/** * Adds another <code>ECPoints.F2m</code> to <code>this</code> without * checking if both points are on the same curve. Used by multiplication * algorithms, because there all points are a multiple of the same point * and hence the checks can be omitted. * @param b The other <code>ECPoints.F2m</code> to add to * <code>this</code>. * @return <code>this + b</code> */ internal F2mPoint AddSimple(F2mPoint b) { if (this.IsInfinity) { return(b); } if (b.IsInfinity) { return(this); } F2mFieldElement x2 = (F2mFieldElement)b.X; F2mFieldElement y2 = (F2mFieldElement)b.Y; // Check if b == this or b == -this if (this.x.Equals(x2)) { // this == b, i.e. this must be doubled if (this.y.Equals(y2)) { return((F2mPoint)this.Twice()); } // this = -other, i.e. the result is the point at infinity return((F2mPoint)this.curve.Infinity); } ECFieldElement xSum = this.x.Add(x2); F2mFieldElement lambda = (F2mFieldElement)(this.y.Add(y2)).Divide(xSum); F2mFieldElement x3 = (F2mFieldElement)lambda.Square().Add(lambda).Add(xSum).Add(this.curve.A); F2mFieldElement y3 = (F2mFieldElement)lambda.Multiply(this.x.Add(x3)).Add(x3).Add(this.y); return(new F2mPoint(curve, x3, y3, withCompression)); }
/* (non-Javadoc) * @see Org.BouncyCastle.Math.EC.ECPoint#twice() */ public override ECPoint Twice() { // Twice identity element (point at infinity) is identity if (this.IsInfinity) { return(this); } // if x1 == 0, then (x1, y1) == (x1, x1 + y1) // and hence this = -this and thus 2(x1, y1) == infinity if (this.x.ToBigInteger().Sign == 0) { return(this.curve.Infinity); } F2mFieldElement lambda = (F2mFieldElement)this.x.Add(this.y.Divide(this.x)); F2mFieldElement x2 = (F2mFieldElement)lambda.Square().Add(lambda).Add(this.curve.A); ECFieldElement ONE = this.curve.FromBigInteger(BigInteger.One); F2mFieldElement y2 = (F2mFieldElement)this.x.Square().Add( x2.Multiply(lambda.Add(ONE))); return(new F2mPoint(this.curve, x2, y2, withCompression)); }