From 31060298d794ea045f840c98226ead89fd51d7cb Mon Sep 17 00:00:00 2001
From: Xor0v0 <Xor0v0@163.com>
Date: Sun, 7 Jul 2024 02:25:17 +0800
Subject: [PATCH] First commit

---
 .github/workflows/ci.yml                      |  29 +
 docs/.DS_Store                                | Bin 0 -> 6148 bytes
 docs/crypto/.DS_Store                         | Bin 0 -> 6148 bytes
 docs/crypto/lets-hash-it-out/code/.DS_Store   | Bin 0 -> 6148 bytes
 docs/crypto/lets-hash-it-out/code/Cargo.toml  |  23 +
 .../code/bits_vecs-1709319118230              |   1 +
 docs/crypto/lets-hash-it-out/code/exp.ipynb   |  47 ++
 .../code/src/bin/verify-bls-pedersen.rs       |  74 +++
 docs/crypto/lets-hash-it-out/code/src/bls.rs  |  18 +
 docs/crypto/lets-hash-it-out/code/src/data.rs | 531 ++++++++++++++++++
 docs/crypto/lets-hash-it-out/code/src/hash.rs |  29 +
 docs/crypto/lets-hash-it-out/code/src/lib.rs  |   9 +
 .../lets-hash-it-out/lets-hash-it-out.md      | 114 ++++
 docs/crypto/oven.md                           | 198 +++++++
 docs/imgs/welcome.jpg                         | Bin 0 -> 1007584 bytes
 docs/index.md                                 |  12 +
 mkdocs.yml                                    | 102 ++++
 17 files changed, 1187 insertions(+)
 create mode 100644 .github/workflows/ci.yml
 create mode 100644 docs/.DS_Store
 create mode 100644 docs/crypto/.DS_Store
 create mode 100644 docs/crypto/lets-hash-it-out/code/.DS_Store
 create mode 100644 docs/crypto/lets-hash-it-out/code/Cargo.toml
 create mode 100644 docs/crypto/lets-hash-it-out/code/bits_vecs-1709319118230
 create mode 100644 docs/crypto/lets-hash-it-out/code/exp.ipynb
 create mode 100644 docs/crypto/lets-hash-it-out/code/src/bin/verify-bls-pedersen.rs
 create mode 100644 docs/crypto/lets-hash-it-out/code/src/bls.rs
 create mode 100644 docs/crypto/lets-hash-it-out/code/src/data.rs
 create mode 100644 docs/crypto/lets-hash-it-out/code/src/hash.rs
 create mode 100644 docs/crypto/lets-hash-it-out/code/src/lib.rs
 create mode 100644 docs/crypto/lets-hash-it-out/lets-hash-it-out.md
 create mode 100644 docs/crypto/oven.md
 create mode 100644 docs/imgs/welcome.jpg
 create mode 100644 docs/index.md
 create mode 100644 mkdocs.yml

diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
new file mode 100644
index 0000000..4529cb0
--- /dev/null
+++ b/.github/workflows/ci.yml
@@ -0,0 +1,29 @@
+name: ci
+on:
+  push:
+    branches:
+      - master
+      - main
+permissions:
+  contents: write
+jobs:
+  deploy:
+    runs-on: ubuntu-latest
+    steps:
+      - uses: actions/checkout@v4
+      - name: Configure Git Credentials
+        run: |
+          git config user.name github-actions[bot]
+          git config user.email 41898282+github-actions[bot]@users.noreply.github.com
+      - uses: actions/setup-python@v5
+        with:
+          python-version: 3.x
+      - run: echo "cache_id=$(date --utc '+%V')" >> $GITHUB_ENV
+      - uses: actions/cache@v4
+        with:
+          key: mkdocs-material-${{ env.cache_id }}
+          path: .cache
+          restore-keys: |
+            mkdocs-material-
+      - run: pip install mkdocs-material
+      - run: mkdocs gh-deploy --force
diff --git a/docs/.DS_Store b/docs/.DS_Store
new file mode 100644
index 0000000000000000000000000000000000000000..5008ddfcf53c02e82d7eee2e57c38e5672ef89f6
GIT binary patch
literal 6148
zcmeH~Jr2S!425mzP>H1@V-^m;4Wg<&0T*E43hX&L&p$$qDprKhvt+--jT7}7np#A3
zem<@ulZcFPQ@L2!n>{z**<q8>++&mCkOWA81W14cNZ<zv;LbK1Poaz?KmsK2CSc!(
z0ynLxE!0092;Krf2c+FF_Fe*7ECH>lEfg7;MkzE(HCqgga^y>{tEnwC%0;vJ&^%eQ
zLs35+`xjp>T0<F0fCPF1$Cyrb|F7^5{eNG?83~ZUUlGt@xh*qZDeu<Z%US-OSsOPv
j)R!Z4KLME7ReXlK;d!wEw5GODWMKRea10D2@KpjYNUI8I

literal 0
HcmV?d00001

diff --git a/docs/crypto/.DS_Store b/docs/crypto/.DS_Store
new file mode 100644
index 0000000000000000000000000000000000000000..ca58bb03b3bade322a8a16c0b4a01a5e99c8bf1b
GIT binary patch
literal 6148
zcmeHK!A`?447Fj0N?ghXao~_2=wW{lrt$^*0T@FJ)GCwM?)f^-d;lNAb8Mzos|4bJ
z5VED@IgXvUPihhq5ij=ZIZ;hS6`CN6G9hA~oH{Y*8Ia2w4Q=R-UeGra3;jit<X%%p
z541zx!~CCMX(-X2cHQHAd7t|2-~+yl=~LUTy0k(}_4a&m{(kj({hht~wEj`tc5{^D
zAYE6T0cXG&a0Z-#0|U6TMXEDJ@0|f>z!^9&Am>9s6O4vgu^b)fN(lgzXLJ$hQcFlo
zFpP#-5i=0hP@smgl^Cqyum|&thFMX=iLLlx+xfG2;j%l{55=80Dthk>I0It_PIXwz
z{eOdBX0pg1hxo`Da0dPv13YV&?E)WVck9vT$z2=JZqY=<FN*?!K6(UTAm_+snbi3p
ZI{czxR+Lr5Uc!O?5GaIr=M4M;10MiLH~jzr

literal 0
HcmV?d00001

diff --git a/docs/crypto/lets-hash-it-out/code/.DS_Store b/docs/crypto/lets-hash-it-out/code/.DS_Store
new file mode 100644
index 0000000000000000000000000000000000000000..47fe905adee1211cdc99e098f0457890c4fd6d7e
GIT binary patch
literal 6148
zcmeHK%}T>S5Z-O8O({YS3Oz1(Em%`2ikDF93mDOZN=;1BV9b^zHHT8jSzpK}@p+ut
z-GIfMMeGdhe)GGV{UH0p7~|tbc*vN|7_*=ua#U&r-L;{HNk-&2Mm7&(8G!W>%uVdC
z1AcpxWh`Y6LGk_j<0#7qgHPUQwzjt0R@>@YcixjMyxh+h+1O8S(7Kc|4l3ObuA*5n
zwRg{ClKW9IOI1M>&LHLXI!Z!WjO8K;Gga&9fYq@&Q@giZI-}#h7&^|XFP10Hpf8Sw
zqt&Wo?d>0&UQD0kmqfm4IytbdWXE6y@1U5~yn1O8%j6L}Rd$s{NDL4I!~ij{*$kL-
z!Rl@{4YYb<fEcJ@0QUz04be4NYE)YXba;Kncnc8)bbL!73WKh}QX@n_xGn|MrQAF*
zxGo33FnO-QQll<sT+IyQn3=1`3s<v)U#N7(U5(Te1H`~O15It(c>bTmFH`%-UoRnx
z7$64z83VjE@g`$flsQ{}EDz6G0qq_d3g(rlfPlVs2>=84k)8_bxIi89T!W=X90mQV
Q9FQ&oiV*6EfnQ+Y3l~R8ga7~l

literal 0
HcmV?d00001

diff --git a/docs/crypto/lets-hash-it-out/code/Cargo.toml b/docs/crypto/lets-hash-it-out/code/Cargo.toml
new file mode 100644
index 0000000..defec20
--- /dev/null
+++ b/docs/crypto/lets-hash-it-out/code/Cargo.toml
@@ -0,0 +1,23 @@
+[package]
+name = "bls-pedersen"
+version = "0.1.0"
+authors = ["Kobi Gurkan <kobigurk@gmail.com>"]
+edition = "2018"
+
+[dependencies]
+ark-std = "0.3"
+ark-ff = "0.3"
+ark-ec = "0.3"
+ark-serialize = "0.3"
+ark-bls12-381 = "0.3"
+ark-crypto-primitives = "0.3"
+rand = "0.8"
+rand_chacha = "0.3"
+hex = "0.4"
+prompt = { git = "https://github.com/kobigurk/zkhack-prompt" }
+blake2s_simd = "0.5.11"
+
+[[bin]]
+name = "verify-bls-pedersen"
+
+[lib]
diff --git a/docs/crypto/lets-hash-it-out/code/bits_vecs-1709319118230 b/docs/crypto/lets-hash-it-out/code/bits_vecs-1709319118230
new file mode 100644
index 0000000..809dd03
--- /dev/null
+++ b/docs/crypto/lets-hash-it-out/code/bits_vecs-1709319118230
@@ -0,0 +1 @@
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diff --git a/docs/crypto/lets-hash-it-out/code/exp.ipynb b/docs/crypto/lets-hash-it-out/code/exp.ipynb
new file mode 100644
index 0000000..626f68c
--- /dev/null
+++ b/docs/crypto/lets-hash-it-out/code/exp.ipynb
@@ -0,0 +1,47 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
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22051646840009088951998032345296732581209744834265571373614728310754428022114, 14740743894720313561972805730889837369209844664677572154427721775280145685380, 49888599474336767018961967840501121549277908070043371526741647080631161900604, 2226428591092427188852297273609125697078037027246847643550392518497016303114, 40457365089919799675424603047068092657065398040089839525215044029661342444427, 47636432557547746134675321919618290785609013406774503800766126591253194174383, 25764426033484082584247659872193844597372551421553143639362878768860742569527, 30952280361789272379718585352021894402169608928074681097327470987684436422468, 23301921066864243609599634820072336449804567113234659617478061398123765131830, 50199846303729111186077032834132520112897642289070389344914371076060369211, 29076616411801817675495903457577928851144543958786020135798181819796919704130, 32749792342878155015696215526918338374559072705954117303807811474393946525128, 51857978415084411058560324300359168036457076359417923703500287849019885509454, 13016277418102391693529419944110516341331482502334457725009941497753099607393, 23088803725380660621874147049352075783590521801750272988072008111941077683043, 10404073213690113210920066878777272797034206423564428988467902512791074554853)\n"
+     ]
+    }
+   ],
+   "source": [
+    "R = GF(0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001)\n",
+    "y = vector(R, [1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1])\n",
+    "A = matrix(R, 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+    "# print(len(A))\n",
+    "\n",
+    "print(A.solve_left(y))"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "SageMath 10.0",
+   "language": "sage",
+   "name": "sagemath"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.9.18"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/docs/crypto/lets-hash-it-out/code/src/bin/verify-bls-pedersen.rs b/docs/crypto/lets-hash-it-out/code/src/bin/verify-bls-pedersen.rs
new file mode 100644
index 0000000..7ea3343
--- /dev/null
+++ b/docs/crypto/lets-hash-it-out/code/src/bin/verify-bls-pedersen.rs
@@ -0,0 +1,74 @@
+use std::fs::File;
+use std::str::FromStr;
+use std::time::{SystemTime, UNIX_EPOCH};
+
+use ark_bls12_381::{Fr, G1Projective};
+use ark_ec::AffineCurve;
+use ark_ff::Zero;
+use ark_serialize::Write;
+use bls_pedersen::{bls::verify, hash::hash_to_curve};
+use bls_pedersen::data::puzzle_data;
+use bls_pedersen::PUZZLE_DESCRIPTION;
+use prompt::{puzzle, welcome};
+use ark_crypto_primitives::crh::pedersen::bytes_to_bits;
+
+fn bytes_to_bits_string(bytes: &[u8]) -> String {
+    let bits = bytes_to_bits(bytes);
+    let mut s = String::with_capacity(bits.len());
+    s.push('[');
+    for bit in bits {
+        if bit {
+            s.push('1');
+        } else {
+            s.push('0');
+        }
+        s.push(',');
+    }
+    s.push(']');
+    return s;
+}
+fn write_msgs_to_file(msgs: Vec<Vec<u8>>) {
+    let mut file = File::create(format!(
+        "bits_vecs-{}",
+        (SystemTime::now().duration_since(UNIX_EPOCH))
+            .unwrap()
+            .as_millis()
+    ))
+    .unwrap();
+    for msg in msgs {
+        let blake = hash_to_curve(&msg).0;
+        let string = bytes_to_bits_string(&blake);
+        file.write_all(string.as_ref()).unwrap();
+        file.write_all(b",").unwrap();
+    }
+}
+
+fn main() {
+    welcome();
+    puzzle(PUZZLE_DESCRIPTION);
+    let (pk, ms, sigs) = puzzle_data();
+    // for (m, sig) in ms.iter().zip(sigs.iter()) {
+    //     verify(pk, m, *sig);
+    // }
+
+    /* Your solution here! */
+    let m = "Xor0v0";
+    let (b2hash, _) = hash_to_curve(m.as_bytes());
+    let bits = bytes_to_bits(&b2hash);
+    let bits: Vec<u8> = bits.into_iter().map(|b| b as u8).collect(); // type convert
+    println!("y = {:?}", &bits);
+    
+    // write_msgs_to_file(ms);
+    // verify(pk, m_bytes, sig);
+
+    let mut bad_sig = G1Projective::zero();
+    let coefs = ["20284227033425027763233277958977844789245805636043480635714394335011252408171", "40373372484032675089701272023472705371805303840181868663339104404091607781329", "20999620817661158104091615115384131286241496732129392405000521390537312494971", "39795697778844093563312417531484776405760123063203633110591175393760864205743", "5796726736068928490460553308900032813546998071383145546045627381895577223970", "46941903732077663432094701053746398472093222319947855682023217104677608549649", "38264845256711204850532729513804414161731671225541275179262594295384214931081", "13019669266149144342339306274977879063578408689675138507240598648278210198921", "9337381890774839500624119557906858050271180596049074104784000305006764464280", "16143802584309919286442705063479484557030812624292717184974162454339619845391", "25606065321629895508765834279099804143267761150118694162340049988018712266835", "32783887872087749278780649035235265828837351921277145439112660681125437597070", 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"32078746170880343517603939060390486337853787813422627870018530041795467024048", "8142336868976197104568138174265305527675719878907524516525697120782143961308", "14809261148170634427377508018882866927675090965130218436540119225926672087998", "27309476398978070699831321615590071441803533651843061967972968559478655031723", "23315944253477676482701727904770517147964931943156386170587644001654445554470", "14315894023065843062443303672831734674526044517229170606213310159694151044157", "19678267285385502993235983364965554745935349264421198183332238163548033261200", "49416875262518607300636812649521535745889866010415167998313565879752926054347", "24793804765942715401457828435152261987384619195189962473083037455433195291475", "48757214700473286151082910794980034114288719883198252997015777155620913065771", "23625015730986339890157331307221610330369623394670555602898513142294727911319", "49834283603445028557147013469224392146030336314694620409074302699663454932715", "9325123436257667437699550328954579676122133560200939781865754921833018438793", "22423478450713570026306595060209155532251576455220666573030177943211747827468", "43815200127849505551383129576726067066103130259759613960576911763376752084661", "20222848571050351142917467282603051545704043659953228592851998830993225165717", "13460248928745155253468419225447255577809796240312924633571372520309738089741", "25743286528123156489973129214229285926037726428701133591698045347437537565798", "15053622949214349162338684655324844540645249343739765232234425777758019324451", "39365154704482869420506008815042047357227040581349085915322647881842568026648", "41444859520742706548425362651101822964045096328556528090264096510997265840210", "43210313769330051547783470309695061075731706639377711933763883384809671219693", "26106401332087002989304070590345191715166134606661430982896208948098170664989", "44666988919637689216112388856190928511469317763070082859437270402734511062955", "22051646840009088951998032345296732581209744834265571373614728310754428022114", "14740743894720313561972805730889837369209844664677572154427721775280145685380", "49888599474336767018961967840501121549277908070043371526741647080631161900604", "2226428591092427188852297273609125697078037027246847643550392518497016303114", "40457365089919799675424603047068092657065398040089839525215044029661342444427", "47636432557547746134675321919618290785609013406774503800766126591253194174383", "25764426033484082584247659872193844597372551421553143639362878768860742569527", "30952280361789272379718585352021894402169608928074681097327470987684436422468", "23301921066864243609599634820072336449804567113234659617478061398123765131830", "50199846303729111186077032834132520112897642289070389344914371076060369211", "29076616411801817675495903457577928851144543958786020135798181819796919704130", "32749792342878155015696215526918338374559072705954117303807811474393946525128", "51857978415084411058560324300359168036457076359417923703500287849019885509454", "13016277418102391693529419944110516341331482502334457725009941497753099607393", "23088803725380660621874147049352075783590521801750272988072008111941077683043", "10404073213690113210920066878777272797034206423564428988467902512791074554853"];
+    let coeffs: Vec<_> = coefs.into_iter().map(|&coef| Fr::from_str(coef).unwrap()).collect();
+    for (coeff, sig) in coeffs.into_iter().zip(sigs) {
+        bad_sig += sig.mul(coeff);
+    }
+
+    // the solution
+    verify(pk, "Xor0v0".as_bytes(), bad_sig.into());
+    println!("YES!");
+}
diff --git a/docs/crypto/lets-hash-it-out/code/src/bls.rs b/docs/crypto/lets-hash-it-out/code/src/bls.rs
new file mode 100644
index 0000000..2c53dfe
--- /dev/null
+++ b/docs/crypto/lets-hash-it-out/code/src/bls.rs
@@ -0,0 +1,18 @@
+use ark_bls12_381::{Bls12_381, G1Affine, G2Affine};
+use ark_ec::{AffineCurve, PairingEngine};
+use std::ops::Neg;
+
+use crate::hash::hash_to_curve;
+use ark_ff::One;
+
+pub fn verify(pk: G2Affine, msg: &[u8], sig: G1Affine) {
+    let (_, h) = hash_to_curve(msg);
+    assert!(Bls12_381::product_of_pairings(&[
+        (
+            sig.into(),
+            G2Affine::prime_subgroup_generator().neg().into()
+        ),
+        (h.into(), pk.into()),
+    ])
+    .is_one());
+}
diff --git a/docs/crypto/lets-hash-it-out/code/src/data.rs b/docs/crypto/lets-hash-it-out/code/src/data.rs
new file mode 100644
index 0000000..977506f
--- /dev/null
+++ b/docs/crypto/lets-hash-it-out/code/src/data.rs
@@ -0,0 +1,531 @@
+use ark_bls12_381::{G1Affine, G2Affine};
+use ark_serialize::CanonicalDeserialize;
+use std::io::Cursor;
+
+pub fn puzzle_data() -> (G2Affine, Vec<Vec<u8>>, Vec<G1Affine>) {
+    let pk_bytes = hex::decode("0113bbda74ea0480677e185568f5e7ad3dbe40fc02ccacba4c735e6e45001640a694d204ad25411f72f928c9fec00f098fc345e4b7ceb95a68a00983f5693d37929c80b09230fafe537ac1fa06c43009dd1efeb1fab2d9d2a816319f08b38f0b").unwrap();
+    let pk = G2Affine::deserialize(&mut Cursor::new(pk_bytes)).unwrap();
+    let ms_strs = [
+        "f2faa8b1bb0f06c6142e788ad836d1f7d1abf95458a08a55593c594056ac225d",
+        "518385d7e176c291bab8f797025de4b26a2b86c8e10f57d2e21b5a742ecb6029",
+        "dd2998c22a1e9ad794e46f4b01602b95b8410bb82f024a4cbc0a29f95076126d",
+        "e4c5c71389ee5551ce5d1c89c2e69401d3d73504b4a397a17a88c9fa9ae94343",
+        "6f76783a8ce3b940bcf4669e585ae07b874361dc33390b6cbac4269e8f156e1c",
+        "8dc9d4c539a4f3dd0096cc49baaaa2d0c52df19e3f50f7ba9152c56588a42118",
+        "b4a70a337b492f4797b6f5b87cb9162f6b002be8c3da19b09f38482f077f5a21",
+        "f8cf5305b77e78646a79bd4728030fc3d5e23e14b25ce0c5b29aad92bbe72618",
+        "a8b8df6e4f20af03b07e3f51d5be40dda33feda50465fb055f8f68d220599839",
+        "922eab5120cc166a3ee965f15c3589cbf3b4c83ba5f9c84da873aa94e7663244",
+        "b73707f30f92cf67583283085c9a4bba494170a9752e5d2cb497c8122bac7754",
+        "dcc696196670023ae99625242f691f0219c8047cc6d79df73ef03ec081d87330",
+        "d9328e64fe230896f4b59edab0901e64d319f68e0f25b43bf526461be513a34e",
+        "9fbd6c67613a1c533dfbc62ba002843e3be0c2d0b276965b9fda5e7e8244e629",
+        "34d58dd4fbc69f70dc72342698a86a99133ae3c3dd70a6f8e5dacceb497f0d11",
+        "bd26f357231397cca2b7f5e3b1c52552c1dfb4cacccfa3bbc819e67a3190a93f",
+        "19ac99ce621328b4b357873cfb8ead4cbab9c154d43a83c216ad2bb42a285a5e",
+        "263eaf7024f4d4e376102e3fe242d95eeaf936dc715056d443e89654b667ca58",
+        "8afb6bfe3a5023743ca26da87718b9479f78d5659305b58d6e66b9ea26c2b617",
+        "e85bd6d7a4f53e1cfba09e16f71de656b918a79e6bd99546a7efb6a18dffd530",
+        "4b8157266851b7a4e0b20347db64f9cffe733dfc78b4158325e9d1611514a662",
+        "5a129ecb74d931158ec4229e5e1c33fd33ab8da1fd5e7db80a9f8c7d57190317",
+        "f48637ca6858fc30c7e692d3a14af8a3ff58822b76f4483daf02eb940954b772",
+        "a879da2a4f9d7d9482468e6b28f1feb219eab003bc9cb9c579fcdb742b150e08",
+        "75ed75164243d9d5ce7c5752036bf04d2b176a9572bff249f9ca65af25344770",
+        "45943ec03b759899cfe7a1c84609d914190f36d64d7e3c995d1d352a3cd5b153",
+        "22e4d444deb404b06cf717547ebae1145c2636fce71aee50d222b8c010a38a22",
+        "41e3251e4a2396a675f5ecfdb0df4e52c0c6f8c3a5ffb60949f478a1db795a58",
+        "738eba8e64942b9c6dfd3f07439772f48907134be4a390e93714b3a4293d4e67",
+        "04ef9af8d1299a90843d7c1aacabe73533e82da215f07eb23a22f953c70bfe08",
+        "6c99db178e75b5215adc28db01fca8de7aaf5343ac190322ed28936c8d51bb5d",
+        "83fee32d141fb5b012f6cb7a782fea2dfe7992e20de4240f342cdb7ad3d21d70",
+        "a92ef9da47163bfeccb3d6f0adac1f5a6bfc396e71053bbb2fbd523781b5d170",
+        "abffa2662081f965d63f52d490d391d4bfc1c02a328813967810a1ebbd98332f",
+        "c77323e94933705fdef3be2d82dfe14a0ef7333aa0b5719c9f4f77d8e26b2b0f",
+        "45cc458dc678a96f7f7a688980e3fbb9fe2668e0e0c1b5002adedf0b225bd438",
+        "8688eedd2f2ae643c46c6e3f08cbae5f0195d39bec42dc5cfee66fe10362b011",
+        "0c4fb36cc7b2bc714287074397f01e773e551b8e05acb596f26a73316c369320",
+        "4c04fed59816cd69b81c7afbe1598b109e80ef532ba30acea8b5b6c3874a832c",
+        "b12bb619aa8705228097cd486aa77a64d0ea7be38536fa3ac89a599fea468850",
+        "5bb32bde69fa90dfe07d9d444b2d8dfe65665476ecfb76ccfe6e4c58956be102",
+        "e8bdc2e2fd901ff22d86ac868a5e579318328d69eba99d7a946c288c5ec1bb70",
+        "4a9799150768a2e1d923e59cddadc7dfb5fd2fe78b264c0d856bc7d0356d8a57",
+        "2679dff8966750176bc09b478dcbeab70fffebc3f376b0188e9171ee779a1b03",
+        "d889d311774e17eed6d6530bb3a81ea578d6759df365fc47b7259e86a5130f10",
+        "dd7259a53bbbd49752c52c6734d21aee5eae02e1140d11d2a96111589e635363",
+        "0127aa01b4e644627c06ce2fe6912300c55b34b463bcca43c6c4a125bb38c025",
+        "a214398a2bf9a09c392b7c617f85d111c66f9a47ef7f3bdd315cfad391310945",
+        "5fd3a216597216c28869f0056d7fe97cad8e5bef9ddb9faa550245b4bdf09f37",
+        "eaa560cd1c987e04413cabb47a4133ba0ab2c143827d55d6cd09936987232b34",
+        "e440c6d66cad779f90cc23cede35072c0ca03ec650735cac9d71acaa2103035c",
+        "dfd0906b3aba1ab4e0add12249a29b953d894430cb13b9d1de4cea09dec2821e",
+        "853bd820a82a988ccd975add69c9a61e023cb1c573b08e32a1ff5f3ea8be3008",
+        "e61f531629bf9dae27060ecd725eee999d965fc86116d4f655ebeb8be57b9d37",
+        "99de834bf3e20de4e7b36000bfe6cb9e84d92051593ba9775b1eb4518513ba08",
+        "ab8279873402b5e2e48a5c708d5b43b504038f349b2ae15dd8f9e6d8cda2154a",
+        "22e54d8e28cb7a1a86727972b589ccf325f07895d7ab4eb75016a0d0a8252809",
+        "0cde6610c6dd844ad62d4e381002682ea233e969917512628973580e31d7af37",
+        "c90a36747e633de248f07ef93ac5310c911cc5f2f627c1cbb68ab1b2302c5737",
+        "b001f87181059a1150646cd15288f57e149de84b9c88bf7fac2a78d57823a33b",
+        "898983879e69781ea87a78fb92e63abb8ab1d86a8f5295b21de3eb1d4a101023",
+        "46b045958cafca38cce7fd6530401fc8419ba644e62261e5d413d666ebe59d4a",
+        "68b2842e316597a72acf64a9b3859306d74821290bb4e5f6c77a516e05ebf004",
+        "0ef85805f493d86d2973617d164067d88e09cc1a72c2da8140934adf1fd4572b",
+        "52657763da19fef8058d4db05605213165f9af89f75b5217fc2348fd52b7a034",
+        "7becb8dc29d22e830a0481f3549c55344cb4878129df6f12a67a9614e48c1538",
+        "80d18571bfee30ee52d88ba6374245b51c622191df47d52f8893f6f7ac9cb821",
+        "918bcd59f8219b859286809785ff3b483580187229c611068f995999ab03b131",
+        "575f10723157497251b1e7eca368415515b2e81a9f090143f61b3b0060de8f1f",
+        "7da0335a661c2ec7696e0b58cf696abac5be3fd822b2a40652120eb76de4116d",
+        "864dd5e12d82969a23911209d42587fb9ddfbf973392b37fd90d0e7dfbc7dd1b",
+        "79cfc41ed601977b07781e04f8b988925b67b4cc49414b4de0841e51c6bf510f",
+        "34000b1a84e5b33c9c441375936f5830abce9f5713935754e80dc02056a7a468",
+        "00741feb243eb7cec41cb236ba4a0432a2984e8e9a0a1bac00efd86c7abea663",
+        "5eec7336bfd1e4020b47990d67509e47a534b31ec8fd98d55410ef5c4415000e",
+        "b2121dde78b947f5a01df3849da1cf99b2070d217e45572c821de71b7d237b38",
+        "2e4ac7a560a8831d37a6db4cf4e11b2de4051e086295f9c4240aa476df82ec0e",
+        "038d22c5061040b8096aaad06fe455f3856a4a6370f3f23f7f26c9f8bf279444",
+        "abca92e9f4df054df48a584b0e09e6c56ab0ce0b6d4da2ef0254c09b39551c6d",
+        "f55ca65fd880099c0902d163d2572f392a0368eb520ed9de5d9a8c42f28cd156",
+        "6c31a2fc6a38cfb6fcdc5c7a0550d1b1b09cf2aa4c9ec682d53dd1b79131aa49",
+        "4ff34daf6a5654791a19ffb92c5a634182c2ac02f92084d394e0a9bd86811d1f",
+        "f838499584145ee92870e1b4bdfccecec877459c8e46452dd912702854b6f952",
+        "e2a1f45419da7807b3d1041e4d717671f8d30eb05d4c5d0ff7cf8bc304a7075c",
+        "e92426dab4875344b960106fbdccf2e9290c111205c14e6599b962bf6a56fb6b",
+        "1045d4d96c10df047f257b83550a43e10057df4119687b5bb50ed89984e45e4f",
+        "c663e8380914efcf1d7521c2877bcac2b6f15d7c7369dec483f60ea885656e42",
+        "e70fd273c87b6d7d944c7d2b671c99655fa40b46fc5b601630890ad332074f49",
+        "15e4ea6fce9310fd5afaf854557bee9baecb46bd239b45c82b6c86019297d12f",
+        "cc0bb69d47fe5ad45db005e9e49ed4f53ef37c0e43a56b1bd2375d6b5adcc235",
+        "699b5e712de2f9ef5f647da8de946a25d0fed88c2ed6b343c65411615d0c9902",
+        "4a83b04b4c9859f7edfe59aba106a7c3e9adf93054e554f5356183fb49e72f5c",
+        "1e1d7b3d68d4e0713eff80ff7ba2c56d7b75a18db83e4c26fae6d16504cda940",
+        "04e925f2cd03fb5c8e2a029217552df2d36402211a26b6a8e1c37d350a461f38",
+        "e86f21ab054b5d763f2c95604f3cbf41652578b875c55b8ee58fc20fe53ee645",
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+        "324e91eedbde1b57d39216fc55f00722b063f511be525d2a1463634fda59f051",
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+        "a613c9f8f87a49a0716afcb9fc359e6ca994e4ede3931c23cc621b83099d525e",
+        "5dc5179f360e8b8b45d991d1ad31335498d4bda0153967d978e22b675b3c3150",
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+        "67588ae977e0876f063ea625a8075f0bc941ca88bad54b1d2185be8b5a1faa57",
+        "c2a90677d0cc0dd615b4e792d81cc0e245a9052110a421bf2c233d562b9b1523",
+        "2d23ff25193bdbbfa8d4025112c101148be68bdb79d6fd54be0538745ba20d4e",
+        "35fac202d26d68ee43881e4da8fc03c7a17cc7750b7b6e712102e1d26ef15151",
+        "c0582b185fab67da016d06ac823e5d1c369844b72d4ef888c40486b6aecbc43c",
+        "8a765f5defda8d16131bf23c5f34c61dca81af401cb0af86f81dbd0a9ecc4733",
+        "f5529acf935401ca86673ecba56b532d24a07d1af8ca4f1d172648fe520f4c00",
+        "fb66d409ff3e41c12849d9418a0564c28b7bfae57bb0b213b61752a3c63c7415",
+        "1abec3653cb31f804091c99f216093ed48001d4f00ba3b32d7601de3a7d5f446",
+        "dc4f013f05c900aed6ccd8d44832c2f9998844be3222e608b70fa91346e42818",
+        "d77ad6403d6d61d5565465f94a1e2b5c03c25cc8182712130823afabc33c7d53",
+        "aa10e79600539e2fd0784bfbeba2532e4715e9d64f62a7d30d643ce78e09d267",
+        "2fac868746ffbefcbede610e4bacdd9164de92af2c847c139cab512b32789a49",
+        "6306cfa7c6927685bc40440d2b6a89166cfe6dd7da60ddcebdbc32bcff586f56",
+        "ec9c7a2362a3b431661876cef97b359e57efed9b420729052e43ddece68aaa1d",
+        "6963142d2c52e94d4ecdd2924e3a976e428c831c31e7ca94cdd3ca48aa979354",
+        "829e794112dd3f027b53b851171208556aac16ee590e2f8e1bc6c8f1dc5e424b",
+        "2761b55879750ea16a9910079723778bb87b2fdf7fe2f8fe44920e9b0a842724",
+        "7364c166e33b4d19e1297b3f15345758e27dbfe0665cdf9021c0cd6a4ae77066",
+        "6dc30dbd7301b830bbccca391c27090809737211b4869cd7a8ce4108c1f7a111",
+        "10f9d1d4b2f9e402ea46344928f9057c38e9007ae921eb1bfa3a5f81e34ef117",
+        "935444a0e9cc0eaef22980d29e9616ee12cfbf1cff2cb0ddb9eae45939f61967",
+        "ed99b6c8740fa59d6501fb9f03a64ea6b87477a99abaf9c5dec1b45f58113236",
+        "9ca05779e9f2ef5f9d9184ab15d71f94101c3ede6959eb34ea15be1625c3cf02",
+        "dcf79f297d63cb8d3cdc2ee489fcf6f24373fc46d2bc81e936d1909c459cc85d",
+        "a6b9e0ed0dfa22a6b72ef2fd1ba110b7906c694bc80047f6ddb9829b57aac959",
+        "867eae7ee7279de48dc125aa082b4220efaa442afc08492379a9a0b64fd14c6e",
+        "85ce5899b239272054df56f12100aa9b123f26e34ce8baeccf297b0bc87e3332",
+        "11c3c209e9a65ffff8f109f44c2fddc9112db347bbb0e9da32820d395872ac0b",
+        "03a477205e854bd877683d3814d15ae97cd573b7d9cad8f439ce8aa4f4bf732b",
+        "d01790e304da9fb59ca4488c7f290a0191400bb5e21ce2c41e35527f448ae356",
+        "53c19cd8b001db822baa805aaadf128c5330b03fd8883bd1927a62dcfab11e61",
+        "4a2b8ef7b1dd486cebd2621705f63a30ff14c92d374efd6a0439749a13c0c93a",
+        "5c7a6e6eec977e86b2de70756df3ac5a4f8c28f1bb3187e6b8799d67be7cd31b",
+        "d13da8dec942a26f17b4f39286ac4751da8c3194beae5cdc96bbd02f94fd594c",
+        "25db54834e6d164cfc899f55eb3fdcbfc1f5d853524ba86917efeefae55c336d",
+        "f74c67ac756ea706997be5b03cf77593c56752886137c015301430f9c1c8cb4a",
+        "9faed2634e72622365cedf388804a8fc443e76a97fcb212e442a38054d8fdf72",
+        "07ad291a13981ba12d4c6a44b604a75ad186e7be9111f73b1e359e8769ff3807",
+        "407af64bd384242a7498122fdd0fbdcceeb468cae1d6220e37ef90192f9d4c15",
+        "0e85673e5cebeb86ebfc91d71b382cf4852bacb340b636f48ff9c6c76fc51f53",
+        "9ca52dfcb4f1d2ef21b0673685c2a554a336e8a91da584d279cb315f4da1d511",
+        "c0421ee508cfe293fcc436e9c83bd026fba13122bfee5dbb4ff39b46c1477419",
+        "c507cf6315a0f047110ce88d17a964111fcb23a929286655d567b4a5549c6156",
+        "09546c1f63bc8813a8ce07e3b207b691c48042105da9415ad9afe2df61deee45",
+        "28a98dbc926017f4a089b6a3be4ceb2bbf5741a2d11e79d2bc3e9993f40b9f06",
+        "28c0575bb619358df4aa839cf8ebf86e4764ff36c93ef0e1292724340aea1513",
+        "5e0b81af6df9892034b89bfa1c8637621967963985bd433cdedbf86c77f9de2b",
+        "3a6bbd112de515a42ddca63ee4ff5fb4f5b5ce9b2e3ee7c18d18a6b9db79131c",
+        "4b74fffbd8f3a4f55965027a2a73ed601cb02cbce9f11cab6698362b0827c65c",
+        "24a2e859207eec5165e6a92b6ab370fb89cc73efa14cb0186f1a351ec0526127",
+        "16e1f1ffd8ed59cd39242e116e2bad8e7c7fa093ccb5202a58dbb7f5daac5650",
+        "e058d3f14634068dc9b64347db8aa0cf2952e8c42520fe2d681b97d33fdabf1d",
+        "c5cbb85553cb0c8b4b2cdab32cb190faab3836c46581e043c3d15462457bac14",
+        "3ed4de18d01b04bb8d1082ebde729059bda85676f1c84c817bdb9d69f0a22e2e",
+        "5da43a8e981cf85f88b53f29068d8d9b8fad383a445c622e544af93a4fde5416",
+        "6563819577585d0e218607710fa900207ef8571cf2a7d13bc2930d17ef5f5736",
+        "7079c2af4b83016bd51da316c0a02eebd7a0dbe3a2a5e0afc49dd97467e1a663",
+        "98fabb8c208e68c83a0eca91f2dd0bb0116d589fd016f6f7b5a099384cf32f23",
+        "2a6bd4d7bac8012fd2f110b9fdd8afe76b7eb67fcb2d5c30289fca59ca7e2948",
+        "dc66311db4dd1d792a9b5f3034c101dd70ad08a6b95f232b9a978a696043060a",
+        "29171a871ed6370691d9a4760fb8708ef9ca6bf5931283424447bab594829850",
+        "8fe80625fb2f18269b81a9a83decfed250428a3e943717c0ace31dba9838ec2c",
+        "20cfdf467b732bc3df22554184cd1fb7502148bcc0ff45ce538d1ef1f49d8659",
+        "4ea892b72b7d7af2de6f8ddaa7e29e5fef3103745f3688c55befddd1ca057227",
+        "0f1cd7cdf5343f5d2e0070640da7cd1fc12450e538f551f716284abde8e3d348",
+        "7af099241bb6df944bd6b598e532fab83a64a24c282158a6ca8b695e7a7b855c",
+        "a47342ac98b49dd420e396ee66e024ec93a83faf1df8f72db8f2ec64a2c43169",
+        "5123d2c53dd28a702e15d9a4219901e66cf0c6720f398706bae8940473a08738",
+        "d1980368e91332ca32ab2ace283318b4054ae169bb63107605ce976cb2f2b43d",
+        "936ed0992fdd340185727ac1a7f24fddc03511b181a2a919b1b771aba50a6b67",
+        "45621f34cbca5cf187b2173d061e043bbde3e3f26a97210fafc614ff2e5e3460",
+        "ea0f773d0b4690a2c499d29c43e59d000ce666fce77a4b13386f8daf98be3246",
+        "93a7da3e85cd6b3e0da306857b50032c3cdc8b7586cfc36ba577842009f9f123",
+        "6ca4a8f3ec8934c08d0a410c31d6b9d4bef62e00e390f528183cde1ae9ce4b33",
+        "4fc48126c21fa7eae5e7d5c8fa918904b81696d941bf0a760d1fb939ef885f27",
+        "8834d03900ccdfc6004cd8020ae6ba81654d24ddcd327c7d8c60e6e404b30d30",
+        "4b6f608b1deb8433c9554ea58305f8ede8928a3e82e59be49ac02fdfb2faff57",
+        "7c58c43ca7f2bbc7953ca033ae85e6bed76e6700a636cc16277c4d464f0abc1b",
+        "0b9bc7cf7a7af76a50537dc8082b4797d0d64bab8c9bd15933a61391a4cdff08",
+        "4e80f7ec80c7264afea594a39a1bebe20df9d75c4aff206417008baaeb6cb329",
+        "4fd761ff8572e140f61c3539f072198053ef00939e937b6bab00b5471367970e",
+        "ff9f7f7159807a3b4ddbca1d0b20108c42135295169248a6b84aa61200d99841",
+        "819cf24a5a96cec107954261c79339640294176de71fd32185ed0f6319891e0a",
+        "539e1954dacf691966cdff84130f67d482cadf6cd12cd887eba79b4b4d5e333d",
+        "4652a15d37a0ce5c2d72c93707bb35db96330e47b532163a7a4caf37081a6544",
+        "2d76603cb5ee977b46f128ebadc82e5a49fce538f58baea13bfdae114cd4096c",
+        "605cce208d96e0423577a6cb990e929e293dfcf50c39f13fcec2221f00088122",
+        "db95ed970d0ab1c83d1d86417253163bde5dbe8fa4efd8744235c538f31c1427",
+        "87d47edbc797295c32f9bde76e6eb7b61d726199a909627bc169c7ca28f74f37",
+        "38de0fc6e932c50c47156eba1b678271d0eb97573db8bb057389dffea7670260",
+        "6cab02884990a85352410f6b1c9172af99566c392c28f291f35af3769d1f2639",
+        "ddad8a3fcc2e77a5ced6f1b210cab5bc29e664817da47733af2221d5c3225f3f",
+        "4b82b78e08d585964e1420cb6e80e7ac382b2c64bc52d8a1ae686674dbfed315",
+        "805e447dbcee73740cded16659f8584ee33659a79aa0e20143f872ffad5b253b",
+        "610d76352b60c7c5600c33906cb9b31603c6491c623d3d3d09852b6be320ab46",
+        "245778d2e424c9cf4d691c57f2103f3cdf8a4422db8d41bcaf60c27cce84490f",
+        "80468e69621fe4da293b59f44ad7f3f8fe2aaa1fc615c29fe739e23f9f4db665",
+        "6bbf0417f00d2b0f671a8088af13cfe0982bf322b66f3d9d33dafb417319982c",
+        "5c60b59ac03d64321fd8051a7257e4911d8742b9485d84c4a49b03dda242566b",
+        "87115dde4421ce6234eb6a56d1f2977b377c889e39464210b14413707ca63e50",
+        "a1a9f6afb0c31b0ae5165d1871e852b7a06611b9bcd084ad7cae37e426404641",
+        "7440598c281de0f9c59375e19098b56d4054b7ce205d3c77603e27619d4e5625",
+        "ce7186a0370d6b33158f86d73cfb411e537228e24ed278e0442517df2205d471",
+        "a9f4337368741b0ff5a41d9d5d17634393fc9e3f3b8be0a2ca6b9db874ef0e5c",
+        "ad6506239c610a3422847c11e39ded9f21778c89f628f958b3f65aace8c88046",
+        "c44b473999c99d4576f178772138e6e05de34c7d51bd2a1be544739fd3e59265",
+        "a5e7ac375e13b40dab89a2c97f98325ea5a0bee8a3716c83f68c5abb28c81e4d",
+        "5d9df5cf874056595e0358eb85a3fac44ae1c304e58f68d97b9ebd0dd91c262b",
+        "0544181c2879218a3bf0ce91c39d11839ea3811eae4dc03b4a606023768f4b66",
+        "368e8a9c97a757f8a814c918a17cc2aaa5a456914e6bd405e57d43b84a32d04f",
+        "5203ed0d2a95fc2323c217cd62576b961f03aa94555adc0477ceb974a0cb3e5f",
+        "57305a038066c54bfb3d56b7fb20199e1d595ec93db5f154fe722c8360ea5025",
+        "24bae06cb2c10374c6dc99963b46ed8ef4bad300057994f00133e400dac54342",
+        "3193723cb258cfe23578ed09514e6174290e50873dfc6db0bd44fb192e1d8b48",
+        "5684a7b43be636074053c71c2f567f67cb8c69931ccf39422e9321dd3213ea11",
+        "891cc6d102db49665ca77892e25d2263ad5514359a9bc94b8a28a2282914350f",
+        "2c55039210c6d73687a1c3509c6d13425f2eb7653d5ca6f17e6fa8d1128dda64",
+        "efa6c0d41df0c56ff92a33bcc455bc546267310d73b6be33825dd2a69c98bf24",
+        "a75e3613dc92587400838c72935ed236fcd2e423fbed9b3e184696261c903c4f",
+        "da65c659744ec21d12a45298c927d53898fe0218b9f264d3b9d0f84fea239a2a",
+        "d6c5a6e8a023efbdaa8be0bea6b448f2689407da5f4d44808952ad10066fbb30",
+        "d1800c23b807b80c5951c48742bda869442e0931aea4e242e7687478afaabd4c",
+        "6e43de753a273eee8841156b9ce7df7c418a032d68c7a91f926e76f024b98516",
+        "f7f0cf3f697fb102916ca02db9a661395fe46634d7feafc158f8c32ecb8c3d67",
+        "d2749753f8de02700ac79a5ca9aa9810647184ab3f2a79503966e777f4adb854",
+        "9b57c18b4e9aa7db5e0b55a4b6ec2db3601e7f0b327dd6b52b40e56f069b1a11",
+        "80446fc818aadf73cb4b2de24cf4fbee4097c44385bfb38b923f1cfa939e4b4f",
+        "4158b81151c6f0e5725a484eeed53fb2e8e0c6308a1e33b2c8a4079bf132f85c",
+        "025d2fcbea21258a3540851be4dbbc7ff51698b2b6fffc1baa614f2eeb42323a",
+        "6191766089b2dbbf77e865c7750daaf927bac2439e1660c733dcb046532abe3b",
+        "b3d60b226c8460b97487f29e14950b814e195b139043eab2f52de50cb2d04939",
+        "f7ec1334115b5fe74475f662d3d0190b4526b2bb5dcfb3e6f235f1e90f61d85a",
+    ];
+    let ms = ms_strs.iter().map(|&m| hex::decode(m).unwrap()).collect();
+    let sigs_strs = [
+        "487df6a1d9149e0c6f205c93deebbedb0605f73f1b0b66f0be2aca4f5b5f1c5c9a8aa226aaceb0b0f6c25a7ea9548106",
+        "8d93bb04c4513d3115ed9d07d682b304752dabccde5ae1ab84a8c95ad7d0a796c2a5d60acc6d1aaab799800928d04a15",
+        "d38e7dccac51022105d0e95bf0a86c8d6f45f05202b90cd2b0d16f4f8c92b181e0312ab0749a136a4ae6d360429bf70d",
+        "653f87932e9780dab00141c04e2dce5b87d74674e02f9faefe7ef085e90905fad27dfdd2cf440d352cd76d52319d3e0a",
+        "0db9d2b7410db49abe6ad049b6f9a9f6be7f3935208175faaf6352a5fcfdd50a8e11c90266361f3436ac2d787175490f",
+        "876398ae20058f8456a90cecd66716f2a7ab1332e3bf4b350f36bee54f0c54d0d275d7d6bbc893510474279f247a9c19",
+        "56325dd67ca2f8f8fa9db425f6102327f9b260ad7d8f3faaf48f44258eb1b95e0140e9fdb21da423f715c6ddd5f17294",
+        "8acc294cdf985806e45b6dc35b21f3e3592e0d2f4174a44ea64c8e1e8bd2bec825cb0cf33f12954318b4fdf2bfc02003",
+        "424f3b81ada755b5e2082948165f343b681dfe3ccc01f3dc61e7c3a90ccf43c9823b61a50f995abdab7bfaee87c3de89",
+        "9bcb6bb486ab4a448d3d854ec9698654398b1be8471abbd3238b663d193731838419dfd446d27c309eb0bd45eb48e30a",
+        "55f2d4ea8539a0dfabdeef2876bf388bb1d42488c87e930df205f06ace50d12516d99d626ab9264ca47c65b9e1c5ea94",
+        "94e48ec56200b8151681e538693ef112010978a74f18b780eb2ca3fdfa73fe63e539e7291969b27c35ca619c060a7d8b",
+        "8d209835f164290e7e5eb80f502c84e5e580532e19ca9fb02fd3c14fc88d8f06e4cd9648c4c698a2c1c62cff96f5b18f",
+        "c67c755ab837bfae5304a73e51bcb2a115820840ca8fca3619285ee5d626cb85f859684b9cd99fbb701b0ed9174e510e",
+        "3d6366453c464bdcf1d9476ec827b800b88c98cfb5b0a9cce2122856a2095b9b1a980f1b654a94e51b96cf4c23683105",
+        "1560706642ef9a81833c7768d0c9a013bc16677dfa72f6802ca84fee257101fc103ef96cea988e8d4f601a5ab9aaaa06",
+        "669f4259090429d4f9525ba9777e40dbef8ee2b13ea379eb4fcf53194918312cc913f7c42aefb885e1b1e415c271c002",
+        "87cb6c52f4fa489b7cf0288e167a5e920b7b2b8756c35489861349fbba2f292745a4172a52ef366c0aa58042a4e51719",
+        "88b77e81fd95c07da6e28015a91342cdb60fac8a7adf43cf2033be353f96fca28019bbb276975e36a4ef2c98ac2b0b96",
+        "825258c4c961e0401d0d874957685ad13c62eb233dae080ff4f063579fb07c85c24e5188f51a513c7ffa1fb5c818fa15",
+        "174f0b5b42277411bd7007d0a0ebcdc020827c1dab931f6080db3f51627cbfdd66949efb4ab8db6164aec629dffead93",
+        "ce9b1af550d516164a1b28603d3a1d13510f73fa112daaba8e63af184dfa96e91f58f6205052a9d47b18ab3f7db04d19",
+        "cea13156f668a6834301cd087a20dd0184199e6698950a2f611374370a0378a9089db3239fdcca30cf75ccef3ce4da8b",
+        "49b41c5f4097c6ef4d05b30d4c6af7582cae4a8aa241761ed361a17e318dc4bdaa0314a23ce2c37173cf0132bd595385",
+        "5aacce3ddeb10cfbc1a60cea18ee7de4a48623dcce3adbc033386da12902eb6a193fcae963cb537affcaa702c5e35315",
+        "39e6871533f2861849940c8fcdc18db326119f8f9e6c8ee48d42be4204aa5f850706841db50419a080126a710e01dc0e",
+        "b839fa46f0216d865e682761e43c06ffc8087ce7d051cda5fcdeb6e41e1c53699ad706305c673e15f2315fdd3b4e2a17",
+        "fbc983296e992316f8fe5d3c45230fee4082f92b620727786ceb80712bc79bbaa33ce26fff147830bbfb767afa189c8e",
+        "5cfd5d433e25b21fb312cf1884582d3e2ddd74dbb4be920b6327fd9b7a9dfe6caf2a5bcdf253859dac1856fbe9124a90",
+        "b225b3b699a38ac2f6fb79f51a37041aa78529bbaffcef3a3d0a041090f9d17a523c6e890f6e5720914510ef5b2d1611",
+        "cf6529468914afb3c2811e60ef55100d594711597c7c223d02794889906ee0114466bce7f6a6c7067f0a21d1badb6a92",
+        "5995a42e27aa71eebbccf92c2d960eda339fd16d0b4d2a14d286d475739222fd374b4db01093246cccf78d741b8f4487",
+        "74bb62485057965749a0d53161c4fc0a42466a9dae26fcc6b578be4d44c59b6b8752948b737eacae01989c82a657e214",
+        "b1d39ded2063328ba512f7d68c27cf3a0db802ae5195450e344265920167ea236bb606bccbc6355090c199042b18ad99",
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+        "c33ee5a52e96e5ad2ae470e0e1f451174a24fcb4faef1b26e6569b43d1048a3b1adb3aa68093007354632e0e8e726c91",
+        "cdf8122b04128267e0d900cbf7b13db5adb3c84c28672883989428fdc2e3c411d3780b8e23590af2111a06d00c33b307",
+        "bdf6c475b11c8446ab2297dc1475266f3741345c11f9682962bfaf25407ae306a76e9d21fd18fc07f98920ae28596f81",
+        "94b6f42420ff96075df9bba0273261c387c7809d6236a2eb9d3cf4edbeb92eabe736a8dd8983c00780fb6022cf569788",
+        "8dcc2fea1129a187a9ac2e0561febaa10eb1876e819727ed3c844a631a7a63f336fc21aaeda70261449db5075a027099",
+        "df10d06d6cb85741247ecd591cfc4489918c9e2cd3547c7aec2567362231ac020570c22ddb02e884a2fd92cba5402403",
+        "affd43c2898812046af4ef6caaabc00ffd4c0d6dcc8e19e3b330797fbcb84ae1199f50d59f1d09597b7d7cd8ad48e714",
+        "b77caa5b8b43b4d2a335a8340c93455a416596aa2ad7c6d32b284d77d3a8df3999b54f5bf5f0a1299da30388a7066509",
+        "6bd277732a85da826abd73c14b3d2735dce77faa40a6054ffb10a58d0362f9f18550a2e8a4c7f44b6f6df834e8e0098b",
+        "87faa87fad33008da38a9e6eff6ef39aff1cf4ba9c8d07e2c04488134909ef60e93d445776333b21706f61c3d088be0f",
+        "a0063f2882284dbc1e1c7e57e17aad42bc8839bc5370ebff539effa988ae2ed5c5a8d943659bbdc0beae3d8adcd90294",
+        "ea791ce7f5dc554d4354c75f1cc8456657756aa44cb132bb65d32f0282717b16a572d86013d22f3cfc04ad96388cb184",
+        "31bb0667ac163582b0b188abfb5270f4b15dc01a4da57fc65099531090253b9b9dfa9c370de9ac0cff5e844ddb2a0e88",
+        "240b36869bf0a7ae0d5d4ac952931d64b658d5ff63ebbe0707b562838d8fd7fb93d7d9d948cdc81fbb5c58ce2ed26582",
+        "4215f027269e33f605141da41f5bdcc8c8e281fa0df4cb1a01efe1289c52368d0cf594b18e45d13b823411162966090e",
+        "5a7735334dd0d4cdc6f52a6933c28d5beca935518bd22738eb7920b42824a6ec1d1c106037d173cd3dce9cdf7b20b380",
+        "4ca28988a37360ee652f5a8b3744c357362cd31e68645795c6a0e22e6d8032082fdb71d3225fa2f2198d8d768d4e9897",
+        "ef5e7b5987a83874b1773df081ef8819914216c8401946407f6af7816f6a9cad3b7fcd22d925658d1b23598729194892",
+        "5b0f9cc10d8ca2bf38fcb62b6d97701f4905c39a405682c62c3d26dd58ed326403a5b2a444066024e37290fbcb1c298d",
+        "067ffcb122c43181eb4c525d2a7b56714262aae808ae24b62aa5ec6e1035a9f6ce6473f19dc470957afa98b437c68814",
+    ];
+    let sigs = sigs_strs
+        .iter()
+        .map(|&s| G1Affine::deserialize(&mut Cursor::new(hex::decode(s).unwrap())).unwrap())
+        .collect();
+
+    (pk, ms, sigs)
+}
diff --git a/docs/crypto/lets-hash-it-out/code/src/hash.rs b/docs/crypto/lets-hash-it-out/code/src/hash.rs
new file mode 100644
index 0000000..4ded35c
--- /dev/null
+++ b/docs/crypto/lets-hash-it-out/code/src/hash.rs
@@ -0,0 +1,29 @@
+use ark_bls12_381::{G1Affine, G1Projective};
+use ark_crypto_primitives::crh::{
+    pedersen::{Window, CRH},
+    CRH as CRHScheme,
+};
+use rand::SeedableRng;
+use rand_chacha::ChaCha20Rng;
+
+#[derive(Clone)]
+struct ZkHackPedersenWindow {}
+
+impl Window for ZkHackPedersenWindow {
+    const WINDOW_SIZE: usize = 1;
+    const NUM_WINDOWS: usize = 256;
+}
+
+pub fn hash_to_curve(msg: &[u8]) -> (Vec<u8>, G1Affine) {
+    let rng_pedersen = &mut ChaCha20Rng::from_seed([
+        1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
+        1, 1,
+    ]);
+    let parameters = CRH::<G1Projective, ZkHackPedersenWindow>::setup(rng_pedersen).unwrap();
+    let b2hash = blake2s_simd::blake2s(msg);
+    (
+        b2hash.as_bytes().to_vec(),
+        CRH::<G1Projective, ZkHackPedersenWindow>::evaluate(&parameters, b2hash.as_bytes())
+            .unwrap(),
+    )
+}
diff --git a/docs/crypto/lets-hash-it-out/code/src/lib.rs b/docs/crypto/lets-hash-it-out/code/src/lib.rs
new file mode 100644
index 0000000..475d53b
--- /dev/null
+++ b/docs/crypto/lets-hash-it-out/code/src/lib.rs
@@ -0,0 +1,9 @@
+pub mod bls;
+pub mod data;
+pub mod hash;
+
+pub const PUZZLE_DESCRIPTION: &str = r#"Alice designed an authentication system in which users gain access by presenting it a signature on a username, which Alice provided.
+One day, Alice discovered 256 of these signatures were leaked publicly, but the secret key wasn't. Phew.
+The next day, she found out someone accessed her system with a username she doesn't know! This shouldn't be possible due to existential unforgeability, as she never signed such a message.
+
+Can you find out how it happend and produce a signature on your username?"#;
diff --git a/docs/crypto/lets-hash-it-out/lets-hash-it-out.md b/docs/crypto/lets-hash-it-out/lets-hash-it-out.md
new file mode 100644
index 0000000..d2622cf
--- /dev/null
+++ b/docs/crypto/lets-hash-it-out/lets-hash-it-out.md
@@ -0,0 +1,114 @@
+---
+title: Crypto - Let's hash it out
+description: 2023 | ZKHACK | Crypto
+---
+
+## 0x00 Puzzle Discription
+
+It all feels random, but it might not be.
+
+> https://zkhack.dev/events/puzzle1.html
+
+## 0x01 Preliminary
+
+1. BLS 签名方案：基于 paring，分为 3 个算法：
+   
+   给定素数阶 $r$ 循环群 $\mathbb{G}$ 的生成元 $g$ ，双线性配对 $e$ 。(公开的)
+
+   - KeyGen: 生成有限域 $GF(r)$ 中的随机标量 $sk$ 作为私钥，然后生成公钥 $pk = sk \cdot g$ .
+   - Sign: 给定消息 $m\in\mathbb{G}$ ，那么该消息的签名为： $\Sigma=sk\cdot m$ .
+   - Verify: 给定 $m, \Sigma, pk$ ，验证等式： $e(m, pk)= e(\Sigma, g)$
+
+   注意， $m, \Sigma$ 是 $G_1$ 元素， $pk,g$ 是 $G_2$ 元素。
+
+2. 一般而言，消息都是任意长度的字符串，也可以理解为字节数组，或者一个比特流。为了使用 BLS 签名方案，则需要进行两步操作：一是把任意长度的字符串映射到固定长度的字符串，二是把固定长度字符串映射到群元素。
+
+   如上所述，Challenge采用的方案是首先用 blake2b hash 算法把消息转换为 256 bits ，然后使用 `hash_to_curve` 技术把 256bits 串映射到群元素（Pedersen hash）。
+
+   - Blake2b Hash (`Cargo.toml` 添加 `blake2s_simd="version"`  )
+        
+        ```Rust
+        fn main() {
+            let msg = "I love you";
+            let msg_bytes = msg.as_bytes();
+            let h = blake2s_simd::blake2s(msg_bytes);
+            println!("{:?}", h);
+        }
+        // Hash(0x7b9db068deeda65efb3f07a3bab9242ad4e5fdbf3bf3f4d229c82f2ebc4beb90)
+        ```
+
+   - Pedersen Hash (`Cargo.toml` 添加 G1 element type of pairing-friendly curve, )
+
+     inputs: 固定长度 bits 串; output: G1 element
+
+     我们首先把 inputs 按照 $r$ 大小分成 $k$ 组， 即 $|bits|=r * k$ 。然后随机在指定配对友好型椭圆曲线的素数阶子群中选择 $k$ 个生成元 $g_1, g_2, \dots, g_k$ 。这些生成元必须是随机均匀取样，使得两两之间的关系是无从知晓的。最后计算 pedersen hash $h=m_1g_1+m_2g_2+\dots+m_kg_k$ 。其中如何把 $r$ 大小的 bits 分组编码成 $m_i$ 需要设计成一个 encoding_function （可以简单地将其转化成 ASCII 码，也可以自定义，比如Zcash）。
+
+     因此，为了生成 pedersen hash 我们需要引入 pairing-friendly curve 、安全随机源、已经实现好的 pedersen primitive。
+
+     ```Rust
+     use ark_bls12_381::{G1Affine, G1Projective};
+     use ark_crypto_primitives::crh::{
+         pedersen::{Window, CRH},
+         CRH as CRHScheme
+     };
+     use blake2s_simd::Hash;
+     use rand::SeedableRng;
+     use rand_chacha::ChaCha20Rng;
+     
+     // Why?
+     #[derive(Clone)]
+     struct PedersenWindow {}
+     
+     impl Window for PedersenWindow {
+         const WINDOW_SIZE: usize = 1;
+         const NUM_WINDOWS: usize = 256;
+     }
+     
+     pub fn hash_to_curve(msg: &[u8]) -> (Vec<u8>, G1Affine) {
+         let rng_pedersen = &mut ChaCha20Rng::from_seed([
+             1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
+             1, 1,
+         ]);
+         let parameters = CRH::<G1Projective, PedersenWindow>::setup(rng_pedersen).unwrap();
+         let b2hash = blake2s_simd::blake2s(msg);
+         (
+             b2hash.as_bytes().to_vec(),
+             CRH::<G1Projective, PedersenWindow>::evaluate(&parameters, b2hash.as_bytes()).unwrap()
+         )
+     }
+     
+     fn main() {
+         let msg = "I love you";
+         let msg_bytes = msg.as_bytes();
+         let (b2hash, phash) = hash_to_curve(msg_bytes);
+         println!("{:?}, {}", &b2hash, &phash);
+     
+         let a: &[u8; 32] = b2hash.as_slice().try_into().unwrap();
+         let aa = Hash::from(a);
+         println!("{:?}", &aa);
+     }
+     // [123, 157, 176, 104, 222, 237, 166, 94, 251, 63, 7, 163, 186, 185, 36, 42, 212, 229, 253, 191, 59, 243, 244, 210, 41, 200, 47, 46, 188, 75, 235, 144], GroupAffine(x=Fp384 "(159228A979000DA250128CABDE97477EEC6A0CADFAE580B7D8AD46F185F4B43AC373CB877FFFEFAB0172AF25562DAF4A)", y=Fp384 "(04CEBA318A27291276178BDD9093432691D6E9D8E7178CC75FAB366225D332012288DF8EB3CA48D828821EA37D78BC3A)")
+     // Hash(0x7b9db068deeda65efb3f07a3bab9242ad4e5fdbf3bf3f4d229c82f2ebc4beb90)
+     ```
+
+## 0x02 Solution
+
+注意到 `hash_to_curve` 函数使用了同样的伪随机数生成器来挑选群生成元 $g_1, g_2, \dots, g_{256}$ ，这意味着每个消息的签名的计算方式为： $\Sigma_i=sk\cdot[b_1(m_i) g_1+b_2(m_i) g_2+\dots+b_{256}(m_i) g_{256}]$ ，其中 $m_i$ 表示第 $i$ 个消息， $b(m_i)$ 表示对第 $i$ 个消息进行 blake2s hash的哈希值，$b_j(m_i)$ 表示哈希值的第 $j$ 位，中括号（[]）里面的内容就是每个 `blake2s hash` 的 `pedersen hash` 结果，最后使用 $sk$ 进行签名。
+
+从上述等式可知：由于 $g_1, g_2, \dots, g_{256}$ 和 $sk$ 均固定，那么任意两个签名之间是可以进行加法运算的，然后得到另一个未知消息的签名。解了这个【线性特性】之后，我们就可以解决这个puzzle了。
+
+题目要我们给我们自定义的名字生成相应的签名，我们首先可直接算出名字的 `blake2s hash`  ，当然我们可以继续计算 `pedersen hash` ，但是由于我们没有 $sk$ 信息，因此没办法直接计算出目标签名。
+
+但是注意到，我们拥有 256 个消息及其签名，这意味我们可以进行线性组合（Linear Combination）。诚然，两个签名相加可以得到一个未知消息的签名，这个消息是不可控的，甚至是无意义的（因为是与生成器相乘的标量是布尔值，如果两个布尔值都为 1 ，那么加起来的结果为 2，显然不可能有某一个 hash 的二进制表示中的某一位是 2）。但是，线性代数教给我们一个利器：线性组合。我们拥有256个消息，那么其 `blake2s hash` 的每一位我们都是知道的，因此把这些消息的二进制表示作为行向量，形成了一个 $256*256$ 的矩阵 $A$ ，我们的目标是生成一个 $1 * 256$ 行向量 $y$ 。那么问题就转换为，寻找一个线性组合解 $x$ ，满足 $xA=y$ 。有了这个线性组合解，我们就可以使用这 256 个消息来构造出我们想要的消息 $m$ ，又因为签名具有线性特性，那么使用这个解去线性组合这 256 个签名得到的就是目标消息的签名。
+
+需要注意的是，由于我们最终需要使用解去线性组合签名，而后续与生成器进行乘法操作时要求标量在 $F_r$ 上，因此在进行矩阵运算时，我们需要把所有的元素都表示在 $F_r$ 中。
+
+数学表达为：
+
+$$
+\vec{x}\cdot sk\cdot \begin{pmatrix} b_1(m_1)&b_2(m_1)&\dots&b_{256}(m_1)\\ b_1(m_2)&b_2(m_2)&\dots&b_{256}(m_2)\\ \vdots&\vdots&\ddots&\vdots\\ b_1(m_{256})&b_2(m_{256})&\dots&b_{256}(m_{256 })\\ \end{pmatrix} \cdot \begin{pmatrix} g_1\\g_2\\\vdots\\g_{256} \end{pmatrix} =\vec{x}\cdot \begin{pmatrix} \Sigma_1\\\Sigma_2\\\vdots\\\Sigma_{256} \end{pmatrix}
+$$
+
+## 0x03 Code
+
+见 `code/` 文件夹。
\ No newline at end of file
diff --git a/docs/crypto/oven.md b/docs/crypto/oven.md
new file mode 100644
index 0000000..d9d6827
--- /dev/null
+++ b/docs/crypto/oven.md
@@ -0,0 +1,198 @@
+---
+title: Crypto - Oven
+description: 2023 | ParadigmCTF | Crypto
+---
+
+## 0x00 Puzzle Discription
+
+> 题目地址： https://github.com/paradigmxyz/paradigm-ctf-2023/tree/main/oven
+
+源码如下：
+
+```python
+#!/usr/bin/env python3
+from Crypto.Util.number import *
+import random
+import os
+import hashlib
+
+FLAG = os.getenv("FLAG", "PCTF{flag}").encode("utf8")
+FLAG = bytes_to_long(FLAG[5:-1])
+assert FLAG.bit_length() < 384
+
+BITS = 1024
+
+
+def xor(a, b):
+    return bytes([i ^ j for i, j in zip(a, b)])
+
+
+# This doesn't really matter right???
+def custom_hash(n):
+    state = b"\x00" * 16
+    for i in range(len(n) // 16):
+        state = xor(state, n[i : i + 16])
+
+    for _ in range(5):
+        state = hashlib.md5(state).digest()
+        state = hashlib.sha1(state).digest()
+        state = hashlib.sha256(state).digest()
+        state = hashlib.sha512(state).digest() + hashlib.sha256(state).digest()
+
+    value = bytes_to_long(state)
+
+    return value
+
+
+def fiat_shamir():
+    p = getPrime(BITS)
+    g = 2
+    y = pow(g, FLAG, p)
+
+    v = random.randint(2, 2**512)
+
+    t = pow(g, v, p)
+    c = custom_hash(long_to_bytes(g) + long_to_bytes(y) + long_to_bytes(t))
+    r = (v - c * FLAG) % (p - 1)
+
+    assert t == (pow(g, r, p) * pow(y, c, p)) % p
+
+    return (t, r), (p, g, y)
+
+
+while True:
+    resp = input("[1] Get a random signature\n[2] Exit\nChoice: ")
+    if "1" in resp:
+        print()
+        (t, r), (p, g, y) = fiat_shamir()
+        print(f"t = {t}\nr = {r}")
+        print()
+        print(f"p = {p}\ng = {g}\ny = {y}")
+        print()
+    elif "2" in resp:
+        print("Bye!")
+        exit()
+```
+
+代码功能：用户可以获取 FLAG 随机签名，生成随机签名的逻辑就在 `fiat-shamir` 函数里。使用了自定义的hash函数 `custom_hash` 来生成哈希，这个函数分别调用了四种不同的hash算法，因此想要破解其随机性目前是不可能的。
+
+另外， `Fiat Shamir` 变换是密码学中非常重要的工具，它的核心在于使用hash算法来生成随机数，为密码协议添加了随机性。FS变换一个典型应用就是为零知识证明系统系统引入了非交互性，进而构造出 snark、stark 等协议。
+
+从上述源码，我们可获得的信息有 `t, r, p, g, y` ，其实 c 是可以求出，即使用题目条件中的 `custom_hash` 函数。那么可能发生的漏洞点集中在 `fiat_shamir`  函数中，它是对 FLAG 进行签名的函数功能部分，重点关注： `r = (v - c * FLAG) % (p - 1)` 。对于这个式子，目前我们可以获得的信息有： `r, c, p` 均是已知值，且 FLAG 的位数已经确定： `assert FLAG.bit_length() < 384` 。 可以联想到 Dan Boneh 在 1996 年提出的 [HNP](https://crypto.stanford.edu/~dabo/pubs/abstracts/dhmsb.html) 问题（模数可变），可使用标准的格算法进行攻击。更加详细基于格攻击的密码分析请参考[论文](https://tpm.fail/tpmfail.pdf)。
+
+## 0x01 Analysis
+
+问题就出在代码： `r = (v - c * FLAG) % (p - 1)` 上，由于 r，c，p均是已知值，于是：
+
+1. 首先对上述式子进行数学变形： $r-v+c*FLAG=0\mod (p-1)$ ，只有 v 和 FLAG 是未知数。
+
+2. 我们可以根据上述式子构建 Lattice：
+   $$
+   M=\begin{pmatrix}
+   (q_1-1)&&&&\\
+   &(q_2-1)&&&\\
+   &&(q_3-1)&&\\
+   c_1&c_2&c_3&1&\\
+   r_1&r_2&r_3&0&K\\
+   \end{pmatrix}
+   $$
+
+解释：
+
+- K是FLAG的一个上界
+- 空白处均为0
+
+3. 根据 Babai 的CVP解决算法，一定存在一个解向量 $\pmb{j}=(l_1,l_2,l_3,FLAG,1)$ ，使得 $\pmb{j}M=\pmb{j_k}$ 成立
+4. 注意到 $\pmb{j_k}$ 在格中是一个短向量，于是我们可以采用 LLL 算法在多项式时间内找到这个短向量。注意，短向量的每一个元素用 64bit 可以表示，于是确定上界 $K=2^{64}$ 。 
+
+#### 小技巧
+
+这里解释一下数据量的问题，如何知道需要多少组数据可以恢复出 FLAG 呢？这个需要使用到 gaussian heuristic 估计最短向量长度，要求的目标向量范数小于这个长度即可。【但是由于这是CTF比赛背景，所以一般情况下可以先用三四五组数据，如果不行，在用上述方法精确计算。这里我先收集了5组数据备用，实际上用了3组数据，就可解出FLAG】。
+
+## 0x02 EXP
+
+完整EXP（需要sage-python环境）：
+
+```python
+from Crypto.Util.number import *
+import hashlib
+
+def xor(a, b):
+    return bytes([i ^^ j for i, j in zip(a, b)]) // 注意你的sage环境的异或操作运算符，这个sage10.0版本
+
+def custom_hash(n):
+    state = b"\x00" * 16
+    for i in range(len(n) // 16):
+        state = xor(state, n[i : i + 16])
+
+    for _ in range(5):
+        state = hashlib.md5(state).digest()
+        state = hashlib.sha1(state).digest()
+        state = hashlib.sha256(state).digest()
+        state = hashlib.sha512(state).digest() + hashlib.sha256(state).digest()
+
+    value = bytes_to_long(state)
+
+    return value
+
+
+
+g = 2
+
+t, r, p, y = [0] * 5 , [0] * 5, [0] * 5, [0] * 5
+t[0] = 77203516334611379622052884088061339907818193440975523438325956774518601252973654146535129884349539724229562993644509567711307331031087898034347437358013492439542334272757402388064753335866738748958633246857368058563448192261648964749496750146315450540579452655462143813022469489449782882109182150142188348915
+r[0] = 116220687218790216091346463439819557695309512176282372943331613053767874084111192169275378671194392846117055362014832383093646731110903547936340541580638231783076185430700045752799252596702505486227877656990705143138976716233681199944248043915239678537679463030334043412573684866623347545004904612417007327217
+p[0] = 120199526136097511651530856988060166616679725925744594620901500430819054365226668422844742178771316732438545888088210068701212930988908604238682153307940417480817112540019257024703372145496636861112290091005527647339212358159274475077103689996624113678044891963676612334769162753166782062809526104431258739517
+y[0] = 113120257926989954605307518460817169666869094087243249194566086300779837721481071230484420555504633839932263287201776945834030877253212748181186108770595676114564711457140738635967367144272960236148346810327070118837330648022676963528356209004524421455348155068637534190736042536625876773755044593606026293621
+
+t[1] = 41870694301936832255997763505666386906032641226067235004722895066736677752643938706563985367861597477876358530714740119529535551345537670465925209944735777464498665457291484991606280197421907773811941255514802343059520166452091324746732103649911088736843268706303230993742963740287185306251052313964374872878
+r[1] = 12006544761341621619143613218949584457040818188588282396732221317912350712975184254483346994199077889478797005980544401923303196850089656891130607887735812677733676744158835380723268515678724429529904080449565289532493612340517128773817940478185157405384294596975266141639161297056291778600404606940053392754
+p[1] = 144976418899543143198454834264506179459614866666312385853989423989111679486891620786778481577472101748200328617607483446519049911023390427543308348494008425688855119367843479385647790189753163858970088620586505610840306212549243890107847423807556106192434514110736278569625282073529181653986405771513594134987
+y[1] = 115167386542298909971939136044531943159982371048242494889745996527683250097061534781946312891817534916886291355204474301571862159042350976750824212346443402817552375266223638549309886922860921533308382456941718605370216473858986207878047206914813902333192745354148659984602740644345120423788258359941122554440
+
+t[2] = 87583398382601313926735945950364130572816213989909728661491063393166341618362097121819023078210854251839415225428442334046015192711593400640556960974162962105001700930842075200923675422451049033428478754684678493480503204152097382431043129863362081278994409790477935899740897031656629902670114002180266872266
+r[2] = 102934065416140965550261549535302192284582871606378190882003659362832329206469482926448881926648454509204767788745574969527319053553977362277660636749471357711849435384231867496681956889560719871615670691536165668156919285052370364456208767031233707532145718791283351837119192545712583721765194876277656314501
+p[2] = 148550372281025138704553107737801144273208690400094973764375300381759456124146034135721454543469874579375457504983315183916592877731262163382903701414433532933994780412246010260680217160047355295328211970740422311833479381733781665221952277321615395653804905426059251551309558237245071919868160643681548296643
+y[2] = 140198181685722792932050421128846820269664976993249152496309458637445728558822919357043381776927596511506695168631000635135982453895569864162220417018046902591680662347467431250148020323787868422484882819040766008876291088199475630773774170507517261352416744218315033367149608507518388781373699289693595499544
+
+t[3] = 84522638373733120165414722745998118253921972157096808350845007682435315263298662575419222718886673005893479175168776223733676055437884841441137160382376309254755315837431162807596684224207280410300146602535834124511928134257346386899792746556440632650091111389088724071203568000188430042064500145669267026805
+r[3] = 18194520459417696159241442307764982202112775710358263541565999857475375951014745782344717997571109484480490257320469370655821185611675102820226656623202547826938945675557174044055104570245311622199906030109190773202049867448625926033119474090713737736579814394048548084259404911639299693897437586858871472420
+p[3] = 103592121279236435866010649601463899558315038309765463516665073413464806869884601040096405354399740035138081866812671953467986059509640644754973422603659825874707510675199511411437487386173194105311776020901134014680450244319046258962912483163270496586124101308664731409973532774829535980996775736651508448187
+y[3] = 14795900031448786771559087453548388682769488350377145090464794455644462363656204398769939585810191748312766604278524960492756615478207654208905403516432929452543777164921589629460212814049479518397521600744701463005793924336243982001830978693343863219168046923285752069874971698699611717027496799587761203398
+
+t[4] = 137831113158715069584199906447354477289195801883097400523644937444161950367086728510388467524069532778534704803863447302183665431906725284462350375136938902398115607751357373983532375894744842377064414618294084293556345908653608825144019924463160996581138334794345538184522294219836499291245958693984828705682
+r[4] = 3997479613798995088324714249284251759517244566415954213469045459939167234231804927756343425727094668124791771030709612850292188541459113635924389128360073088700133564458353848851347410209029075825332791761713207287049093830610503236793718093861017715600469118069736180200062407135030791797264421955154056362
+p[4] = 138872772594377036406739890812487312629206229880091799534033353266413752242871671695030657233827552372256865312690361457743622953282647882392520626248323032818493170021525093526571072858177665184977821075559705014261503440906447428819858532553737164369106583570452357928945241596555378143414688075425304805029
+y[4] = 26528279589882510502916765470759890048295757018825608100058824483278181810141819962488106009190787416456734047325734614749916264837565765983213768504298640943869226245566784325431289650031372028094050672872660334951958006567067601586551947694563576820491204290496425885685101313332190690230962899252834723225
+
+i = 0
+C = [0]
+R = [0]
+while i < 5:
+    C.append(custom_hash(long_to_bytes(g) + long_to_bytes(y[i]) + long_to_bytes(t[i])))
+    R.append(r[i])
+    i += 1
+    
+C = C[1:]
+R = R[1:]
+# print(C)
+# print(R)
+
+M = matrix(ZZ, 5, 5)
+for i in range(3):
+    M[i, i] = p[i]
+    M[3, i] = C[i]
+    M[4, i] = R[i]
+    M[i, 3] = M[i, 4] = 0
+M[3, 3] =  1
+M[4, 4] = 2^64
+M[3, 4]= 0
+    
+v = M.LLL()[0]
+print(v)
+flag = v[3] % p[3]
+print(long_to_bytes(flag))
+
+```
+
+最终的结果为： `pctf{F1at_shAm1R_HNP_g0_Cr4ZyyYy_m0rE_1iK3_f4T_Sh4mIr}`
\ No newline at end of file
diff --git a/docs/imgs/welcome.jpg b/docs/imgs/welcome.jpg
new file mode 100644
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diff --git a/docs/index.md b/docs/index.md
new file mode 100644
index 0000000..71adc66
--- /dev/null
+++ b/docs/index.md
@@ -0,0 +1,12 @@
+# Welcome to ZK Puzzle Writeups
+
+Hi, I am Xor0v0, 
+
+- pursuing a Master's degree in Applied Cryptography (research on Zero Knowledge Proof and Lattice Analysis)
+- web2/web3/Cryptography Security ehthusiast
+- CTFer and zkHACKer
+
+<div align=center><img src="./imgs/welcome.jpg" width="100%"></div>
+
+## Recent Blogs
+{{ blog_content }}
diff --git a/mkdocs.yml b/mkdocs.yml
new file mode 100644
index 0000000..8eaa8ee
--- /dev/null
+++ b/mkdocs.yml
@@ -0,0 +1,102 @@
+site_name: ZK Puzzle Writeups
+site_author: Xor0v0
+site_url: https://xor0v0.github.io/zk-puzzle-writeups/
+copyright: Copyright &copy; 2024 - 2030 Xor0v0
+  
+# Repository
+repo_name: 'Xor0v0/ZK-Puzzle-Writeups'
+repo_url: https://github.com/Xor0v0/ZK-Puzzle-Writeups
+
+nav:
+  - 简介:
+      -首页: index.md
+  - Crypto:
+      - Oven: crypto/oven.md
+      - Let's hash it out: crypto/lets-hash-it-out/lets-hash-it-out.md
+
+# Theme
+theme:
+    name: 'material'
+    # custom_dir: docs/overrides
+    language: 'zh'
+    palette:
+      primary: 'white'
+      accent: 'teal'
+    icon:
+      logo: material/school
+    features:
+      - navigation.tabs
+      - navigation.top
+      - navigation.tracking
+      - search.suggest
+      - search.highlight
+      - search.share
+    font:
+      text: 'Fira Sans'
+      code: 'Fira Mono'
+
+
+plugins:
+    - search
+    - git-revision-date-localized:
+        type: datetime
+        timezone: Asia/Shanghai
+        locale: zh
+    - git-authors
+    - blogging:
+        theme:
+          name: card
+        features:
+          tags:
+            insert: top
+        size: 5
+        paging: false
+        show_total: false
+        dirs:
+          - blockchain
+          - crypto
+          # - misc
+          # - pwn
+          # - reverse
+          # - web
+
+
+extra_javascript:
+    - https://polyfill.io/v3/polyfill.min.js?features=es6
+    - https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js
+    - https://busuanzi.ibruce.info/busuanzi/2.3/busuanzi.pure.mini.js
+
+# Extensions
+markdown_extensions:
+    - admonition
+    - codehilite:
+        guess_lang: false
+        linenums: true
+    - def_list
+    - footnotes
+    - meta
+    - toc:
+        permalink: true
+    - pymdownx.arithmatex:
+        generic: true
+    - pymdownx.caret
+    - pymdownx.critic
+    - pymdownx.details
+    - attr_list
+    - pymdownx.emoji:
+        emoji_index: !!python/name:materialx.emoji.twemoji
+        emoji_generator: !!python/name:materialx.emoji.to_svg
+    - pymdownx.inlinehilite
+    - pymdownx.keys
+    - pymdownx.magiclink
+    - pymdownx.mark
+    - pymdownx.progressbar
+    - pymdownx.smartsymbols
+    - pymdownx.superfences:
+        custom_fences:
+          - name: math
+            class: arithmatex
+            format: !!python/name:pymdownx.arithmatex.fence_mathjax_format
+    - pymdownx.tasklist:
+        custom_checkbox: true
+    - pymdownx.tilde