public EllipticCurve Twist(EllipticCurve e)
{
Field f = e.Field;
FieldElement b = f.Negate(e.B);
return(new EllipticCurve(f, e.A, b));
}
/**
* Define the parameters for computing Tate paring
* @param curve the elliptic curve on which G1 is defined
* @param groupOrder the order of G1
* @param coFactor a BigInteger such that {@code coFactor*groupOrder = #E}, where #E is the number of points on the curve.
*/
public TatePairing(EllipticCurve curve, BigInt groupOrder, BigInt coFactor)
{
this.ec = curve;
this.field = curve.Field;
this.order = groupOrder;
//(p+1)/r
this.finalExponent = (this.field.GetOrder().Add(BigInt.ONE)).Divide(groupOrder);
this.cof = coFactor;
this.twisted = Twist(curve);
this.gt = new ComplexField((Fp)this.field);
}
public static TatePairing nssTate()
{
BigInt p = new BigInt("8D5006492B424C09D2FEBE717EE382A57EBE3A352FC383E1AC79F21DDB43706CFB192333A7E9CF644636332E83D90A1E56EFBAE8715AA07883483F8267E80ED3", 16);
Field field = new Fp(p);
//order =2^159+2^17+1
BigInt orderOfGroup = new BigInt("8000000000000000000000000000000000020001", 16);
//BigInt orderOfE= new BigInt("11711338024714009669995700965425239711927177698599625717955894184681899877662611539569996945969293708404400344208273812850399351303651875378098503534075638");
//co-factor
BigInt cof = new BigInt("11AA00C9256849813A5FD7CE2FDC7054AFD7809E7F7FD948C4B9C1C1E76FFEFF4ECAB83C950112DECB41D6EDA", 16);
FieldElement a4 = field.Negate(BigInt.ValueOf(3));
FieldElement a6 = new BigInt("609993837367998001C95B87A6BA872135E26906DB4C192D6E038486177A3EDF6C50B9BB20DF881F2BD05842F598F3E037B362DBF89F0A62E5871D41D951BF8E", 16);
EllipticCurve ec = new EllipticCurve(field, field.GetZero(), field.GetZero(), field.GetZero(), a4, a6);
return(new TatePairing(ec, orderOfGroup, cof));
}
public static TatePairing ssTate()
{
BigInt p = new BigInt("8BA2A5229BD9C57CFC8ACEC76DFDBF3E3E1952C6B3193ECF5C571FB502FC5DF410F9267E9F2A605BB0F76F52A79E8043BF4AF0EF2E9FA78B0F1E2CDFC4E8549B", 16);
Field field = new Fp(p);
BigInt orderOfGroup = new BigInt("8000000000000000000000000000000000020001", 16);
BigInt cof = new BigInt("117454A4537B38AF9F9159D8EDBFB7E7C7C2E48760E930A461D5F451F9D9210DC70095F4B241FF57F1BB0549C", 16);
//curve
//y^2=x^3+x
FieldElement a = field.GetOne();
FieldElement b = field.GetZero();
EllipticCurve ec = new EllipticCurve(field, a, b);
return(new TatePairing(ec, orderOfGroup, cof));
}
public static TatePairing ssTate2()
{
BigInt p = new BigInt("8780710799663312522437781984754049815806883199414208211028653399266475630880222957078625179422662221423155858769582317459277713367317481324925129998224791", 10);
Field field = new Fp(p);
BigInt orderOfGroup = new BigInt("730750818665451621361119245571504901405976559617", 10);
BigInt cof = new BigInt("12016012264891146079388821366740534204802954401251311822919615131047207289359704531102844802183906537786776", 10);
//curve
//y^2=x^3+x
FieldElement a4 = field.GetOne();
FieldElement a6 = field.GetZero();
EllipticCurve ec = new EllipticCurve(field, field.GetZero(), field.GetZero(), field.GetZero(), a4, a6);
return(new TatePairing(ec, orderOfGroup, cof));
}
