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# JNI for mcl (experimental)
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This library provides functionality to compute the optimal ate pairing
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over Barreto-Naehrig (BN) curves.
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# Initialization
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Load the library `mcl_bn256`.
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```
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import com.herumi.mcl.*;
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System.loadLibrary("mcl_bn256");
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```
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# Classes
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* `G1` ; The cyclic group instantiated as E(Fp)[r] where where r = p + 1 - t.
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* `G2` ; The cyclic group instantiated as the inverse image of E'(Fp^2)[r].
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* `GT` ; The cyclic group in the image of the optimal ate pairing.
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* `e : G1 x G2 -> GT`
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* `Fr` ; The finite field with characteristic r.
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# Methods and Functions
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## Fr
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* `Fr::setInt(int x)` ; set by x
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* `Fr::setStr(String str)` ; set by str such as "123", "0xfff", etc.
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* `Fr::setRand()` ; randomly set
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* `Bn256.neg(Fr y, Fr x)` ; `y = -x`
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* `Bn256.add(Fr z, Fr x, Fr y)` ; `z = x + y`
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* `Bn256.sub(Fr z, Fr x, Fr y)` ; `z = x - y`
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* `Bn256.mul(Fr z, Fr x, Fr y)` ; `z = x * y`
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* `Bn256.div(Fr z, Fr x, Fr y)` ; `z = x / y`
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## G1
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* `G1::set(String x, String y)` ; set by (x, y)
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* `G1::hashAndMapToG1(String m)` ; take SHA-256 of m and map it to an element of G1
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* `G1::setStr(String str)` ; set by the result of `toString()` method
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* `Bn256.neg(G1 y, G1 x)` ; `y = -x`
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* `Bn256.dbl(G1 y, G1 x)` ; `y = 2x`
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* `Bn256.add(G1 z, G1 x, G1 y)` ; `z = x + y`
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* `Bn256.sub(G1 z, G1 x, G1 y)` ; `z = x - y`
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* `Bn256.mul(G1 z, G1 x, Fr y)` ; `z = x * y`
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## G2
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* `G2::set(String xa, String xb, String ya, String yb)` ; set by ((xa, xb), (ya, yb))
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* `G2::setStr(String str)` ; set by the result of `toString()` method
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* `Bn256.neg(G2 y, G2 x)` ; `y = -x`
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* `Bn256.dbl(G2 y, G2 x)` ; `y = 2x`
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* `Bn256.add(G2 z, G2 x, G2 y)` ; `z = x + y`
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* `Bn256.sub(G2 z, G2 x, G2 y)` ; `z = x - y`
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* `Bn256.mul(G2 z, G2 x, Fr y)` ; `z = x * y`
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## GT
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* `GT::setStr(String str)` ; set by the result of `toString()` method
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* `Bn256.mul(GT z, GT x, GT y)` ; `z = x * y`
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* `Bn256.pow(GT z, GT x, Fr y)` ; `z = x ^ y`
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## pairing
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* `Bn256.pairing(GT e, G1 P, G2 Q)` ; e = e(P, Q)
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# BLS signature sample
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```
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String xa = "12723517038133731887338407189719511622662176727675373276651903807414909099441";
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String xb = "4168783608814932154536427934509895782246573715297911553964171371032945126671";
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String ya = "13891744915211034074451795021214165905772212241412891944830863846330766296736";
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String yb = "7937318970632701341203597196594272556916396164729705624521405069090520231616";
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G2 Q = new G2(xa, xb, ya, yb); // fixed point of G2
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Fr s = new Fr();
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s.setRand(); // secret key
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G2 pub = new G2();
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Bn256.mul(pub, Q, s); // public key = sQ
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String m = "signature test";
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G1 H = new G1();
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H.hashAndMapToG1(m); // H = Hash(m)
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G1 sign = new G1();
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Bn256.mul(sign, H, s); // signature of m = s H
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GT e1 = new GT();
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GT e2 = new GT();
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Bn256.pairing(e1, H, pub); // e1 = e(H, s Q)
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Bn256.pairing(e2, sign, Q); // e2 = e(s H, Q);
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assertBool("verify signature", e1.equals(e2));
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```
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# Make test
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```
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cd java
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make test_bn256
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```
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# Sample code
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[Bn256Test.java](https://github.com/herumi/mcl/blob/master/java/Bn256Test.java)
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