >= rng_psize) rng_pptr -= rng_psize;
|
|
}
|
|
|
|
// Mix in the current time (w/milliseconds) into the pool
|
|
function rng_seed_time() {
|
|
rng_seed_int(new Date().getTime());
|
|
}
|
|
|
|
// Initialize the pool with junk if needed.
|
|
if (rng_pool == null) {
|
|
rng_pool = new Array();
|
|
rng_pptr = 0;
|
|
var t;
|
|
if (typeof window !== "undefined" && window.crypto) {
|
|
if (window.crypto.getRandomValues) {
|
|
// Use webcrypto if available
|
|
var ua = new Uint8Array(32);
|
|
window.crypto.getRandomValues(ua);
|
|
for (t = 0; t < 32; ++t) rng_pool[rng_pptr++] = ua[t];
|
|
} else if (navigator.appName == "Netscape" && navigator.appVersion < "5") {
|
|
// Extract entropy (256 bits) from NS4 RNG if available
|
|
var z = window.crypto.random(32);
|
|
for (t = 0; t < z.length; ++t) rng_pool[rng_pptr++] = z.charCodeAt(t) & 255;
|
|
}
|
|
}
|
|
while (rng_pptr < rng_psize) {
|
|
// extract some randomness from Math.random()
|
|
t = Math.floor(65536 * Math.random());
|
|
rng_pool[rng_pptr++] = t >>> 8;
|
|
rng_pool[rng_pptr++] = t & 255;
|
|
}
|
|
rng_pptr = 0;
|
|
rng_seed_time();
|
|
//rng_seed_int(window.screenX);
|
|
//rng_seed_int(window.screenY);
|
|
}
|
|
|
|
function rng_get_byte() {
|
|
if (rng_state == null) {
|
|
rng_seed_time();
|
|
rng_state = prng_newstate();
|
|
rng_state.init(rng_pool);
|
|
for (rng_pptr = 0; rng_pptr < rng_pool.length; ++rng_pptr) rng_pool[rng_pptr] = 0;
|
|
rng_pptr = 0;
|
|
//rng_pool = null;
|
|
}
|
|
// TODO: allow reseeding after first request
|
|
return rng_state.next();
|
|
}
|
|
|
|
function rng_get_bytes(ba) {
|
|
var i;
|
|
for (i = 0; i < ba.length; ++i) ba[i] = rng_get_byte();
|
|
}
|
|
|
|
export function SecureRandom() {}
|
|
|
|
SecureRandom.prototype.nextBytes = rng_get_bytes;
|
|
|
|
// prng4.js - uses Arcfour as a PRNG
|
|
|
|
function Arcfour() {
|
|
this.i = 0;
|
|
this.j = 0;
|
|
this.S = new Array();
|
|
}
|
|
|
|
// Initialize arcfour context from key, an array of ints, each from [0..255]
|
|
function ARC4init(key) {
|
|
var i, j, t;
|
|
for (i = 0; i < 256; ++i) this.S[i] = i;
|
|
j = 0;
|
|
for (i = 0; i < 256; ++i) {
|
|
j = (j + this.S[i] + key[i % key.length]) & 255;
|
|
t = this.S[i];
|
|
this.S[i] = this.S[j];
|
|
this.S[j] = t;
|
|
}
|
|
this.i = 0;
|
|
this.j = 0;
|
|
}
|
|
|
|
function ARC4next() {
|
|
var t;
|
|
this.i = (this.i + 1) & 255;
|
|
this.j = (this.j + this.S[this.i]) & 255;
|
|
t = this.S[this.i];
|
|
this.S[this.i] = this.S[this.j];
|
|
this.S[this.j] = t;
|
|
return this.S[(t + this.S[this.i]) & 255];
|
|
}
|
|
|
|
Arcfour.prototype.init = ARC4init;
|
|
Arcfour.prototype.next = ARC4next;
|
|
|
|
// Plug in your RNG constructor here
|
|
function prng_newstate() {
|
|
return new Arcfour();
|
|
}
|
|
|
|
// Pool size must be a multiple of 4 and greater than 32.
|
|
// An array of bytes the size of the pool will be passed to init()
|
|
var rng_psize = 256;
|