JavaBLS签名聚合

定义：BLS签名聚合是将n不同消息的n签名聚合为一个与其余签名长度范围相同的短签名。组合的短签名，连同原始消息和公钥，应该使验证器确信每条消息都是由公钥的所有者签名的。关于它的更多细节可以在论文中找到

我已成功地将BLS签名聚合到库的顶部。但是结果得到了非常糟糕的性能，出于某种原因，我无法用本机API包装它

对于我想切换到的服务器，它们提供256位的 3型BN（Barreto-Naehrig）椭圆曲线

但它们的实现需要比我所能提供的更多的数学知识。我被困在生成私钥的第一步

你能帮我建立一个简单的例子来签名和验证一条消息吗

以下是我从IAIK-JCE获得的代码示例：

   /**
     * Contains some basic pairing examples, including the usage of Type-2 and
     * Type-3 curves and hashing onto curves (onto curve 1 for Type-2 and onto
     * curve 1 and 2 for Type-3 pairings). Note that hashing to curve 2 is not
     * possible in case of Type-2 pairings.
     *
     * @param size the size of the curve to be used
     * @throws NoSuchAlgorithmException
     */
    private static void run(final int size) throws NoSuchAlgorithmException {
        // create Type-3 pairing
        final Pairing pairing3 = AtePairingOverBarretoNaehrigCurveFactory
                .getPairing(PairingTypes.TYPE_3, size);

        EllipticCurve g1 = pairing3.getGroup1();
        EllipticCurve g2 = pairing3.getGroup2();
        GenericField target = pairing3.getTargetGroup();


        System.out.println("---");
        System.out.println("Type-3 pairing:");
        System.out.println("G1: " + g1);
        System.out.println("G2: " + g2);
        System.out.println("target group: " + target);

        // obtain generators of the two curves
        ECPoint g1Generator = g1.getGenerator();
        ECPoint g2Generator = g2.getGenerator();

        System.out.println("---");
        System.out.println("p = " + g1Generator);
        System.out.println("q = " + g2Generator);

        // compute pairing of p and q
        GenericFieldElement t = pairing3.pair(g1Generator, g2Generator);

        System.out.println("---");
        System.out.println("e(p,q) = " + t);

        // hash onto curve 1
        final ECPoint p2 = g1.hashToPoint(iaik.utils.Util.toByteArray("Test hashing onto curve 1"));


        // get scalars
        final SecureRandom random = SecurityStrength
                .getSecureRandom(SecurityStrength.getSecurityStrength(g1.getField().getFieldSize()));
        BigInteger k1 = new BigInteger(size - 1, random);
        BigInteger k2 = new BigInteger(size - 1, random);

        // multiply points from curve 2 with scalars
        ECPoint r = g2Generator.clone().multiplyPoint(k1);
        ECPoint s = g2Generator.clone().multiplyPoint(k2);

        System.out.println("r: " + r);
        System.out.println("s: " + s);


        // compute pairing of p2 and r, and p2 and s
        GenericFieldElement[] ts = pairing3.pair(p2, new ECPoint[]{r, s});

        System.out.println("e(p2,r) = " + ts[0]);
        System.out.println("e(p2,s) = " + ts[1]);

        // hash onto curve 2
        final ECPoint q2 = g2.hashToPoint(iaik.utils.Util.toByteArray("Test hashing onto curve 2"));

        // multiply points from curve 1 with scalars
        r = g1Generator.clone().multiplyPoint(k1);
        s = g1Generator.clone().multiplyPoint(k2);

        // compute pairing of q2 and r, and q2 and s
        ts = pairing3.pair(new ECPoint[]{r, s}, q2);

        System.out.println("e(r,q2) = " + ts[0]);
        System.out.println("e(s,q2) = " + ts[1]);

        System.out.println("---");
    }

    @Override
    public boolean run() {
        System.out.println("IAIK Pairing Demo");
        System.out.println();

        try {
            run(256);
        } catch (final Exception e) {
            System.out.println("Error: " + e.getMessage());

            return false;
        }

        return true;
    }

    public static void main(final String[] args) {
        new Main().run();
    }

它输出：

---
Type-3 pairing:
G1: ext. Jacobian E/F_ba139ec2401edc28fb605c6b53e289b51311aca0d477df46feee89b1622c349b w. a=00000000, b=00000003
G2: ext. Jacobian E/F_ba139ec2401edc28fb605c6b53e289b51311aca0d477df46feee89b1622c349b/(X^2-ba139ec2401edc28fb605c6b53e289b51311aca0d477df46feee89b1622c349a) w. a=00000000 + 00000000i, b=00000003 + 00000003i
target group: (F_ba139ec2401edc28fb605c6b53e289b51311aca0d477df46feee89b1622c349b/(X^2-ba139ec2401edc28fb605c6b53e289b51311aca0d477df46feee89b1622c349a))/(X^6-(00000001 + 00000001i))
---
p = (00000001 : ba139ec2401edc28fb605c6b53e289b51311aca0d477df46feee89b1622c3499 : 00000001 : 00000001)
q = (699235e63bd94d51548c2e1d57dd658d238fd96fe418721c59172a4eb324274c + 0f3516436dbce492a68ebb406bc515ab8ebd2925caf01c711e75c422e6c8aca3i : 88357041e9bd66d654703ddbee1b0de7a9c0f6a430791e083176a5610efef314 + 737ce191f291c8845d5ca6cc8a76f0d20f31fd3b444e88984e1b267846268d8ai : 00000001 + 00000000i : 00000001 + 00000000i)
---
e(p,q) = (a94dd52af16ac4c868f6a65e8afbd7b7da5ac83b6bf3dc56006a02cb2593cd0c + 7bd8e09b5b3a3848d37eab855ff7b36d1bc4d6585868faf39af11e9e05a1d2aai, 60f12ec3f44243e53f9439a119838b7d5705ccbf6a2bbca5adeddc386f17f586 + 5f7cab2ac94c95ecb2e88d6bb3e65d81a0116ca60fdb4f0f3eb2614f149e1c9ai, 2983e255eec9d20f9f898506358c5f69ecffc8d936c68f879fe771e0335d87d4 + 905a0fcee353d979c5ab5eccd43e475eaf36dd4f4caa92b5f0d48c9a974be3dai, 3953c0b4af9af99855b6d2d15c0f5f2db3abee65ca116d272a5fe18c78a2cc1f + 0d8a8da7526ae1d1982a535aa1cd95a076b1811673cae0b2170e37d2ed812c33i, 996d381cba84679590b2a0c32b68e48a99a376ef3a8b85008c0ad29d015da991 + 1138dd84e4751228c237dec20b72b8068f64e629ba2c97ca0e1eb3a2aa07849ei, 702e0ff820b114eb8dc3b9e97300c6f990ba3dc763cb5685cfdc53182991d1db + 5c0d866b8a0d1a0fe00b0daa3b4f2240a9eb4117fcf7192096003f3344f1c8f3i)
r: (521e690d616b00bf994f0827ed59263320f973f6835166c3f607765ff49fb660 + 132f56183169a3f320c9bdc8b49e0ae86e75c7fc1d89de0ba986600865dc27cdi : 1cc33a0c3acda1614c43dc33d73c25c91513165a1132e57c97d3098c5ced1007 + 06161ead9e5c8e2ea35283528901f1114b6206afc114d9f2e88883bf8fdb6661i : 1d43f333046c2017d6c603e485437ee765f198dca362edb8262e9e44e5cf99c7 + b3496dcf8c0c376c65b3ee53cdb835c6d14920e26f6ac2c32e9d4c130046f14ai : 2b3d51a144d7c9cf8a11c6e778ab1f8937382bee36a750b83bc91e5dc018a5ed + 3f14d2c593f26bfec90c4f3d6fd8e7b27e43ba534ffd1febf258dd788847fb4ei)
e(p2,r) = (1e48382aecd4ea0a6eed04ce592f06791fab0dcd027c00766f98137a71d606e5 + 04e5e74366d03bd9a54499a3323b2e7b72eeb99f5ee8fe46a18395f634b6224ci, 24de58759cf1377d5830c830d1d0902cc66c1c3f1361aa1a4507266f98e1ec21 + 661afc8e156c2e39f426213fdab207302257f0e5960a980567dfa9a11b45f0dei, b544aa91abf6b3892fbc40593a1d464475b9b69be7b2967515aeb3f2c0907369 + aee0c0ee0d6c7bac2abce6472b81e9c8b8f071da26ebbbc2d286f93083b40899i, 8fc0ffa9c2cfbe7e282223808036887a20ce5438569b07d34950b873381d0727 + b1bd58a6cb88de43970d4d970c8c15dc14892c1f501d400afc153848fe136f97i, 84451776a746ac0553eef99fec947d9893193fd0f7c35c7a2a8b202e42f2ac7b + 34a481a6f50337a35189ced27e7f496951d4ff142c5385f27b8138686dcb7043i, ae24a6c1b9da20a41b8792f4ac4d99839d099037a59310e59060a7d169f7502f + 30bae55cda364da63fe6bd193ac0301592457570b1524fbcab7f2b596edf49bei)
e(p2,s) = (5a9fd1aafedfb6a596b3e2781ed2e97056e06fb0f09357b69af4aa76aa8ff1ed + 88259021e86c2118933c50285f20ce74b7b0cedbd7197e1a533a116ba18cd9f1i, 9e4faf20f6782d34a7e25ebffbbe272774e11facf737165f299eb6a26969e9e3 + 287f56a8bf324f6f56a82e2dda966f2184420f26aed784bfcb38cde9a2407405i, 14a30d4b1d971f7c1a7cc61f56ee44eacf6ba9e99c370ef593f68717cffa0493 + 6d208db7ab26560b0f2179cf7c824d4935fa3a07be7f4169f3e6c59b37a5de0ai, 12e704b8a0f97a34c4b0b870b8d50d8bb37aef5412581df7c5ed260c6d82c349 + 1bfe6d1d4baaf16cd3b5ee733d4e614c5cc19dca1cf3cec70e01e240768f79d3i, a894c1f62057620313de3c26470ce44c6d510fc850950b6e2c7478cb1d7dd3f3 + 2911de4f9dd95e2b7896b903c19e6d630d627853035239f187af3d7596e4cc4fi, 4b64d86c73ae1ea37780c187aed4e35057e007653d4d61ab34c14d1227686cc3 + 9e9200baea012a0c0d1fe914360f5a4bbfdbd032e5607ac7dc3177950aa18a58i)
e(r,q2) = (6f8cf3a0658e883bc366107dca53b0d76b0f6f6f7ef74cb4e61b2aa8ab601e8b + 35b9be4155c4434ede6bde0672c39ec0c4f462ee8c27a06415fd18a53ccaf5cei, 4b1b8eb429cb3a71b7e27b017a740ae4f7b6359e5c044f4cd6c2c588834c0169 + 2867122dd3f54bab64bcec5df5b4300c6ea7fcc6f4969d9e5935cdaacaee817di, 17bc103e92added726cd25c7141f707210212036e5252ad7cd24060fc254df6a + 010d499c20ade19e48e410460b1932dc112fd7953da08b5cfd89b53a99f2244bi, 18358eb20e9efb4aa4baef1b64f0fa2df2e17e7b05cfc4d7e5d9eeed3b784076 + 5f9b23465fd8cf3f5daf81bde23e45972e2c6376c066cccb7877617ebf4d7483i, 61d4ff939fcfb7de27becd5bdf311a98593fa2ca1ab34eeb369882cb821ea108 + 0a093f1713d049952218cd0852e2f3e023bb7ee8665c56cce69b6bc3c474e131i, afadf9f17edda1bd4e01cdae14bc0305baf40394da29edf0841b2e8633d12513 + 59845d3902056aa215bb12ccfdefe5060e42e2e8f6a614d3150b8ee185525f29i)
e(s,q2) = (57dcf60ee4369e9858d1dd467f5ec891e461fea0c94cb6bd9bc82aed91d907fb + 91f2801c495392b484f9d21d7181b9a03dfd4b087160ec4d070388f258f095e1i, 8b9241d6475e23fd2a2bd234fd8cbfba4063693d40e0b38640ea817cb8b79712 + 584db86871f773a37e3772b1ecf6f2df98da96cacafcd9a6857fae64789e6ea6i, 4d21aef28f52b15504f2acff346112f3f62301631acc2896c91cb73a0f2ecf3f + 2a069b2403057f081e40d88882df4f69b09360116566dde6635eba4be128a5a9i, 5005c52502d0e10132c013566f529ab1756bf6484dbc95c005ac819f0efd51b0 + 805cad8dd3d4d609c4ba20a774e2e5fda8ff44f5dd306538203c7dbca3453ebei, 8d77f775f53b4b5e2bd3c841237841849c22c6d13b3920ce24489fa5f453eba9 + a162fe065ebf64fb4e126cab783e4a925043442f780c0366d179a043e279beb6i, 8c26c60b80127e0544fea0ac66934c00fc909dadab8d1f22f3ee7f0db037dd2b + abccff963161c1947b9d470cae596506a3f1ae84f660e1861410e095a5d2f9efi)
---