From cb2ff5c1ad7da34dcd0d1de664ccd8c0ee043c42 Mon Sep 17 00:00:00 2001
From: Sean Bowe <ewillbefull@gmail.com>
Date: Wed, 7 Sep 2016 01:20:21 -0600
Subject: [PATCH] Added serialization and test vectors for U256 and Fp
 elements.

---
 Cargo.toml             |     7 +
 src/arith.rs           |    38 +
 src/fields/fp.rs       |    16 +
 src/lib.rs             |     2 +
 tests/fp_vectors.rs    | 20086 +++++++++++++++++++++++++++++++++++++++
 tests/serialization.rs |    23 +
 6 files changed, 20172 insertions(+)
 create mode 100644 tests/fp_vectors.rs
 create mode 100644 tests/serialization.rs

diff --git a/Cargo.toml b/Cargo.toml
index 64cbc7e..f72fe0f 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -14,3 +14,10 @@ name = "fp"
 
 [dependencies]
 rand = "0.3.14"
+rustc-serialize = "0.3"
+byteorder = "0.5"
+
+[dev-dependencies.bincode]
+version = "0.6.0"
+default-features = false
+features = ["rustc-serialize"]
diff --git a/src/arith.rs b/src/arith.rs
index 2631f3b..ac08c5e 100644
--- a/src/arith.rs
+++ b/src/arith.rs
@@ -1,11 +1,49 @@
 use std::cmp::Ordering;
 use rand::Rng;
 
+use rustc_serialize::{Encodable, Encoder, Decodable, Decoder};
+use byteorder::{ByteOrder, BigEndian};
+
 /// 256-bit, stack allocated biginteger for use in prime field
 /// arithmetic.
 #[derive(Copy, Clone, Debug, PartialEq, Eq)]
 pub struct U256([u64; 4]);
 
+impl Encodable for U256 {
+    fn encode<S: Encoder>(&self, s: &mut S) -> Result<(), S::Error> {
+        let mut buf = [0; 32];
+
+        BigEndian::write_u64(&mut buf[0..], self.0[3]);
+        BigEndian::write_u64(&mut buf[8..], self.0[2]);
+        BigEndian::write_u64(&mut buf[16..], self.0[1]);
+        BigEndian::write_u64(&mut buf[24..], self.0[0]);
+
+        for i in 0..32 {
+            try!(s.emit_u8(buf[i]));
+        }
+
+        Ok(())
+    }
+}
+
+impl Decodable for U256 {
+    fn decode<S: Decoder>(s: &mut S) -> Result<U256, S::Error> {
+        let mut buf = [0; 32];
+
+        for i in 0..32 {
+            buf[i] = try!(s.read_u8());
+        }
+
+        let mut n = [0; 4];
+        n[3] = BigEndian::read_u64(&buf[0..]);
+        n[2] = BigEndian::read_u64(&buf[8..]);
+        n[1] = BigEndian::read_u64(&buf[16..]);
+        n[0] = BigEndian::read_u64(&buf[24..]);
+
+        Ok(n.into())
+    }
+}
+
 impl Ord for U256 {
     #[inline]
     fn cmp(&self, other: &U256) -> Ordering {
diff --git a/src/fields/fp.rs b/src/fields/fp.rs
index 4700036..3c47b9f 100644
--- a/src/fields/fp.rs
+++ b/src/fields/fp.rs
@@ -4,6 +4,8 @@ use std::fmt;
 use std::marker::PhantomData;
 use super::FieldElement;
 
+use rustc_serialize::{Encodable, Encoder, Decodable, Decoder};
+
 use arith::U256;
 
 pub trait FpParams {
@@ -44,6 +46,20 @@ pub fn const_fp<P: FpParams, I: Into<U256>>(i: I) -> Fp<P> {
     Fp(i.into(), PhantomData)
 }
 
+impl<P: FpParams> Encodable for Fp<P> {
+    fn encode<S: Encoder>(&self, s: &mut S) -> Result<(), S::Error> {
+        let normalized = U256::from(*self);
+
+        normalized.encode(s)
+    }
+}
+
+impl<P: FpParams> Decodable for Fp<P> {
+    fn decode<S: Decoder>(s: &mut S) -> Result<Fp<P>, S::Error> {
+        Fp::new(try!(U256::decode(s))).ok_or_else(|| s.error("integer is not less than modulus"))
+    }
+}
+
 impl<P: FpParams> Fp<P> {
     pub fn from_str(s: &str) -> Option<Self> {
         let ints: Vec<_> = {
diff --git a/src/lib.rs b/src/lib.rs
index 7ae7fef..a0414d4 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -1,4 +1,6 @@
 extern crate rand;
+extern crate rustc_serialize;
+extern crate byteorder;
 
 mod arith;
 mod fields;
diff --git a/tests/fp_vectors.rs b/tests/fp_vectors.rs
new file mode 100644
index 0000000..06651fa
--- /dev/null
+++ b/tests/fp_vectors.rs
@@ -0,0 +1,20086 @@
+extern crate bn;
+mod serialization;
+
+use bn::*;
+use self::serialization::*;
+
+#[test]
+fn serialization_and_deserialization() {
+    {
+        let mut a = Fr::one();
+        let b = Fr::from_str("17").unwrap();
+
+        for _ in 0..10000 {
+            a = a * b;
+
+            assert_eq!(reserialize(a), a);
+        }
+    }
+    {
+        let mut a = Fq::one();
+        let b = Fq::from_str("17").unwrap();
+
+        for _ in 0..10000 {
+            a = a * b;
+
+            assert_eq!(reserialize(a), a);
+        }
+    }
+}
+
+#[test]
+fn test_invalid_representations() {
+    // Fr
+    {
+        // modulus - 1 is representable
+        from_hex::<Fr>("30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000000").unwrap();
+
+        // modulus is not representable
+        assert!(from_hex::<Fr>("30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001").is_none());
+
+        // ridiculously large numbers
+        assert!(from_hex::<Fr>("f0644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001").is_none());
+        assert!(from_hex::<Fr>("ffffffffffffffffffffffffffffffffffffffffffffffff0000000000000000").is_none());
+    }
+
+    // Fq
+    {
+        // modulus - 1 is representable
+        from_hex::<Fq>("30644e72e131a029b85045b68181585d97816a916871ca8d3c208c16d87cfd46").unwrap();
+
+        // modulus is not representable
+        assert!(from_hex::<Fq>("30644e72e131a029b85045b68181585d97816a916871ca8d3c208c16d87cfd47").is_none());
+
+        // ridiculously large numbers
+        assert!(from_hex::<Fq>("f0644e72e131a029b85045b68181585d97816a916871ca8d3c208c16d87cfd47").is_none());
+        assert!(from_hex::<Fq>("ffffffffffffffffffffffffffffffffffffffffffffffff0000000000000000").is_none());
+    }
+}
+
+#[test]
+fn fr_vectors() {
+    let expected = vec![
+        "0000000000000000000000000000000000000000000000000000000000000001",
+        "0000000000000000000000000000000000000000000000000000000000000003",
+        "2042def740cbc01bd03583cf0100e59370229adafbd0f5b62d414e62a000000d",
+        "1eced988f1c4e0f7f7433f99dc0eb1b89dd2a1b7c00a6e1a5df4900b27c8a6b3",
+        "02363a20539db6638514cb4ba7ec49c91b2c5d405b7e5c021d3a0bf834f2ef0a",
+        "09889144b32647e7a6a9ec0646bbabe83d9b7d9188c3bdcd3b002c55c9aa80ef",
+        "014ced1876c520cc926b880803323cb80b4554f8c2588032f6cb727157371641",
+        "179da4e61ae3117b9b12f86f5aa4f14e1fc3b46bf05d1423900f9ce6228b6d40",
+        "067140865d6292881384dc2252b9dd20111c942dc2364e8c98f1da3c28da888f",
+        "2ca25f36b7b20358489b49421b20f6a10eacf80e7f3d2bfce7593d0777fef418",
+        "2bf0a17a3fa0670820f4f2469774a98f9bcd6a5e490e97d6e11f361c914cfe8c",
+        "29a228ca3b4b8ed9cf1c2957a826aaf9cc3d1bdccc99996092b42907e8d763d4",
+        "296a1aae3b4d8c87257609dba587338419937a3f7a8e37234deca0eb9b761478",
+        "05c9dd8d3da17bb45967ad595e6440ba84243707a5b2a45568f22731b7f2055c",
+        "2e99a1f1b911be2b5eae798a1bdb87ec8b6b66015af43114d4c4f0c3081808d8",
+        "0500c67659a93bcd482ce6e2e198e671bff5e9bf276891b0c7f79200da6dd6b5",
+        "020a4cdd4381c2c7e2a1885ac88036bbacc0d6aac38ca1113c10efe9226e5744",
+        "29329d9432d2146f11a0d9e2578c09f7f1182b9cb20f988c6bad57bcb614e48f",
+        "09507fcafb26bb82d68228ef5f5ed7b71aab295bbe4cdc759df141917d11d79e",
+        "00a0ba7dcf0405380408feb28cdeeb784a19d0b9679d1adc005e9f1ab34f251a",
+        "067517b1a7f50aa3a3c9dd3db988b0e2e87a8e6b3fb1184b8a06cc3529141132",
+        "13e5c7527050b265295b9739cd2f95312932bfb62ce4c159c0ab92a61f0dcdab",
+        "2a737c37b6881ca875205b949c313108f54eee116d876d4685a88e77a88a7589",
+        "1103f082a016eea4c4dde6b7caf6d5f23d45007920eacd4ac8c952a9ece70d33",
+        "12f45350d4c50366dd0c88a77ce35b802cf1e6929210449ff83a73a627ae8a9b",
+        "18b04aa529992886a880fbabdcc834a983bf07bfb23cfa7bba660aec0a10a8ae",
+        "03820dad30db55157ce87fc6812ec0a4e659e7547b18206d5844a6d1f28399e1",
+        "030dfdd27e4e180392ec965b8bf2586d3203fe8931be034c966c37433625fd9a",
+        "08a9b73efb3282526bee3e609fb408449503b70f617b3bab42919108852cf44b",
+        "184b6a8fd93b49422099e5d75090dce92edf553115452635bbc8e623ce312ad3",
+        "030273cc32bbe84b480930f2313491a19c00e2dd39fbd30993603bb8b5495e95",
+        "1622dd450399ca70b99e94f60d87490b1078ff0dc3ce82cb32fd7dce0c4a4499",
+        "0195e53a05f7b95040d27b2819f7b23b40c0871dbc476e3c102e4cb64904483e",
+        "2910b512191aae4c5f27f90aea2f41b3b0e0f2042d57ebc8dc51901d06b10024",
+        "2e795bc0783c41c950330abcbd7e92a6d7e558787e7f579b4c2e4aaf9f66630f",
+        "0c34e777e38a18cb4edc5e9d3f4f07dbb1b074f38347dd53a015be494f24c0b0",
+        "277348139e45c362741e424e4dc10b94df979bbf14f7c4b6dc144a0a0c593e1c",
+        "1dff63c029e19454c2360a88baf804cafa60f6a50cbb71a79715c2832cf47408",
+        "23e84f6518e9bab5af850cf1f38a873fe8be0c2f786d1d4e1fdaf32d46150500",
+        "211b26970071c65390a8c6d822423ab281aae480a12a6fc836b40884a4337e53",
+        "296abf4e45cc54ba75225ebac4fe863d5cfe725105cadfc9f9357f791d7ffdd9",
+        "22cf34de7b862a2c4874a03b7ce9a9ac8e748e4741a7d01ef7e443430a543b33",
+        "2fca5ad500e198625c9d542e0d4aefdcda28d246edf9a83f34c57ac1cfe98a34",
+        "2a471ed73102e6918e55b0ef00822a5281ef0e49b4586cce10ab2671ddf95731",
+        "2210b49819b69ca317b63ccfe3a4fed4fcc9b9b368dee5d988624487f7cd7d99",
+        "0ac117037c41ac977dfac11e614ff3c1f0604fdf1e934addd96ca426a2d56c45",
+        "18a0c2a40073a85c4a4cec75dc9e049a18def78960c7429a9c6abc1cde4d1c42",
+        "229574d27795392985547b551380cda18972a32c2caf87b910746ebda6615ca8",
+        "1c6f0bc008a80d5d36cf483df553e24ac4f969d7a02f45e93181441d79fb72fc",
+        "1060b506a53a740169a80954eb5fcfc6b261cfca0c021a8113841bfa2b10d3df",
+        "23ecc4f3237f76dc81fbbb8e467d253ebb6b4e99b9f2c607daec1bb599a63108",
+        "2350041950c0d7144e6790f939fa4f2f53165b82e6f5c1c730b7129ff1dd6075",
+        "179de2653b84e8e5d925b21cf206b9886ffe9df14dd300ef48341707f3a8e43a",
+        "16c670be2c945714cf9e5b30cc54b846a86ade34ca2f19e95cb9782cd1a1f4f6",
+        "2a6ac3b3bd2a3ca35792323fe39384b7ba44fd70b8788bfb9a28f0397e6c58f2",
+        "27c800eb72d3f1ac091747cedb323b02178e9cab5951f1b1c97b70430bc93f49",
+        "0acb5953cf1583df3f5be7fc264a01d561642171ed8ad66cb0750ef84637919a",
+        "239f76d1622590038d64e710422cda6cb6e3e12d1593b07b08faea2dd71848de",
+        "2dab87d5e027c3aa07b95691cf313088176763b92a1a101142b202224c889319",
+        "2ebb685e594b7ae133c381606c8fc1c7a07ec46c653b1d5e73734362bc8cc31b",
+        "238274a880a47a28cec6660f31ca766e7c024fb458f7e1df5cc8d9f1fa49b364",
+        "27c5e092fa1ee06da63928770d5ecc7931845869260b3966d6523ea526db2789",
+        "00dcdcb4cc0015ab8b8bfca1d52e335275b6fb39b58d41c2b30367a104dc2fec",
+        "22c7f9595340b66a5f0781fc8c6856facc2228ef749ebe8f4e26a3c9ab74465c",
+        "2ea0cafc90188c763ae65f132d3d5c873e4bf9a50ceb079874d1c346ab8fb63d",
+        "180066c34e34c473953b3e66d98660e733729376074b231198e921d4ae28ac75",
+        "0cc81637599da9f5b8285737283752575daedabd7b463e02992933126b59e167",
+        "274ced6e1efb4148e7fb778afdb6e7a41a5af073df6c43b7103f291efac8ca76",
+        "2dccf0cb2b0c9165392462712673c4075a99d1f1e3118ffb3deadcda415768a6",
+        "1d0128b4b0f47f814b2fb6491f03654541725612c465267f02b73ed28074fbc1",
+        "264770a08b4fcfe8dcde0161cb4cfe1d851227fa5538adcdef80827636d95f92",
+        "08cd18d2188a1b7e7103b95a1b7022cb56f14916b5b5a8b4db2b7305d222fb1c",
+        "2b0fa450d5c7dda8eb466723cd25e0b762968e52fb8a558225ad2b0b3c9f15e4",
+        "0fb89c9eb27d7e49d4988722e645714fe5be1fd5d1dd7b9f475a10222aef9fb0",
+        "2384e79d245f048e6433b04a3c7e527a736c198c67682a23cccc127e0fe341c3",
+        "240c04ce80bb543b5b9dc19abacc681c8c58778141349e9e3f492515c54dbfdd",
+        "1b2c3e4505b9325d56c1fe596f839bc3bc023ca08485a3f71f575994e61e4e9a",
+        "2c341055bdfd39ae1c9012b5456790d9e6bb603a56cd215b8fc7ff5df23babda",
+        "2a618fada6222167ec179c0d2d5a3db64b07d04a0d8ce903ffcd878708131fc6",
+        "098505eda76826a820e63e004a19ce3c16fbc465d5c294e4710121781e476016",
+        "2198b95feb3a29a0bc7439a763caf039448143e464d12c3a5753fa4b4039b97e",
+        "23e150228a041db5a598c4955ad4b763b2edb6208b5f4caccf790d0a2d927215",
+        "1806b48868d9900275573f4e57ecc9257f0b8787527a2b96d2e24f1cfd4b6ac1",
+        "2b7b0225bd8e48a401ab3a10507845bf3110c5959980023d166dc4be0aabdadf",
+        "1b5d5b3c9f454b4019116206d223c708bba4ee71138fffb32ed8674943c72486",
+        "2a495d1c7fcaa4f27be5914c7c6fed4fb65ee46e6d7974a55141d9bab30b39b4",
+        "1fddf00cfacfef6cf8dd5e88e04298fd376934a40938aee523338677258469ca",
+        "01fd18b9683b1aac8675185d5d06773aaab0e19112ddc9bb63e2c63bcde49db0",
+        "140899d53f48c9b200a48a8618dda9f24ba27a9acdb63dcf633107feae16fe98",
+        "0a0a0501eb8fbabf040f420ecad8797db587601e3deab6a01ce4b0d306be7cc6",
+        "2fa5a098db8149032e6bb899bc0b97c6b2ffdd6cfcc955d17ea2afe6a3cc3990",
+        "26162db3d4a6e6172f0b8d1d7ec1f706f9eeb7c6d3b0c2a510d7d0e04fe4eda6",
+        "1fc0dbbbbdea0ffaf2864ccca1b7e937efadd6987ad73881c5fd534ce2ae55ff",
+        "00dc4562c8483647fe1d924d50c574fb00b53973333cf3f42b24cb0412d1949c",
+        "2fcdf1fcbdfbec79a47715a340effb55d042f522b0b86acbd4c2c286d8afbbc1",
+        "0b11546ba7759df51528a4b9656d09ab5c2b7423ea82ed36d7acb01fe96cc8b7",
+        "2f3dc23b191c92d0a582a35f19c25831bc60fe3aa228c3e00e70fd371f72e80b",
+        "17b160611d7b3fbffd972f516d72b933980f325db9220cb1f953f74d166badfd",
+        "17e5ddf96d4c64ebb06179a3544afca2bae78fc1089031906aea8afae5610147",
+        "012ae487cf528b8197e4333b56705d7c31c92545607e6edbb0105717f5e33f66",
+        "03a07c50c596fe0ebae61d554d46b055a6fb0de2da4a5434e026052292ef06ac",
+        "27d9bc26fda4e6554de6d29b88934c53cae2eaee241ae7be961598f41118a7cc",
+        "0a772b263180a8fd6c99db42be795b3d2944d4858fd84d307cc438dd82541cd1",
+        "1ff90c2b7d3df22a1dd77b407e7f499d7ce6c7d5d3dfe360c485b6c49ccefcad",
+        "0253973b5ebdc95b42002fb7695d51aeb1410ba1aeb24d98fac263963e527daf",
+        "29912c9332807ec705d49f06c24b30caa6b9cc764dd223510e0fd21faf1aa1e4",
+        "2c9482d7500b2eb22073cba5e6793b8bdc684e2b979df3b18e340ac27141b147",
+        "25ef1f7f3369c7490da551cdee2eb521d4c058ff26c9ce503174f4b776a62134",
+        "2850f791ce002da71a143489ca75f103cdb06faacf0cc1cb42d3f16f007c6ac8",
+        "1b2dfc7f783b9a94a2374d632c7f2b9261c64f3384e7879f8777c761a0f38916",
+        "1dab259a8cd28a888944dc62f0d71f77fbea3cec30777146eee454d8a38862e3",
+        "0ff237bdb85a4d1d59d1771a372d85bc4c929c13bd11dc5ab547efbdac506d72",
+        "03ccca3ce8529946b5971cb7b6cee1b7f0603d1a14fdb2399a0b754616881106",
+        "0ae33319df196d3e6a9d381c5e9216bef5f269ccdd9bea3228bef871ec64a5ce",
+        "29c85de273bf79ddd69170fb339c8935870d452eea31b4814181315098fe04b9",
+        "192ee992c2734232d8cbcab87466cb7e4bd75498bf744bf0fca69ae2598170fc",
+        "0adf8249950d832031f2c04795d1be24b8e819970b3bcabb6fd36c577c87d171",
+        "1b91d0bd5d309d5f45f5df4d86d97c1958157dc4cde3c9328fb649d4c2a2660c",
+        "0e4c23d81ec837f232fe6760a9bf81bb664af07b329d66e89e6f91916869c3d2",
+        "0c53fc069fc35d46b0c407bab69c9b6e2fb9c5376628f2a01e0d15c33f0594d3",
+        "10c10f5778177ea594ccd59c145dd1d6b98d79f29ee7df7cf350250629ea3749",
+        "0591aff9a9a7aab76de4b8daaae1c7d99ed89fde5cdef42b7e043f537bc06cbc",
+        "2ba5d15ac6497c83a9febd0295a25541876fd36f81d09b0042cb7237d73ab5f2",
+        "1fb87964fdc64b2daacc9dae6e72c02785f508eef8b768518f3454e330dc2165",
+        "0aec2e9eeb137a1c543d268adecf786041461fdc60744b2f22578e631caab5b7",
+        "24646eb97864a13313b58b69196a7a12b9d050b193367f130eb8c10a49a186ad",
+        "1dec3036641c822b85e64b8de5bc408c76c6838d0a3014a6e27e1272b9bb9483",
+        "18c693429e6f97f4e5c28f4919fccedc3a1bcd5ccfee44aa43016d433900b84c",
+        "09a1de0b073437aa7865181f666739ec4c8d44d97f68d2d7d5e5df25076f327f",
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+        "1665a557b4a74548ceec6f598ab5684f32bcaa867c12e8d1abdd6acee1285792",
+        "2fd5d39615c3cfbe8ccc5e362e635cfe06c588e9bc0cb1d95c1df71dad1c0b7d",
+        "100e6f9483e9c38ce0a7fe26cfd8bd1d915a967ef85e9c3126b6f97b8c67ab0f",
+        "02f04bc9ea7e55f3901d844e427bc348f934f48551eb0b60051f9ee756a6aa3c",
+        "18bf6a3dc3320590adae58baf410b4367785d21d0a38e1fd8ad0b5ac73ecf609"
+    ];
+
+    let mut acc = Fr::one();
+    for i in 0..10000 {
+        assert_eq!(expected[i], into_hex(acc).unwrap());
+        assert_eq!(from_hex::<Fr>(expected[i]).unwrap(), acc);
+
+        acc = acc * acc + acc + acc.inverse().unwrap();
+    }
+}
+
+#[test]
+fn fq_vectors() {
+    let expected = vec![
+        "0000000000000000000000000000000000000000000000000000000000000001",
+        "0000000000000000000000000000000000000000000000000000000000000003",
+        "2042def740cbc01bd03583cf0100e593ba56470b9af68708d2c05d6490535391",
+        "05f549777735c612f97ae4737de107ce0595b32ccf5ba7ee06a25fa9a2ba0eea",
+        "2ecf34b8dbbfe5e592318b8cf427541f4c551b51ee16a867e93e39c422c6a50f",
+        "1260525bab1c9c950c71d326d27739281d924642444eb1e28d89ad86527abf3a",
+        "1b213b761a8d7ce50d5fd9d49b622cb313616e35a5f63ce76fecedeecd6008f7",
+        "0b3416313ac7b8a9b8a21ac6f99b79650030ea3734f1bc44f6ddf2b1f165a31f",
+        "01e1f4b6ad51008b0c5600c5a4bdce24a1b6be8ab5edecbd787e6ff240879d06",
+        "00e8f6be5da3bf89090b5d67beefe2a5eb2f0d68ce6d1e02e3692cd5096ae814",
+        "215bfcd121aa7d454bdb580991fb0f243ce34b5f1ec06041c71521ee10947a5a",
+        "19115c86cbae9fb9c4f61e969fedfbe27e7e75fcfda36d4e3b2a7c709bbfd6b8",
+        "1572d83ab93864779443927b2242de6cee6ca78aab08b2c7cdea7b3f6a85510a",
+        "119d10392fe113229b54d55a9ee47e7e0ab76be9888b74063d62ccf9142623c7",
+        "00d47de4eb5564df4e529261dedc204b225393b21c63b9967ae29453c08b20a3",
+        "28d4eb92490cdda8f4c4a30dd3b69660976df6f5edd4cc82012a59c7bb36526e",
+        "28d8ce14a0f33783d491f05664ebcdfc1e190622cd401890c1b9d1607624688d",
+        "0885337961faf877d85b48f48299c985486f00e6c8713ec81ebc5b24a23983ba",
+        "14db54281f8da4f1fa7f0afa4b74da72053a7c81855c7cae1325352095b197dd",
+        "2349b6d2be7e0e4e7eaea80770dffd071e9deab05961f3e56390ce5a3d50d964",
+        "1975f1de23f5db35731be127435f13df653ec06568547da7623e19acade0e7e6",
+        "27884e0b76d8b50818c2f2edfaa4dda7b6ae7fcb24a35f99d2e04c53c20fa3c5",
+        "2a2a0544945290541a9e9d9d7c5f0c05904f410e88b652acf1b962f983a0d733",
+        "1bf21a5a5d0cab6e45abe913fcf726029f50875c01ac08293aa27c564c90f3c2",
+        "2adac2a90fe7b3379553d99431db5368e388fa860e6275ec2bcb700d7a93b770",
+        "0e63c0422577d23028a75ee874f48fe0bc14b6565fe61eb9d1c7f7ce39ac7eb1",
+        "25c89507ad6897220aeefb7f48488fc9678f2444e4d474e3bbbe2ea51b15f7a7",
+        "078b71268721c7730538701f69cac167a74bee611d237356aaa81e2f61767451",
+        "0770f755457fe141f00253a014936da08be114f270cbafc8581c85cbac863a94",
+        "05f0a185cb2f8fc20d68aafb4252fa2a37493ece0f5bb43af2406e862b983298",
+        "0782e0657304c6a0c7d0dcde40ff742167b01627fb0bd922f30dde7dedc5c878",
+        "1530766a98137455233cfb15efe7ca290f85314db58d8b8bbf446cbcf3e2733a",
+        "1f5fcc3188f33e3cb06ce20a6860ca09335b00f5251c46b97cd28fea4de48e91",
+        "1707d4a4ee435585f058eac63df31213dc31ecab65b059c247782cf4cd48085e",
+        "0894a6b8d7ad2f42ca6dc74ed99b683fa90b7b21ff42f02de4ee0f1e2014c709",
+        "2a9db23063cb0378077748dc8fdc9a8c1a8b60df1f2771d7826a2469a0653ed3",
+        "076f1d650c6e573f6e514f6fc4f82e7c84d300bcf9b104bdc3ebcb2c1b4acec3",
+        "16bce4d0c28b3262a881e411bba6fb3fca60c78e6feac147b36df909643ab78e",
+        "2953930772628ed515b5a027ec6682461d6d5805e1912cf73b9a27de811d81b0",
+        "1af43181b671e1a31f9b25d24f8e4630e2e65b477b7be3f71e6d5298ab03083a",
+        "2179f20b570e1d2eecec15d55483df01bae8a620e012d3ce32d2bceacd9830cf",
+        "0e8a11edea0b665f53966f2c50969e003254ea89f52ac0fb9be3ad4752078b05",
+        "11e4a771b935751deb8cd87c7c69fbea26eb033e881bc52edd78bf101fd2681c",
+        "304ea13bff87738f62e5326ecb22a2e1b6bb0eca1c3b088d1823a1fa482284ca",
+        "13db78213a39e51cae0865bd95f69b72b8ac34c0748b293859072e872801591d",
+        "06cf3514f813970a3ee0d75dc70d17e0242f10ad6035bc5f3b8b35a2de0a8068",
+        "13f8c74ccb4d3f84c17ca64e39c9e151dd2cf7c9f00bf536e72980cd75311a80",
+        "166a9be59eb30dc2c4f8eaf9c37d5094c8e1b2375404211334e06608b710b440",
+        "09a120454a26b498d77a45779d4fe2ab826f93b2d1c517a802ae2e3e7f853717",
+        "25f34f924510cbde1fb3d87c88a5696acfb68af12d370c0b1517f4fa3665d559",
+        "1c4b47c5f9e588c821ef143647b6ce3fef68915329e0116f3f76d46c77b9c331",
+        "0acb4919089194f5972c1da624ff8401100d8237f68b1c0e71dadb516ca2f824",
+        "187f1c154441162104ea7965b5d27a10a9b7b528a91d780acdda23aa92f315d2",
+        "223afa3fc397123fe6d3967052dccc3a04e5e75de5e593a8ece4e0f672c6eef4",
+        "1efc13b2c11ec0da2e1267f098330d64c9b5469dfd5728e00105273c96f9e0d3",
+        "168ba1b8734422348cb5879a4aae9562a21e713c7953d67c1f0fbbadd589e101",
+        "15fb65284fbec31df2f24332eb32a952c52cf4864648cb635d95372312cdbc91",
+        "2345e115fdad31c8c2b9089eb26d1333f41a87172903e0b3d7a4124b0387f3ab",
+        "0fc7d5bf552a738d7fafbe04dba0576d113de3224228d82b9eff7ed8e942b4a1",
+        "173e16f25c37fadf2e56381eb0028a69e1673cc2054ba67864b1f9a66e77edac",
+        "2da98ec3674ae10c2d0f92e6cafa6fabab34339b3240f665041abd00ddb8aa2f",
+        "2e7b3e6d73f0d586042b54893443d6c54d4971ccf7e429668324ccf0a263c065",
+        "059013c25894ff83f179b5cd901cd9d42f8e13dbeedf130eb20ccb158595c84b",
+        "2f511f88a173aee9f87397ae6bfcd989fa401968ca9b5fce13ff0eba40555407",
+        "0874438b67acb0a0e64a0c90a6fb4ba40430732c64e2ef025494faedb4da2820",
+        "0a8732d539929279b1456e0af59b8675c7af3e07644d8a92c5384fd5b939708c",
+        "1a1d77575dee2df307f2327a99dc65633b73796b0ef2af21da6942e8fd16dc03",
+        "282b3a33a74ced5b9535bb6fe82566c21f0e52256f77dc4b23e224000bc03a70",
+        "1a5172f63055afa1a670e089b7d49c48170fb89ad856642ecd9a2e03970e2908",
+        "2ef049132b2b3d4ecb4676db7f9395f7ce447ea49460fe5a5892490efae2898b",
+        "2ef146d78d5f9dff1c25064efd8e7e0a1bdcc80399a18561341a58294e23c76b",
+        "2ce6a25496a9eab487ad96bc833dc183dda5102395c2394f3570f3a90e96d41a",
+        "13c6115503ea13c0b63d52320c560f1aafa715fc2566adf7e5f4ba37210aec48",
+        "2635e273f55a3bb4c508c649e1de745d6b9ee9746b48dccf4f08c9d273191810",
+        "060dc1d65174834b3e98f51922c600bf577e9040ff4e1118fb2cb540606d9efe",
+        "1e38029a8908e26a1fb88132e601a3cdda459106fb52465e9eacfd83a2b7c459",
+        "1d622d30ca3f804ae02d907c0fc90460bc72275fcd3dc5b1624e9a0287038a39",
+        "14b19d523e95dc0208943d3bcee467dccf0eb9b564e6d77046ec7e4624b38a7a",
+        "2c4c96ec451d55a86aa7b25b422ae3a68e860af0c0fdb5c8b90fd726fa5dae97",
+        "22f19185dc8be39264b8400f93e1c298c9cdd38a420c5b8d87c3401a6c0cd13c",
+        "2fe919d2543f16c321b8dcf317df2fc9be2bb24f93811b41c93d5dd21a160c2e",
+        "2d1bb5ca45b8fda9433ce9ec3c82bff09c996c076eea723e9c3ab89d599ea680",
+        "0bd64d47f7900b3af16afc2d8293d0ba368ea54f56aa1f547938425ff84c2639",
+        "2cb8f11a964d3f5c93745a23b7c28ecb0df14c8024a969c69b792b4fa6827d96",
+        "1135a959bad1c3e8628fe0f5d55fa018f9555d351770868f6979e3a0809346d9",
+        "125f3f80fd54bf564c7a1c4d0235ab919ccbb6f6afd653e39f710f0dc7e19638",
+        "288e1b93db9338a87f9162b2ab0978044e2fe7f7b718e772d10ccfde067391da",
+        "2bf1a17375e218794884f058909fffaf800b8077f57816dec71b08d2db3a7f64",
+        "25a9c69d857652aceb8ba2704cdd5d8961cf4694b4e89e7055aea583985c6548",
+        "1d47c1ee35f6ab93bc15d4b1152e431591a284b6008dc49deade7fff2c4effd1",
+        "29b5852e3ccb455d47860ab9d9e5923a1a66a1860ce8757ddb445c2b12aff9c5",
+        "2234106ac504ce454c67c95a7f346fccba3326049292d485a9221cae18584745",
+        "0702048f294a5307517476799642787181b1efba649bd38c4b09592d17eacb8b",
+        "2a9d0447413d43abcd42e5502358bb342a4b67b5fafb83c0f935a848e82c4319",
+        "1b1a04731d00b8e78a3156b596ddd8b44014b567fe0a050d05d80cbcd7c388e2",
+        "2ccc634009e42f1c7902609e4c191f4ce891b8d8f2c398907fd365e925f1dc73",
+        "29061e82b5a2dd76cd0eebd84459aa56cbcd992406b925bcbbfc93e797973292",
+        "1c3d69e67f97b7cc5f488a48f7671e78ea361531e22b45dc2dd39d55fc5bcfe2",
+        "1950814cf01f0d2bf4415aff7fecae415e519acaa92395418b00850f5cf92124",
+        "1ad752b910ffa646aedd1faf43d3623799eec4e7e6c32857243e5d8598fa4958",
+        "0792af789f38996fb0f92b4d9c81adcfc955a543a90762e458d43b3474de5a03",
+        "1a0b1e5ea51c6d2ca362db1a0ab43162380f104b2b293bd7adde8d29de5ef7ad",
+        "27221fd507dea3f1b07299d9f4e04768f4737b9b32ceebb97ed6112c40809366",
+        "287da7b8d51f9114d031f6698238112cd32bdc14415a44c97ce38ea27a97bf08",
+        "01bfe2e88fcb21eccf75c5c2c46c10d93bdafb90f057e32e518349f8366863c4",
+        "114be96a4c00007f60d76c24184386d7369cdadc3031106389d117cbab36c6e3",
+        "250ee6d871e7a7bb95650330e8645f6d9e56eb3a8f3d0035c33297abc00eb093",
+        "08b89feaf1bc2d916dc8bc634c12c7439fdf6e0811af775d2e27076fbef188ed",
+        "193eaaf269884c1a4eae680e893b53614f5becba1ecca6ddee7c54e0364091ee",
+        "0ddee0ff996dd9de99a11b1f274fd89ad8458469929969f2fe7cef00acb5c315",
+        "2a927a4e7988dd83cbaaf9ebd15fc5c721ec69722d329376790ece43048606af",
+        "1167dcfc80bf5e16857e0b5aece55311494d479eea5b4a00cd900ac165a0ea92",
+        "0c554ac1f20b5ed8c0455fe6ec0eb1000f3dfeaaf4a42a82b54b645bc97fc168",
+        "0915b29acd1637d255d83fd375a493b20549d4c0bc5339e45723c8c60acc27f3",
+        "11cdd08c240eb373d9aa4425771d689d64c94621de50ea3d8de233f00abe727c",
+        "1f8f762bbdb7aa1361d3feac09a4f302dd5b84f83ac0fbbdf54aac18d94668e6",
+        "2ca6bf013787d31e303deb65938c2a693a386153652bd246cbe92615ace959db",
+        "089aafc428d2dfd89d9900c61853c20d8bce991f8b9897612ef58ffb18bf9653",
+        "0e31271d4934c28f7f5b4893f78e0379c93303cf5e2bd7597085a143b96eec4f",
+        "18bdc4b6e541294487090bd5b27d184a3341b9a13b0ebd196a2e72041dfb4049",
+        "0bac4228567e965f514f36de597aa76c7d8f2ccbf24a28dd6b41a82d8c55ae7d",
+        "2661052ecd6bc850113e8ad4000d6746accb2a280877f0aa8868303bb59e86f0",
+        "2821ae3f64ec950d3dad7e9fd3d4fa27c0217d68db44e2e8680c4bb9cf8c284d",
+        "18bfc8c135ffc8dc0716c3da478b29b675e69677ebfb418d4eb828603c8f700a",
+        "254551c52dd71e5f0ccc7e2c1293a244ff9f9088c5c3fdbcfec90e3817844448",
+        "0a0651fb8d1176ab2f1ace02bac4dd9300771db0739efd3402d4545d0810679f",
+        "12e59ce548880245b8c6a1659873a9205f4798ab6d0eddd312f174eab047e364",
+        "2affcd40193dc4638700e9eda5cb72fe49de2ccd281578c808585aaadaea00a4",
+        "0f8b53a5b07861c7b9fae244b5e0cd19e2244616f3dd5fc70dc8e3a1f26b006d",
+        "09746b46da861b549453f52e045f21808ffb3ed4a95046bfc846ac448a960d3d",
+        "0f9b94f845f5ff7c82882ad5c20071c1da3808d64cbcacbd9ccb7093e281cce4",
+        "1d04a0140a9ebf6d261caf0a6628bc3bf1c0774b41c5bb13a1b31e5af5a7756f",
+        "19dee7ec53a89834d3b6fa49307411b513540de9ace666828915ee459f350c9f",
+        "2dde5647410a41cadba404ff99c754e08a1244b3e0bdb34ad2abccffc8168617",
+        "11949285821245bf388451b051c7585a9c2965b058e3c53ce95f999fa7b38d07",
+        "23d504bf3add3f5e92d4019206a8d4e214cfc9b6d599b65f0b22c3e584630374",
+        "2de4d8e8af79c9540f0ee6023dc04c045ab8bbcbd860f5b1509f5890476b0b1d",
+        "0aa6826d4c87044a788a447aeee552bd5cca2a002650143525ffa0d2895722b4",
+        "177b830b53cae79d9906bc2b2f03e10eab77a94481e704c8b759cf97c9c4080e",
+        "03f4b43752ff07f878db812e6bf809330f32e2fc84b3bcb82ae0f1f5278f8936",
+        "2de3076e3ea73b2eea66ca0e01c502a2f8f71dc06a1597417f0c3d068ba5586f",
+        "1a2e336f39f3d431784a4e44df028219f703ae207276efbff7ec57bb80cc57f1",
+        "042e7ed52d87b601f0af92d01c4cecbc593964ab19ca88bfd053873bc3d829ca",
+        "13f8e71d7b8027f054cdae21aa38eb7372fa47892126132121c462692ce4c6d1",
+        "08ebbe75b08dc35bee9f2c6fafa7e1e0715595215ccabe92d81361459c643a1d",
+        "2b52ddab6722d87dd8b720ea8e2942f83db6ed4d7b7084a6272662acee1438f0",
+        "0801deb4292ac18454faa177d462a6ca83cb4a5549de6b3964aea3904131cbc5",
+        "2b970ef6a757e39ea2793fc60220b18400d21d8400962c4cf9092b44767b5ea5",
+        "08ad6ff1355f710abc654d53fb1b4273b56783c0ebce82674fc2724f02a60310",
+        "0456de29eb92b64486f8cf1f5411f1e7cf44e1e26df9668963324c33e24b2505",
+        "0e7132a0410928546cfd61fc8cc6f9e34612aeb9b30f5f525f73c919fb8be2bc",
+        "0113c78f2f7701c452ae4e4be38658446da7e3c37a5ae9cfbd23122038f647d3",
+        "14c54eb543f3927eb9e26fe3a8b428af4f436c9da54d739eae07587ae2da3eb5",
+        "1164a09fa55b57b0e3c0c35943b8aaf1ef00bd8cc47479aef44d6b56fd557ac6",
+        "0f47e5275df07c737e703036a11b411c74f4f688f05d07b4f417a9ce7b3abb9f",
+        "06b925b4459e50f1a1267e94805bfd6f6964f5402978c86409eea9acd7d200da",
+        "1b79c664c691fc1eca0211e6438d12ace2154922624bbee7537c2f98aa70f4d0",
+        "064a28499d7993d7b6878ccadc2497a12b90d30da9b588008ad00175f5c87568",
+        "1b9d45305ab0a71b25fc9c77222d096d89d7e38b7bad65526c41392c9cc6ed25",
+        "0a8b4caa1652d0f981840cdadf8d603d2f2ed35e0b7f8a6c40b716ed9ff43587",
+        "0eac03baf5335451eb594055f44d864340e0bb45279469e69829039844ee0a1f",
+        "185e6a1e5bd6175797423d681dd39c04411d8e86395122819ef8f798ecca18aa",
+        "208f1ffc5197251dc3e76671fad4f4c48a0ac0a0332b201ad2bda0d7e1dd7b04",
+        "0b6ed667fa12387e452f2df3ed7814acda983dc6a5ca848fd7c9b532c117369d",
+        "121ff89d826a0408213ad8ebd1f334a7e016f2a158e8db147459c0ff94994515",
+        "23c7694a3e9c9a63823b014557e09dfb699f14b903825691252b1653425bff49",
+        "2451aeb6ce54d16ec2a6b23cb33bc8676ff8e8f56771fb50fde1abfbc2a6d3e9",
+        "0031abea5a650a7015d01a6d98495903063831b4ccae1bd92fa6bdab184bad99",
+        "1c787698b4f082afebcf4229e502d96efac8001d4dd011d0aac0f3e82f3e181b",
+        "16fd1d5b15031b91a98017c0accaf34ff159a93042a84b78b5d3d33aeab577eb",
+        "0463cf787ef275639011b199a7a1a42be1a89d306088d1f3129f9bf395ce16a8",
+        "0dedd9207786c975f7a249943e72760c1d22aa4bd32486d953fe2711bcca29f6",
+        "1186ec4b5a29dee9d79f4ce8157d1b3693d79d475cc38fa12c540ad2a19c1ab0",
+        "0369d8d700e3541b0049d998a022161a73fe61b5170ef1ab395556cb9992b8ee",
+        "16aec409424ca844ced972fdd95890db57bcea8a186e68172e1035a2e7366126",
+        "0252b07dee53f0aba0ccb9d8d9e4f5268ad1b72815d7f64ab26e41b555acd388",
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+        "10fb8b5339ce5ce52f93aad84ba2a19d7efc79ef30d8f78551c9cdb90be565a3",
+        "040d8ecc62f78456e4b36aeba98248115dc2e649005ba897e52d095707a99648",
+        "0c4e34fbd5bc4163e60b1b7a5943e93fa2de19cf4bf34406de021ee93f8650b1",
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+        "11f667444d0235d35ea5519fa90b888517f1c5e31128e20a02eb9d9cfbf43c51",
+        "27d4b6c9a610982e824ea82924d9f554868093b22e95d3f936ec56651af8af78",
+        "281b5aa07a5e9dac69ee2795d3830743d1d03cd651ef00342b5a41d8202e3b0d",
+        "076cf00cf46a9ed4a988bd46e5757926ea8d8ddd0e2a64278aeaa1d11a3588f8",
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+        "062b8ffd7c22d07d3822ffe9e6691f6151c540d8e75cf33083fd7bc2a8dfa678",
+        "137684603727c5566281869fc283641dd871103fb93f594537f18b2297d4d086",
+        "10231174a196c63c97bc37f9feb3a5c296f4d186b64a49de8ec309c9844a3a19",
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+        "1b8424ddca6303d0fc74383a2f34e5d8139ad8382ad6eaeb93d7a52fca696448",
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+        "10cebf15ee2d227b472d1997ad6466639fd5ca6f65f4ed71c2f4a4e8108fb808",
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+        "16d1ee75be1bc0dc862a40c18a682ea13e11da0d9cd0155f6bf49f4766583fee",
+        "04c5c01e69b915bfd03c263b1fd92e5dc9047b054050d96e643212fe189ed550",
+        "12b5c306a0c9c2395d5c8136e0ab2bbc87ddb5208f952c43133e3bb006f163ef",
+        "2ed3a29fc700319e791423611cb9338f091fc6a3a27dd4149142bef7b8c6a6ae",
+        "18d0bbd2f7b6549b9a6fd031da5e90c70117b249ecba30324391adfa2dccf40a",
+        "1d0141680ed9d4c565c23ceb32ef14bb1cc850da92b68b42ead2fff263a50dc3",
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+        "0b309588aa15ca721b860e9e16b63e4bc0c9fdbf9f33c803864c2186faf546fa",
+        "1d26d1b2fa587e552742939e1f7a5c1094284d73ea26300dc0164296d1add353",
+        "0dd88cf71704e5a22780414827f9d3f901e26a7eaa03bf02fbb9d257459e29b7",
+        "13e02ee85bb3a1dbd4140760f883735c44a9df7b7cf6fe36ef47cc029243bfaf",
+        "26b072961338627a467fe65b4d9b840eb6adeb62c880880949506c200b72b159",
+        "1b99c0d332ed873997650ab60f2546a58c5db89db8eedc577cf360dd05c5a175",
+        "1d595d764c0920d9b829e486845d24357400a14735b0cdeab09274be0c087f20",
+        "1f0807972bcdcd4223e8fcc5d9aa66dcb3547763dccf039be8810e36d86b59b5",
+        "1129abbc9892b557c6cc1bc5e887dbf3bac555fae48d14dd29dd7fe047306cec",
+        "06fe41202ffcc22a7175c24e1276c68be31fd025a5f7701d7a58e2dea387f3bf",
+        "11c8c337e529eb09ec48a2af3d260ab53f5f5e1a075080d6a92a29b99b206ab9",
+        "2d0faba58fce65e3d9f4506917a2e349e6a83d7f240c011d7020479e27e2b457",
+        "2f4f26f8db0b4bf38398616c1e30563e92c2b3d6273ea31310d6c09327d7166a",
+        "17745d3a6e217f23fdf7e9b249f9667ca49665c4130661f5ad6ba3d2b9997263",
+        "2b1cf0745a1fb1b55808db2eccdcd5a075618ae476f231baee9b36f8957e691c",
+        "23cc30c9d4cfdee0d8a61d2d70bd59b9d37be22c8bece8f7d3b11eece18d77ac",
+        "2714194c494be47166bc32801e3b7bafa83073f5054d5e39ce9e536d2797ace5",
+        "1ae0089176f96175631a459a378462df32b6bacc53e06dd95ecc1638d6694e6d",
+        "15c1bac5b8fbfe6770f6cfba64bc668ba6fa58aa3a0b7886ae97be77652b99c9",
+        "03b9f1628697c6da5226d87f8f93503f6bdf47aed5f78b6faea742c36fe62057",
+        "2c828412192724cfdc6af3b165d3d0c0a8c71c4659b3df1b150a79c9ad0bb5bc",
+        "018b680160db10cbb31241f5b637c06e62fcfbfe58492dfeab1b4e3799abe82d",
+        "0b535a898c2dbf2a4f65d15207f368185a9c8306ad8e5c5edb86be8e84ecff50",
+        "29324096c65af5453b3396d4bc3e4027d340bdf010ebb3a24e6468e896147463",
+        "2b178d913c35ef5f24d35af5c1defd0f525456328267130cd04b0a337266ff9a",
+        "0427f640bd8e11be9e83acfdedafd4e4b69ae12e663cb9fd447e2e73089a2f03",
+        "29a30a42fde8bf7f79bc57abff5ba6ac4c4e77993a37ec07f9914c99dd8d1b3f",
+        "12933a990c79258d28d90e9fb5fa451ba219206ae6e7cd56339b4ac5f6e9c6e5",
+        "2ca30dc3c18dc52f9e8fd59d80cecfc41c2210163c044a9cfc46a8234abe44a1",
+        "15039ba21746a75f4052e59167c8fe61befa3c228b67688926692ae34a8f8af9",
+        "0d013043d7f43c1c3d7aa1e9771d4f38eeee78d6992f2a84a7c64c20632e54cf",
+        "24770a0fcfc79a72d55c7a7f90d1a66494c745643aab2a08b4b47562d643a4ce",
+        "00f5edbb6253299639f0e366835edff5a941a1e29c954571283455bfaf94c0ce",
+        "28d5f124104d0ed06f3225e41b28bb431e7271e383935f708e558ba5d05bf667",
+        "00b8c2bb4918bc3a3bb76636f0a1173374c803aadb1003dc414a5fbb46e81174",
+        "08d20b914f6a7b4115a092b4976ea22ecea0ae58cfdf1679320b6b6bae9152c2",
+        "017b4defb2cc581e394d666ea82c4b09e56b57a1b503c8a29b2053b5c4b49a15",
+        "0591f82cb330a66704560c33f4189e8395e2646d0e0bcc8afae9d061dd928cbd",
+        "0d45e88a959bdd51c13a22e35cf22e30d9ef425fcca3aaef605e6359a0e7bcb2",
+        "15d320a4187dfe9ddef4378687932e16ff24583e7f9872855b566cef8d6fa00f",
+        "05cc9867eaf7a58de61bed98fea0df793ad0e6b9224a3566cac59ca647de5fe4",
+        "14418f317207f95eacc37db9e6bfd42d2594abda2e09e4d8bf853366453431c5",
+        "045456a3b2f901ba8a4cb79701218c4cad120a11830d7ce95f33130a0d994aea",
+        "1ad7a2c79c70078007734dc96d3647224a8e51bf7be88fdbd9e7dd12a65846ea",
+        "289469ff983ad3a6b33ce1d25435381344d13a3dc7b0b15f15389dccb078ecea",
+        "2da5ecce164e53c79a705da5ec8d46efdb8fc2fe102ac7e4307cf8c9f71540b7",
+        "19a4a3a81f818d5cd64a8858047f7312e16a074ee00a5730f07f35b611a06d8d",
+        "140239abfb94dbe1c517b537c230e0e36b15e6ff28e249d1573e412d2e6392c1",
+        "046ff7e86f24a11fb0e200a979f7c7a27a4dcc114a368fd618153b68c37e35a1"
+    ];
+
+    let mut acc = Fq::one();
+    for i in 0..10000 {
+        assert_eq!(expected[i], into_hex(acc).unwrap());
+        assert_eq!(from_hex::<Fq>(expected[i]).unwrap(), acc);
+
+        acc = acc * acc + acc + acc.inverse().unwrap();
+    }
+}
diff --git a/tests/serialization.rs b/tests/serialization.rs
new file mode 100644
index 0000000..d7c94af
--- /dev/null
+++ b/tests/serialization.rs
@@ -0,0 +1,23 @@
+extern crate bincode;
+extern crate rustc_serialize;
+
+use self::bincode::SizeLimit::Infinite;
+use self::bincode::rustc_serialize::{encode, decode};
+use self::rustc_serialize::{Encodable, Decodable};
+use self::rustc_serialize::hex::{FromHex, ToHex};
+
+pub fn into_hex<S: Encodable>(obj: S) -> Option<String> {
+    encode(&obj, Infinite).ok().map(|e| e.to_hex())
+}
+
+pub fn from_hex<S: Decodable>(s: &str) -> Option<S> {
+    let s = s.from_hex().unwrap();
+
+    decode(&s).ok()
+}
+
+pub fn reserialize<S: Encodable + Decodable>(obj: S) -> S {
+    let s = into_hex(obj).unwrap();
+
+    from_hex(&s).unwrap()
+}