mcl/java/java.md

JNI for mcl (experimental)

This library provides functionality to compute the optimal ate pairing over Barreto-Naehrig (BN) curves.

Initialization

Load the library mcl_bn256.

import com.herumi.mcl.*;

System.loadLibrary("mcl_bn256");

Classes

• G1 ; The cyclic group instantiated as E(Fp)[r] where where r = p + 1 - t.
• G2 ; The cyclic group instantiated as the inverse image of E'(Fp^2)[r].
• GT ; The cyclic group in the image of the optimal ate pairing.
  • e : G2 x G1 -> GT
• Fr ; The finite field with characteristic r.

Methods and Functions

Fr

• Fr::setInt(int x) ; set by x
• Fr::setStr(String str) ; set by str such as "123", "0xfff", etc.
• Fr::setRand() ; randomly set
• Bn256.neg(Fr y, Fr x) ; y = -x
• Bn256.add(Fr z, Fr x, Fr y) ; z = x + y
• Bn256.sub(Fr z, Fr x, Fr y) ; z = x - y
• Bn256.mul(Fr z, Fr x, Fr y) ; z = x * y
• Bn256.div(Fr z, Fr x, Fr y) ; z = x / y

G1

• G1::set(String x, String y) ; set by (x, y)
• G1::hashAndMapToG1(String m) ; take SHA-256 of m and map it to an element of G1
• G1::setStr(String str) ; set by the result of toString() method
• Bn256.neg(G1 y, G1 x) ; y = -x
• Bn256.dbl(G1 y, G1 x) ; y = 2x
• Bn256.add(G1 z, G1 x, G1 y) ; z = x + y
• Bn256.sub(G1 z, G1 x, G1 y) ; z = x - y
• Bn256.mul(G1 z, G1 x, Fr y) ; z = x * y

G2

• G2::set(String xa, String xb, String ya, String yb) ; set by ((xa, xb), (ya, yb))
• G2::setStr(String str) ; set by the result of toString() method
• Bn256.neg(G2 y, G2 x) ; y = -x
• Bn256.dbl(G2 y, G2 x) ; y = 2x
• Bn256.add(G2 z, G2 x, G2 y) ; z = x + y
• Bn256.sub(G2 z, G2 x, G2 y) ; z = x - y
• Bn256.mul(G2 z, G2 x, Fr y) ; z = x * y

GT

• GT::setStr(String str) ; set by the result of toString() method
• Bn256.mul(GT z, GT x, GT y) ; z = x * y
• Bn256.pow(GT z, GT x, Fr y) ; z = x ^ y

pairing

• Bn256.pairing(GT e, G2 Q, G1 P) ; e = e(Q, P)

BLS signature sample

String xa = "12723517038133731887338407189719511622662176727675373276651903807414909099441";
String xb = "4168783608814932154536427934509895782246573715297911553964171371032945126671";
String ya = "13891744915211034074451795021214165905772212241412891944830863846330766296736";
String yb = "7937318970632701341203597196594272556916396164729705624521405069090520231616";

G2 Q = new G2(xa, xb, ya, yb); // fixed point of G2

Fr s = new Fr();
s.setRand(); // secret key
G2 pub = new G2();
Bn256.mul(pub, Q, s); // public key = sQ

String m = "signature test";
G1 H = new G1();
H.hashAndMapToG1(m); // H = Hash(m)
G1 sign = new G1();
Bn256.mul(sign, H, s); // signature of m = s H

GT e1 = new GT();
GT e2 = new GT();
Bn256.pairing(e1, pub, H); // e1 = e(s Q, H)
Bn256.pairing(e2, Q, sign); // e2 = e(Q, s H);
assertBool("verify signature", e1.equals(e2));

Make test

cd java
make test_bn256

Sample code

Bn256Test.java