mirror of https://github.com/moparisthebest/mail
553 lines
14 KiB
JavaScript
553 lines
14 KiB
JavaScript
/**
|
|
* @constructor
|
|
* Constructs a new bignum from another bignum, a number or a hex string.
|
|
*/
|
|
sjcl.bn = function(it) {
|
|
this.initWith(it);
|
|
};
|
|
|
|
sjcl.bn.prototype = {
|
|
radix: 24,
|
|
maxMul: 8,
|
|
_class: sjcl.bn,
|
|
|
|
copy: function() {
|
|
return new this._class(this);
|
|
},
|
|
|
|
/**
|
|
* Initializes this with it, either as a bn, a number, or a hex string.
|
|
*/
|
|
initWith: function(it) {
|
|
var i=0, k, n, l;
|
|
switch(typeof it) {
|
|
case "object":
|
|
this.limbs = it.limbs.slice(0);
|
|
break;
|
|
|
|
case "number":
|
|
this.limbs = [it];
|
|
this.normalize();
|
|
break;
|
|
|
|
case "string":
|
|
it = it.replace(/^0x/, '');
|
|
this.limbs = [];
|
|
// hack
|
|
k = this.radix / 4;
|
|
for (i=0; i < it.length; i+=k) {
|
|
this.limbs.push(parseInt(it.substring(Math.max(it.length - i - k, 0), it.length - i),16));
|
|
}
|
|
break;
|
|
|
|
default:
|
|
this.limbs = [0];
|
|
}
|
|
return this;
|
|
},
|
|
|
|
/**
|
|
* Returns true if "this" and "that" are equal. Calls fullReduce().
|
|
* Equality test is in constant time.
|
|
*/
|
|
equals: function(that) {
|
|
if (typeof that === "number") { that = new this._class(that); }
|
|
var difference = 0, i;
|
|
this.fullReduce();
|
|
that.fullReduce();
|
|
for (i = 0; i < this.limbs.length || i < that.limbs.length; i++) {
|
|
difference |= this.getLimb(i) ^ that.getLimb(i);
|
|
}
|
|
return (difference === 0);
|
|
},
|
|
|
|
/**
|
|
* Get the i'th limb of this, zero if i is too large.
|
|
*/
|
|
getLimb: function(i) {
|
|
return (i >= this.limbs.length) ? 0 : this.limbs[i];
|
|
},
|
|
|
|
/**
|
|
* Constant time comparison function.
|
|
* Returns 1 if this >= that, or zero otherwise.
|
|
*/
|
|
greaterEquals: function(that) {
|
|
if (typeof that === "number") { that = new this._class(that); }
|
|
var less = 0, greater = 0, i, a, b;
|
|
i = Math.max(this.limbs.length, that.limbs.length) - 1;
|
|
for (; i>= 0; i--) {
|
|
a = this.getLimb(i);
|
|
b = that.getLimb(i);
|
|
greater |= (b - a) & ~less;
|
|
less |= (a - b) & ~greater;
|
|
}
|
|
return (greater | ~less) >>> 31;
|
|
},
|
|
|
|
/**
|
|
* Convert to a hex string.
|
|
*/
|
|
toString: function() {
|
|
this.fullReduce();
|
|
var out="", i, s, l = this.limbs;
|
|
for (i=0; i < this.limbs.length; i++) {
|
|
s = l[i].toString(16);
|
|
while (i < this.limbs.length - 1 && s.length < 6) {
|
|
s = "0" + s;
|
|
}
|
|
out = s + out;
|
|
}
|
|
return "0x"+out;
|
|
},
|
|
|
|
/** this += that. Does not normalize. */
|
|
addM: function(that) {
|
|
if (typeof(that) !== "object") { that = new this._class(that); }
|
|
var i, l=this.limbs, ll=that.limbs;
|
|
for (i=l.length; i<ll.length; i++) {
|
|
l[i] = 0;
|
|
}
|
|
for (i=0; i<ll.length; i++) {
|
|
l[i] += ll[i];
|
|
}
|
|
return this;
|
|
},
|
|
|
|
/** this *= 2. Requires normalized; ends up normalized. */
|
|
doubleM: function() {
|
|
var i, carry=0, tmp, r=this.radix, m=this.radixMask, l=this.limbs;
|
|
for (i=0; i<l.length; i++) {
|
|
tmp = l[i];
|
|
tmp = tmp+tmp+carry;
|
|
l[i] = tmp & m;
|
|
carry = tmp >> r;
|
|
}
|
|
if (carry) {
|
|
l.push(carry);
|
|
}
|
|
return this;
|
|
},
|
|
|
|
/** this /= 2, rounded down. Requires normalized; ends up normalized. */
|
|
halveM: function() {
|
|
var i, carry=0, tmp, r=this.radix, l=this.limbs;
|
|
for (i=l.length-1; i>=0; i--) {
|
|
tmp = l[i];
|
|
l[i] = (tmp+carry)>>1;
|
|
carry = (tmp&1) << r;
|
|
}
|
|
if (!l[l.length-1]) {
|
|
l.pop();
|
|
}
|
|
return this;
|
|
},
|
|
|
|
/** this -= that. Does not normalize. */
|
|
subM: function(that) {
|
|
if (typeof(that) !== "object") { that = new this._class(that); }
|
|
var i, l=this.limbs, ll=that.limbs;
|
|
for (i=l.length; i<ll.length; i++) {
|
|
l[i] = 0;
|
|
}
|
|
for (i=0; i<ll.length; i++) {
|
|
l[i] -= ll[i];
|
|
}
|
|
return this;
|
|
},
|
|
|
|
mod: function(that) {
|
|
var neg = !this.greaterEquals(new sjcl.bn(0));
|
|
|
|
that = new sjcl.bn(that).normalize(); // copy before we begin
|
|
var out = new sjcl.bn(this).normalize(), ci=0;
|
|
|
|
if (neg) out = (new sjcl.bn(0)).subM(out).normalize();
|
|
|
|
for (; out.greaterEquals(that); ci++) {
|
|
that.doubleM();
|
|
}
|
|
|
|
if (neg) out = that.sub(out).normalize();
|
|
|
|
for (; ci > 0; ci--) {
|
|
that.halveM();
|
|
if (out.greaterEquals(that)) {
|
|
out.subM(that).normalize();
|
|
}
|
|
}
|
|
return out.trim();
|
|
},
|
|
|
|
/** return inverse mod prime p. p must be odd. Binary extended Euclidean algorithm mod p. */
|
|
inverseMod: function(p) {
|
|
var a = new sjcl.bn(1), b = new sjcl.bn(0), x = new sjcl.bn(this), y = new sjcl.bn(p), tmp, i, nz=1;
|
|
|
|
if (!(p.limbs[0] & 1)) {
|
|
throw (new sjcl.exception.invalid("inverseMod: p must be odd"));
|
|
}
|
|
|
|
// invariant: y is odd
|
|
do {
|
|
if (x.limbs[0] & 1) {
|
|
if (!x.greaterEquals(y)) {
|
|
// x < y; swap everything
|
|
tmp = x; x = y; y = tmp;
|
|
tmp = a; a = b; b = tmp;
|
|
}
|
|
x.subM(y);
|
|
x.normalize();
|
|
|
|
if (!a.greaterEquals(b)) {
|
|
a.addM(p);
|
|
}
|
|
a.subM(b);
|
|
}
|
|
|
|
// cut everything in half
|
|
x.halveM();
|
|
if (a.limbs[0] & 1) {
|
|
a.addM(p);
|
|
}
|
|
a.normalize();
|
|
a.halveM();
|
|
|
|
// check for termination: x ?= 0
|
|
for (i=nz=0; i<x.limbs.length; i++) {
|
|
nz |= x.limbs[i];
|
|
}
|
|
} while(nz);
|
|
|
|
if (!y.equals(1)) {
|
|
throw (new sjcl.exception.invalid("inverseMod: p and x must be relatively prime"));
|
|
}
|
|
|
|
return b;
|
|
},
|
|
|
|
/** this + that. Does not normalize. */
|
|
add: function(that) {
|
|
return this.copy().addM(that);
|
|
},
|
|
|
|
/** this - that. Does not normalize. */
|
|
sub: function(that) {
|
|
return this.copy().subM(that);
|
|
},
|
|
|
|
/** this * that. Normalizes and reduces. */
|
|
mul: function(that) {
|
|
if (typeof(that) === "number") { that = new this._class(that); }
|
|
var i, j, a = this.limbs, b = that.limbs, al = a.length, bl = b.length, out = new this._class(), c = out.limbs, ai, ii=this.maxMul;
|
|
|
|
for (i=0; i < this.limbs.length + that.limbs.length + 1; i++) {
|
|
c[i] = 0;
|
|
}
|
|
for (i=0; i<al; i++) {
|
|
ai = a[i];
|
|
for (j=0; j<bl; j++) {
|
|
c[i+j] += ai * b[j];
|
|
}
|
|
|
|
if (!--ii) {
|
|
ii = this.maxMul;
|
|
out.cnormalize();
|
|
}
|
|
}
|
|
return out.cnormalize().reduce();
|
|
},
|
|
|
|
/** this ^ 2. Normalizes and reduces. */
|
|
square: function() {
|
|
return this.mul(this);
|
|
},
|
|
|
|
/** this ^ n. Uses square-and-multiply. Normalizes and reduces. */
|
|
power: function(l) {
|
|
if (typeof(l) === "number") {
|
|
l = [l];
|
|
} else if (l.limbs !== undefined) {
|
|
l = l.normalize().limbs;
|
|
}
|
|
var i, j, out = new this._class(1), pow = this;
|
|
|
|
for (i=0; i<l.length; i++) {
|
|
for (j=0; j<this.radix; j++) {
|
|
if (l[i] & (1<<j)) {
|
|
out = out.mul(pow);
|
|
}
|
|
pow = pow.square();
|
|
}
|
|
}
|
|
|
|
return out;
|
|
},
|
|
|
|
/** this * that mod N */
|
|
mulmod: function(that, N) {
|
|
return this.mod(N).mul(that.mod(N)).mod(N);
|
|
},
|
|
|
|
/** this ^ x mod N */
|
|
powermod: function(x, N) {
|
|
var result = new sjcl.bn(1), a = new sjcl.bn(this), k = new sjcl.bn(x);
|
|
while (true) {
|
|
if (k.limbs[0] & 1) { result = result.mulmod(a, N); }
|
|
k.halveM();
|
|
if (k.equals(0)) { break; }
|
|
a = a.mulmod(a, N);
|
|
}
|
|
return result.normalize().reduce();
|
|
},
|
|
|
|
trim: function() {
|
|
var l = this.limbs, p;
|
|
do {
|
|
p = l.pop();
|
|
} while (l.length && p === 0);
|
|
l.push(p);
|
|
return this;
|
|
},
|
|
|
|
/** Reduce mod a modulus. Stubbed for subclassing. */
|
|
reduce: function() {
|
|
return this;
|
|
},
|
|
|
|
/** Reduce and normalize. */
|
|
fullReduce: function() {
|
|
return this.normalize();
|
|
},
|
|
|
|
/** Propagate carries. */
|
|
normalize: function() {
|
|
var carry=0, i, pv = this.placeVal, ipv = this.ipv, l, m, limbs = this.limbs, ll = limbs.length, mask = this.radixMask;
|
|
for (i=0; i < ll || (carry !== 0 && carry !== -1); i++) {
|
|
l = (limbs[i]||0) + carry;
|
|
m = limbs[i] = l & mask;
|
|
carry = (l-m)*ipv;
|
|
}
|
|
if (carry === -1) {
|
|
limbs[i-1] -= this.placeVal;
|
|
}
|
|
return this;
|
|
},
|
|
|
|
/** Constant-time normalize. Does not allocate additional space. */
|
|
cnormalize: function() {
|
|
var carry=0, i, ipv = this.ipv, l, m, limbs = this.limbs, ll = limbs.length, mask = this.radixMask;
|
|
for (i=0; i < ll-1; i++) {
|
|
l = limbs[i] + carry;
|
|
m = limbs[i] = l & mask;
|
|
carry = (l-m)*ipv;
|
|
}
|
|
limbs[i] += carry;
|
|
return this;
|
|
},
|
|
|
|
/** Serialize to a bit array */
|
|
toBits: function(len) {
|
|
this.fullReduce();
|
|
len = len || this.exponent || this.bitLength();
|
|
var i = Math.floor((len-1)/24), w=sjcl.bitArray, e = (len + 7 & -8) % this.radix || this.radix,
|
|
out = [w.partial(e, this.getLimb(i))];
|
|
for (i--; i >= 0; i--) {
|
|
out = w.concat(out, [w.partial(Math.min(this.radix,len), this.getLimb(i))]);
|
|
len -= this.radix;
|
|
}
|
|
return out;
|
|
},
|
|
|
|
/** Return the length in bits, rounded up to the nearest byte. */
|
|
bitLength: function() {
|
|
this.fullReduce();
|
|
var out = this.radix * (this.limbs.length - 1),
|
|
b = this.limbs[this.limbs.length - 1];
|
|
for (; b; b >>>= 1) {
|
|
out ++;
|
|
}
|
|
return out+7 & -8;
|
|
}
|
|
};
|
|
|
|
/** @this { sjcl.bn } */
|
|
sjcl.bn.fromBits = function(bits) {
|
|
var Class = this, out = new Class(), words=[], w=sjcl.bitArray, t = this.prototype,
|
|
l = Math.min(this.bitLength || 0x100000000, w.bitLength(bits)), e = l % t.radix || t.radix;
|
|
|
|
words[0] = w.extract(bits, 0, e);
|
|
for (; e < l; e += t.radix) {
|
|
words.unshift(w.extract(bits, e, t.radix));
|
|
}
|
|
|
|
out.limbs = words;
|
|
return out;
|
|
};
|
|
|
|
|
|
|
|
sjcl.bn.prototype.ipv = 1 / (sjcl.bn.prototype.placeVal = Math.pow(2,sjcl.bn.prototype.radix));
|
|
sjcl.bn.prototype.radixMask = (1 << sjcl.bn.prototype.radix) - 1;
|
|
|
|
/**
|
|
* Creates a new subclass of bn, based on reduction modulo a pseudo-Mersenne prime,
|
|
* i.e. a prime of the form 2^e + sum(a * 2^b),where the sum is negative and sparse.
|
|
*/
|
|
sjcl.bn.pseudoMersennePrime = function(exponent, coeff) {
|
|
/** @constructor */
|
|
function p(it) {
|
|
this.initWith(it);
|
|
/*if (this.limbs[this.modOffset]) {
|
|
this.reduce();
|
|
}*/
|
|
}
|
|
|
|
var ppr = p.prototype = new sjcl.bn(), i, tmp, mo;
|
|
mo = ppr.modOffset = Math.ceil(tmp = exponent / ppr.radix);
|
|
ppr.exponent = exponent;
|
|
ppr.offset = [];
|
|
ppr.factor = [];
|
|
ppr.minOffset = mo;
|
|
ppr.fullMask = 0;
|
|
ppr.fullOffset = [];
|
|
ppr.fullFactor = [];
|
|
ppr.modulus = p.modulus = new sjcl.bn(Math.pow(2,exponent));
|
|
|
|
ppr.fullMask = 0|-Math.pow(2, exponent % ppr.radix);
|
|
|
|
for (i=0; i<coeff.length; i++) {
|
|
ppr.offset[i] = Math.floor(coeff[i][0] / ppr.radix - tmp);
|
|
ppr.fullOffset[i] = Math.ceil(coeff[i][0] / ppr.radix - tmp);
|
|
ppr.factor[i] = coeff[i][1] * Math.pow(1/2, exponent - coeff[i][0] + ppr.offset[i] * ppr.radix);
|
|
ppr.fullFactor[i] = coeff[i][1] * Math.pow(1/2, exponent - coeff[i][0] + ppr.fullOffset[i] * ppr.radix);
|
|
ppr.modulus.addM(new sjcl.bn(Math.pow(2,coeff[i][0])*coeff[i][1]));
|
|
ppr.minOffset = Math.min(ppr.minOffset, -ppr.offset[i]); // conservative
|
|
}
|
|
ppr._class = p;
|
|
ppr.modulus.cnormalize();
|
|
|
|
/** Approximate reduction mod p. May leave a number which is negative or slightly larger than p.
|
|
* @this {sjcl.bn}
|
|
*/
|
|
ppr.reduce = function() {
|
|
var i, k, l, mo = this.modOffset, limbs = this.limbs, aff, off = this.offset, ol = this.offset.length, fac = this.factor, ll;
|
|
|
|
i = this.minOffset;
|
|
while (limbs.length > mo) {
|
|
l = limbs.pop();
|
|
ll = limbs.length;
|
|
for (k=0; k<ol; k++) {
|
|
limbs[ll+off[k]] -= fac[k] * l;
|
|
}
|
|
|
|
i--;
|
|
if (!i) {
|
|
limbs.push(0);
|
|
this.cnormalize();
|
|
i = this.minOffset;
|
|
}
|
|
}
|
|
this.cnormalize();
|
|
|
|
return this;
|
|
};
|
|
|
|
/** @this {sjcl.bn} */
|
|
ppr._strongReduce = (ppr.fullMask === -1) ? ppr.reduce : function() {
|
|
var limbs = this.limbs, i = limbs.length - 1, k, l;
|
|
this.reduce();
|
|
if (i === this.modOffset - 1) {
|
|
l = limbs[i] & this.fullMask;
|
|
limbs[i] -= l;
|
|
for (k=0; k<this.fullOffset.length; k++) {
|
|
limbs[i+this.fullOffset[k]] -= this.fullFactor[k] * l;
|
|
}
|
|
this.normalize();
|
|
}
|
|
};
|
|
|
|
/** mostly constant-time, very expensive full reduction.
|
|
* @this {sjcl.bn}
|
|
*/
|
|
ppr.fullReduce = function() {
|
|
var greater, i;
|
|
// massively above the modulus, may be negative
|
|
|
|
this._strongReduce();
|
|
// less than twice the modulus, may be negative
|
|
|
|
this.addM(this.modulus);
|
|
this.addM(this.modulus);
|
|
this.normalize();
|
|
// probably 2-3x the modulus
|
|
|
|
this._strongReduce();
|
|
// less than the power of 2. still may be more than
|
|
// the modulus
|
|
|
|
// HACK: pad out to this length
|
|
for (i=this.limbs.length; i<this.modOffset; i++) {
|
|
this.limbs[i] = 0;
|
|
}
|
|
|
|
// constant-time subtract modulus
|
|
greater = this.greaterEquals(this.modulus);
|
|
for (i=0; i<this.limbs.length; i++) {
|
|
this.limbs[i] -= this.modulus.limbs[i] * greater;
|
|
}
|
|
this.cnormalize();
|
|
|
|
return this;
|
|
};
|
|
|
|
|
|
/** @this {sjcl.bn} */
|
|
ppr.inverse = function() {
|
|
return (this.power(this.modulus.sub(2)));
|
|
};
|
|
|
|
p.fromBits = sjcl.bn.fromBits;
|
|
|
|
return p;
|
|
};
|
|
|
|
// a small Mersenne prime
|
|
sjcl.bn.prime = {
|
|
p127: sjcl.bn.pseudoMersennePrime(127, [[0,-1]]),
|
|
|
|
// Bernstein's prime for Curve25519
|
|
p25519: sjcl.bn.pseudoMersennePrime(255, [[0,-19]]),
|
|
|
|
// NIST primes
|
|
p192: sjcl.bn.pseudoMersennePrime(192, [[0,-1],[64,-1]]),
|
|
p224: sjcl.bn.pseudoMersennePrime(224, [[0,1],[96,-1]]),
|
|
p256: sjcl.bn.pseudoMersennePrime(256, [[0,-1],[96,1],[192,1],[224,-1]]),
|
|
p384: sjcl.bn.pseudoMersennePrime(384, [[0,-1],[32,1],[96,-1],[128,-1]]),
|
|
p521: sjcl.bn.pseudoMersennePrime(521, [[0,-1]])
|
|
};
|
|
|
|
sjcl.bn.random = function(modulus, paranoia) {
|
|
if (typeof modulus !== "object") { modulus = new sjcl.bn(modulus); }
|
|
var words, i, l = modulus.limbs.length, m = modulus.limbs[l-1]+1, out = new sjcl.bn();
|
|
while (true) {
|
|
// get a sequence whose first digits make sense
|
|
do {
|
|
words = sjcl.random.randomWords(l, paranoia);
|
|
if (words[l-1] < 0) { words[l-1] += 0x100000000; }
|
|
} while (Math.floor(words[l-1] / m) === Math.floor(0x100000000 / m));
|
|
words[l-1] %= m;
|
|
|
|
// mask off all the limbs
|
|
for (i=0; i<l-1; i++) {
|
|
words[i] &= modulus.radixMask;
|
|
}
|
|
|
|
// check the rest of the digitssj
|
|
out.limbs = words;
|
|
if (!out.greaterEquals(modulus)) {
|
|
return out;
|
|
}
|
|
}
|
|
};
|
|
|