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mail/src/lib/sjcl/ecc.js

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sjcl.ecc = {};
/**
* Represents a point on a curve in affine coordinates.
* @constructor
* @param {sjcl.ecc.curve} curve The curve that this point lies on.
* @param {bigInt} x The x coordinate.
* @param {bigInt} y The y coordinate.
*/
sjcl.ecc.point = function(curve,x,y) {
if (x === undefined) {
this.isIdentity = true;
} else {
this.x = x;
this.y = y;
this.isIdentity = false;
}
this.curve = curve;
};
sjcl.ecc.point.prototype = {
toJac: function() {
return new sjcl.ecc.pointJac(this.curve, this.x, this.y, new this.curve.field(1));
},
mult: function(k) {
return this.toJac().mult(k, this).toAffine();
},
/**
* Multiply this point by k, added to affine2*k2, and return the answer in Jacobian coordinates.
* @param {bigInt} k The coefficient to multiply this by.
* @param {bigInt} k2 The coefficient to multiply affine2 this by.
* @param {sjcl.ecc.point} affine The other point in affine coordinates.
* @return {sjcl.ecc.pointJac} The result of the multiplication and addition, in Jacobian coordinates.
*/
mult2: function(k, k2, affine2) {
return this.toJac().mult2(k, this, k2, affine2).toAffine();
},
multiples: function() {
var m, i, j;
if (this._multiples === undefined) {
j = this.toJac().doubl();
m = this._multiples = [new sjcl.ecc.point(this.curve), this, j.toAffine()];
for (i=3; i<16; i++) {
j = j.add(this);
m.push(j.toAffine());
}
}
return this._multiples;
},
isValid: function() {
return this.y.square().equals(this.curve.b.add(this.x.mul(this.curve.a.add(this.x.square()))));
},
toBits: function() {
return sjcl.bitArray.concat(this.x.toBits(), this.y.toBits());
}
};
/**
* Represents a point on a curve in Jacobian coordinates. Coordinates can be specified as bigInts or strings (which
* will be converted to bigInts).
*
* @constructor
* @param {bigInt/string} x The x coordinate.
* @param {bigInt/string} y The y coordinate.
* @param {bigInt/string} z The z coordinate.
* @param {sjcl.ecc.curve} curve The curve that this point lies on.
*/
sjcl.ecc.pointJac = function(curve, x, y, z) {
if (x === undefined) {
this.isIdentity = true;
} else {
this.x = x;
this.y = y;
this.z = z;
this.isIdentity = false;
}
this.curve = curve;
};
sjcl.ecc.pointJac.prototype = {
/**
* Adds S and T and returns the result in Jacobian coordinates. Note that S must be in Jacobian coordinates and T must be in affine coordinates.
* @param {sjcl.ecc.pointJac} S One of the points to add, in Jacobian coordinates.
* @param {sjcl.ecc.point} T The other point to add, in affine coordinates.
* @return {sjcl.ecc.pointJac} The sum of the two points, in Jacobian coordinates.
*/
add: function(T) {
var S = this, sz2, c, d, c2, x1, x2, x, y1, y2, y, z;
if (S.curve !== T.curve) {
throw("sjcl.ecc.add(): Points must be on the same curve to add them!");
}
if (S.isIdentity) {
return T.toJac();
} else if (T.isIdentity) {
return S;
}
sz2 = S.z.square();
c = T.x.mul(sz2).subM(S.x);
if (c.equals(0)) {
if (S.y.equals(T.y.mul(sz2.mul(S.z)))) {
// same point
return S.doubl();
} else {
// inverses
return new sjcl.ecc.pointJac(S.curve);
}
}
d = T.y.mul(sz2.mul(S.z)).subM(S.y);
c2 = c.square();
x1 = d.square();
x2 = c.square().mul(c).addM( S.x.add(S.x).mul(c2) );
x = x1.subM(x2);
y1 = S.x.mul(c2).subM(x).mul(d);
y2 = S.y.mul(c.square().mul(c));
y = y1.subM(y2);
z = S.z.mul(c);
return new sjcl.ecc.pointJac(this.curve,x,y,z);
},
/**
* doubles this point.
* @return {sjcl.ecc.pointJac} The doubled point.
*/
doubl: function() {
if (this.isIdentity) { return this; }
var
y2 = this.y.square(),
a = y2.mul(this.x.mul(4)),
b = y2.square().mul(8),
z2 = this.z.square(),
c = this.x.sub(z2).mul(3).mul(this.x.add(z2)),
x = c.square().subM(a).subM(a),
y = a.sub(x).mul(c).subM(b),
z = this.y.add(this.y).mul(this.z);
return new sjcl.ecc.pointJac(this.curve, x, y, z);
},
/**
* Returns a copy of this point converted to affine coordinates.
* @return {sjcl.ecc.point} The converted point.
*/
toAffine: function() {
if (this.isIdentity || this.z.equals(0)) {
return new sjcl.ecc.point(this.curve);
}
var zi = this.z.inverse(), zi2 = zi.square();
return new sjcl.ecc.point(this.curve, this.x.mul(zi2).fullReduce(), this.y.mul(zi2.mul(zi)).fullReduce());
},
/**
* Multiply this point by k and return the answer in Jacobian coordinates.
* @param {bigInt} k The coefficient to multiply by.
* @param {sjcl.ecc.point} affine This point in affine coordinates.
* @return {sjcl.ecc.pointJac} The result of the multiplication, in Jacobian coordinates.
*/
mult: function(k, affine) {
if (typeof(k) === "number") {
k = [k];
} else if (k.limbs !== undefined) {
k = k.normalize().limbs;
}
var i, j, out = new sjcl.ecc.point(this.curve).toJac(), multiples = affine.multiples();
for (i=k.length-1; i>=0; i--) {
for (j=sjcl.bn.prototype.radix-4; j>=0; j-=4) {
out = out.doubl().doubl().doubl().doubl().add(multiples[k[i]>>j & 0xF]);
}
}
return out;
},
/**
* Multiply this point by k, added to affine2*k2, and return the answer in Jacobian coordinates.
* @param {bigInt} k The coefficient to multiply this by.
* @param {sjcl.ecc.point} affine This point in affine coordinates.
* @param {bigInt} k2 The coefficient to multiply affine2 this by.
* @param {sjcl.ecc.point} affine The other point in affine coordinates.
* @return {sjcl.ecc.pointJac} The result of the multiplication and addition, in Jacobian coordinates.
*/
mult2: function(k1, affine, k2, affine2) {
if (typeof(k1) === "number") {
k1 = [k1];
} else if (k1.limbs !== undefined) {
k1 = k1.normalize().limbs;
}
if (typeof(k2) === "number") {
k2 = [k2];
} else if (k2.limbs !== undefined) {
k2 = k2.normalize().limbs;
}
var i, j, out = new sjcl.ecc.point(this.curve).toJac(), m1 = affine.multiples(),
m2 = affine2.multiples(), l1, l2;
for (i=Math.max(k1.length,k2.length)-1; i>=0; i--) {
l1 = k1[i] | 0;
l2 = k2[i] | 0;
for (j=sjcl.bn.prototype.radix-4; j>=0; j-=4) {
out = out.doubl().doubl().doubl().doubl().add(m1[l1>>j & 0xF]).add(m2[l2>>j & 0xF]);
}
}
return out;
},
isValid: function() {
var z2 = this.z.square(), z4 = z2.square(), z6 = z4.mul(z2);
return this.y.square().equals(
this.curve.b.mul(z6).add(this.x.mul(
this.curve.a.mul(z4).add(this.x.square()))));
}
};
/**
* Construct an elliptic curve. Most users will not use this and instead start with one of the NIST curves defined below.
*
* @constructor
* @param {bigInt} p The prime modulus.
* @param {bigInt} r The prime order of the curve.
* @param {bigInt} a The constant a in the equation of the curve y^2 = x^3 + ax + b (for NIST curves, a is always -3).
* @param {bigInt} x The x coordinate of a base point of the curve.
* @param {bigInt} y The y coordinate of a base point of the curve.
*/
sjcl.ecc.curve = function(Field, r, a, b, x, y) {
this.field = Field;
this.r = Field.prototype.modulus.sub(r);
this.a = new Field(a);
this.b = new Field(b);
this.G = new sjcl.ecc.point(this, new Field(x), new Field(y));
};
sjcl.ecc.curve.prototype.fromBits = function (bits) {
var w = sjcl.bitArray, l = this.field.prototype.exponent + 7 & -8,
p = new sjcl.ecc.point(this, this.field.fromBits(w.bitSlice(bits, 0, l)),
this.field.fromBits(w.bitSlice(bits, l, 2*l)));
if (!p.isValid()) {
throw new sjcl.exception.corrupt("not on the curve!");
}
return p;
};
sjcl.ecc.curves = {
c192: new sjcl.ecc.curve(
sjcl.bn.prime.p192,
"0x662107c8eb94364e4b2dd7ce",
-3,
"0x64210519e59c80e70fa7e9ab72243049feb8deecc146b9b1",
"0x188da80eb03090f67cbf20eb43a18800f4ff0afd82ff1012",
"0x07192b95ffc8da78631011ed6b24cdd573f977a11e794811"),
c224: new sjcl.ecc.curve(
sjcl.bn.prime.p224,
"0xe95c1f470fc1ec22d6baa3a3d5c4",
-3,
"0xb4050a850c04b3abf54132565044b0b7d7bfd8ba270b39432355ffb4",
"0xb70e0cbd6bb4bf7f321390b94a03c1d356c21122343280d6115c1d21",
"0xbd376388b5f723fb4c22dfe6cd4375a05a07476444d5819985007e34"),
c256: new sjcl.ecc.curve(
sjcl.bn.prime.p256,
"0x4319055358e8617b0c46353d039cdaae",
-3,
"0x5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b",
"0x6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296",
"0x4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5"),
c384: new sjcl.ecc.curve(
sjcl.bn.prime.p384,
"0x389cb27e0bc8d21fa7e5f24cb74f58851313e696333ad68c",
-3,
"0xb3312fa7e23ee7e4988e056be3f82d19181d9c6efe8141120314088f5013875ac656398d8a2ed19d2a85c8edd3ec2aef",
"0xaa87ca22be8b05378eb1c71ef320ad746e1d3b628ba79b9859f741e082542a385502f25dbf55296c3a545e3872760ab7",
"0x3617de4a96262c6f5d9e98bf9292dc29f8f41dbd289a147ce9da3113b5f0b8c00a60b1ce1d7e819d7a431d7c90ea0e5f")
};
/* Diffie-Hellman-like public-key system */
sjcl.ecc._dh = function(cn) {
sjcl.ecc[cn] = {
/** @constructor */
publicKey: function(curve, point) {
this._curve = curve;
this._curveBitLength = curve.r.bitLength();
if (point instanceof Array) {
this._point = curve.fromBits(point);
} else {
this._point = point;
}
this.get = function() {
var pointbits = this._point.toBits();
var len = sjcl.bitArray.bitLength(pointbits);
var x = sjcl.bitArray.bitSlice(pointbits, 0, len/2);
var y = sjcl.bitArray.bitSlice(pointbits, len/2);
return { x: x, y: y };
}
},
/** @constructor */
secretKey: function(curve, exponent) {
this._curve = curve;
this._curveBitLength = curve.r.bitLength();
this._exponent = exponent;
this.get = function() {
return this._exponent.toBits();
}
},
/** @constructor */
generateKeys: function(curve, paranoia, sec) {
if (curve === undefined) {
curve = 256;
}
if (typeof curve === "number") {
curve = sjcl.ecc.curves['c'+curve];
if (curve === undefined) {
throw new sjcl.exception.invalid("no such curve");
}
}
if (sec === undefined) {
var sec = sjcl.bn.random(curve.r, paranoia);
}
var pub = curve.G.mult(sec);
return { pub: new sjcl.ecc[cn].publicKey(curve, pub),
sec: new sjcl.ecc[cn].secretKey(curve, sec) };
}
};
};
sjcl.ecc._dh("elGamal");
sjcl.ecc.elGamal.publicKey.prototype = {
kem: function(paranoia) {
var sec = sjcl.bn.random(this._curve.r, paranoia),
tag = this._curve.G.mult(sec).toBits(),
key = sjcl.hash.sha256.hash(this._point.mult(sec).toBits());
return { key: key, tag: tag };
}
};
sjcl.ecc.elGamal.secretKey.prototype = {
unkem: function(tag) {
return sjcl.hash.sha256.hash(this._curve.fromBits(tag).mult(this._exponent).toBits());
},
dh: function(pk) {
return sjcl.hash.sha256.hash(pk._point.mult(this._exponent).toBits());
}
};
sjcl.ecc._dh("ecdsa");
sjcl.ecc.ecdsa.secretKey.prototype = {
sign: function(hash, paranoia, fakeLegacyVersion, fixedKForTesting) {
if (sjcl.bitArray.bitLength(hash) > this._curveBitLength) {
hash = sjcl.bitArray.clamp(hash, this._curveBitLength);
}
var R = this._curve.r,
l = R.bitLength(),
k = fixedKForTesting || sjcl.bn.random(R.sub(1), paranoia).add(1),
r = this._curve.G.mult(k).x.mod(R),
ss = sjcl.bn.fromBits(hash).add(r.mul(this._exponent)),
s = fakeLegacyVersion ? ss.inverseMod(R).mul(k).mod(R)
: ss.mul(k.inverseMod(R)).mod(R);
return sjcl.bitArray.concat(r.toBits(l), s.toBits(l));
}
};
sjcl.ecc.ecdsa.publicKey.prototype = {
verify: function(hash, rs, fakeLegacyVersion) {
if (sjcl.bitArray.bitLength(hash) > this._curveBitLength) {
hash = sjcl.bitArray.clamp(hash, this._curveBitLength);
}
var w = sjcl.bitArray,
R = this._curve.r,
l = this._curveBitLength,
r = sjcl.bn.fromBits(w.bitSlice(rs,0,l)),
ss = sjcl.bn.fromBits(w.bitSlice(rs,l,2*l)),
s = fakeLegacyVersion ? ss : ss.inverseMod(R),
hG = sjcl.bn.fromBits(hash).mul(s).mod(R),
hA = r.mul(s).mod(R),
r2 = this._curve.G.mult2(hG, hA, this._point).x;
if (r.equals(0) || ss.equals(0) || r.greaterEquals(R) || ss.greaterEquals(R) || !r2.equals(r)) {
if (fakeLegacyVersion === undefined) {
return this.verify(hash, rs, true);
} else {
throw (new sjcl.exception.corrupt("signature didn't check out"));
}
}
return true;
}
};
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