380 lines
12 KiB
JavaScript
380 lines
12 KiB
JavaScript
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;
|
|
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;
|
|
}
|
|
|
|
var
|
|
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);
|
|
}
|
|
}
|
|
|
|
var
|
|
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);
|
|
var U = new sjcl.ecc.pointJac(this.curve,x,y,z);
|
|
if (!U.isValid()) { throw "FOOOOOOOO"; }
|
|
return U;
|
|
},
|
|
|
|
/**
|
|
* 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] = {
|
|
publicKey: function(curve, point) {
|
|
this._curve = curve;
|
|
if (point instanceof Array) {
|
|
this._point = curve.fromBits(point);
|
|
} else {
|
|
this._point = point;
|
|
}
|
|
},
|
|
|
|
secretKey: function(curve, exponent) {
|
|
this._curve = curve;
|
|
this._exponent = exponent;
|
|
},
|
|
|
|
generateKeys: function(curve, paranoia) {
|
|
if (typeof curve == "number") {
|
|
curve = sjcl.ecc.curves['c'+curve];
|
|
if (curve === undefined) {
|
|
throw new sjcl.exception.invalid("no such curve");
|
|
}
|
|
}
|
|
var sec = sjcl.bn.random(curve.r, paranoia), 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());
|
|
}
|
|
};
|
|
|
|
sjcl.ecc._dh("dsa");
|
|
|
|
sjcl.ecc.dsa.secretKey.prototype = {
|
|
sign: function(hash, paranoia) {
|
|
var R = this._curve.r,
|
|
l = R.bitLength(),
|
|
k = kkkk = sjcl.bn.random(R.sub(1), paranoia).add(1),
|
|
r = this._curve.G.mult(k).x.mod(R),
|
|
s = sjcl.bn.fromBits(hash).add(r.mul(this._exponent)).inverseMod(R).mul(kkkk).mod(R);
|
|
return sjcl.bitArray.concat(r.toBits(l), s.toBits(l));
|
|
}
|
|
};
|
|
|
|
sjcl.ecc.dsa.publicKey.prototype = {
|
|
verify: function(hash, rs) {
|
|
var w = sjcl.bitArray,
|
|
R = this._curve.r,
|
|
l = R.bitLength(),
|
|
r = sjcl.bn.fromBits(w.bitSlice(rs,0,l)),
|
|
s = sjcl.bn.fromBits(w.bitSlice(rs,l,2*l)),
|
|
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,
|
|
corrupt = sjcl.exception.corrupt;
|
|
|
|
if (r.equals(0) || s.equals(0) || r.greaterEquals(R) || s.greaterEquals(R) || !r2.equals(r)) {
|
|
throw (new corrupt("signature didn't check out"));
|
|
}
|
|
return true;
|
|
}
|
|
}
|