diff --git a/docs/.DS_Store b/docs/.DS_Store
new file mode 100644
index 0000000..031730b
Binary files /dev/null and b/docs/.DS_Store differ
diff --git a/docs/crypto/2+2=5/.DS_Store b/docs/crypto/2+2=5/.DS_Store
new file mode 100644
index 0000000..72a188b
Binary files /dev/null and b/docs/crypto/2+2=5/.DS_Store differ
diff --git a/docs/crypto/2+2=5/code/.DS_Store b/docs/crypto/2+2=5/code/.DS_Store
new file mode 100644
index 0000000..8e7f5bf
Binary files /dev/null and b/docs/crypto/2+2=5/code/.DS_Store differ
diff --git a/docs/crypto/2+2=5/code/Dockerfile b/docs/crypto/2+2=5/code/Dockerfile
new file mode 100644
index 0000000..457de94
--- /dev/null
+++ b/docs/crypto/2+2=5/code/Dockerfile
@@ -0,0 +1,19 @@
+FROM rust:1.67
+
+WORKDIR /usr/src/app
+
+COPY ./jolt ./jolt
+COPY ./server ./server
+
+WORKDIR /usr/src/app/server
+
+RUN cargo build --release
+
+# run the server once just to download the toolchain, this will crash but we do not care
+# god has already forgiven me for this
+# (also this has nothing to do with the challenge itself)
+RUN (echo "" | ./target/release/challenge); true
+
+RUN apt update && apt install -y socat
+
+ENTRYPOINT ["socat", "-t", "900", "-T", "120", "TCP4-LISTEN:5555,reuseaddr,fork", "EXEC:./target/release/challenge"]
diff --git a/docs/crypto/2+2=5/code/diff.patch b/docs/crypto/2+2=5/code/diff.patch
new file mode 100644
index 0000000..b91470a
--- /dev/null
+++ b/docs/crypto/2+2=5/code/diff.patch
@@ -0,0 +1,19 @@
+diff --git a/jolt-core/src/r1cs/jolt_constraints.rs b/jolt-core/src/r1cs/jolt_constraints.rs
+index 5fb0d871..295dce32 100644
+--- a/jolt-core/src/r1cs/jolt_constraints.rs
++++ b/jolt-core/src/r1cs/jolt_constraints.rs
+@@ -289,13 +289,8 @@ impl<F: JoltField> R1CSConstraintBuilder<F> for UniformJoltConstraints {
+ 
+         // if (rd != 0 && update_rd_with_lookup_output == 1) constrain(rd_val == LookupOutput)
+         // if (rd != 0 && is_jump_instr == 1) constrain(rd_val == 4 * PC)
+-        let rd_nonzero_and_lookup_to_rd =
++        let _rd_nonzero_and_lookup_to_rd =
+             cs.allocate_prod(JoltIn::Bytecode_RD, JoltIn::OpFlags_LookupOutToRd);
+-        cs.constrain_eq_conditional(
+-            rd_nonzero_and_lookup_to_rd,
+-            JoltIn::RD_Write,
+-            JoltIn::LookupOutput,
+-        );
+         let rd_nonzero_and_jmp = cs.allocate_prod(JoltIn::Bytecode_RD, JoltIn::OpFlags_IsJmp);
+         let lhs = JoltIn::Bytecode_ELFAddress + (PC_START_ADDRESS - PC_NOOP_SHIFT);
+         let rhs = JoltIn::RD_Write;
diff --git a/docs/crypto/2+2=5/code/jolt b/docs/crypto/2+2=5/code/jolt
new file mode 160000
index 0000000..0cc7aa3
--- /dev/null
+++ b/docs/crypto/2+2=5/code/jolt
@@ -0,0 +1 @@
+Subproject commit 0cc7aa31981ff8503fe256706d2aa9c320abd1cd
diff --git a/docs/crypto/2+2=5/code/readme.txt b/docs/crypto/2+2=5/code/readme.txt
new file mode 100644
index 0000000..86fd34b
--- /dev/null
+++ b/docs/crypto/2+2=5/code/readme.txt
@@ -0,0 +1,9 @@
+# Author: @gio-d3141
+# Dockerfile should build fine (will take a while) but the setup is kind of cursed, DM me if necessary
+
+git clone git@github.com:a16z/jolt.git
+cd jolt
+
+# just the latest commit at time of writing
+git checkout 0cc7aa31981ff8503fe256706d2aa9c320abd1cd
+git apply ../diff.patch
diff --git a/docs/crypto/2+2=5/code/server/.gitignore b/docs/crypto/2+2=5/code/server/.gitignore
new file mode 100644
index 0000000..2f7896d
--- /dev/null
+++ b/docs/crypto/2+2=5/code/server/.gitignore
@@ -0,0 +1 @@
+target/
diff --git a/docs/crypto/2+2=5/code/server/Cargo.lock b/docs/crypto/2+2=5/code/server/Cargo.lock
new file mode 100644
index 0000000..6bae215
--- /dev/null
+++ b/docs/crypto/2+2=5/code/server/Cargo.lock
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diff --git a/docs/crypto/2+2=5/code/server/Cargo.toml b/docs/crypto/2+2=5/code/server/Cargo.toml
new file mode 100644
index 0000000..6ecbae9
--- /dev/null
+++ b/docs/crypto/2+2=5/code/server/Cargo.toml
@@ -0,0 +1,19 @@
+[package]
+name = "challenge"
+version = "0.1.0"
+edition = "2021"
+
+[dependencies]
+jolt-sdk = { path = "../jolt/jolt-sdk", features = ["host"] }
+guest = { package = "challenge-guest", path = "./guest" }
+
+hex = "0.4.3"
+sha3 = { version = "0.10.8", default-features = false }
+
+[workspace]
+members = ["guest"]
+
+[patch.crates-io]
+ark-ff = { git = "https://github.com/a16z/arkworks-algebra", branch = "optimize/field-from-u64" }
+ark-ec = { git = "https://github.com/a16z/arkworks-algebra", branch = "optimize/field-from-u64" }
+ark-serialize = { git = "https://github.com/a16z/arkworks-algebra", branch = "optimize/field-from-u64" }
diff --git a/docs/crypto/2+2=5/code/server/guest/Cargo.toml b/docs/crypto/2+2=5/code/server/guest/Cargo.toml
new file mode 100644
index 0000000..edf7a42
--- /dev/null
+++ b/docs/crypto/2+2=5/code/server/guest/Cargo.toml
@@ -0,0 +1,14 @@
+[package]
+name = "challenge-guest"
+version = "0.1.0"
+edition = "2021"
+
+[[bin]]
+name = "guest"
+path = "./src/lib.rs"
+
+[features]
+guest = []
+
+[dependencies]
+jolt = { package = "jolt-sdk", path = "../../jolt/jolt-sdk" }
diff --git a/docs/crypto/2+2=5/code/server/guest/src/lib.rs b/docs/crypto/2+2=5/code/server/guest/src/lib.rs
new file mode 100644
index 0000000..0be1208
--- /dev/null
+++ b/docs/crypto/2+2=5/code/server/guest/src/lib.rs
@@ -0,0 +1,26 @@
+#![cfg_attr(feature = "guest", no_std)]
+#![no_main]
+
+#[jolt::provable]
+fn two_plus_two() -> u16 {
+    let mut n: u16 = 2;
+
+    #[cfg(any(target_arch = "riscv32", target_arch = "riscv64"))]
+    unsafe {
+        core::arch::asm!(
+            "li {n}, 2",
+            "add {n}, {n}, {n}",
+            n = inout(reg) n,
+        );
+    }
+
+    #[cfg(target_arch = "x86_64")]
+    unsafe {
+        core::arch::asm!(
+            "mov {n}, 2",
+            "add {n}, {n}, {n}",
+            n = inout(reg) n,
+        );
+    }
+    n
+}
diff --git a/docs/crypto/2+2=5/code/server/proof b/docs/crypto/2+2=5/code/server/proof
new file mode 100644
index 0000000..aa6e67b
--- /dev/null
+++ b/docs/crypto/2+2=5/code/server/proof
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\ No newline at end of file
diff --git a/docs/crypto/2+2=5/code/server/rust-toolchain.toml b/docs/crypto/2+2=5/code/server/rust-toolchain.toml
new file mode 100644
index 0000000..76734e5
--- /dev/null
+++ b/docs/crypto/2+2=5/code/server/rust-toolchain.toml
@@ -0,0 +1,3 @@
+[toolchain]
+channel = "nightly-2024-08-01"
+targets = ["riscv32im-unknown-none-elf"]
diff --git a/docs/crypto/2+2=5/code/server/rustfmt.toml b/docs/crypto/2+2=5/code/server/rustfmt.toml
new file mode 100644
index 0000000..ebf4780
--- /dev/null
+++ b/docs/crypto/2+2=5/code/server/rustfmt.toml
@@ -0,0 +1,5 @@
+edition = "2021"
+tab_spaces = 4
+newline_style = "Unix"
+use_try_shorthand = true
+use_field_init_shorthand = true
\ No newline at end of file
diff --git a/docs/crypto/2+2=5/code/server/src/main.rs b/docs/crypto/2+2=5/code/server/src/main.rs
new file mode 100644
index 0000000..3aac6d8
--- /dev/null
+++ b/docs/crypto/2+2=5/code/server/src/main.rs
@@ -0,0 +1,41 @@
+use jolt_sdk::RV32IHyraxProof;
+
+pub fn main() {
+    let (_prove_two_plus_two, verify_two_plus_two) = guest::build_two_plus_two();
+
+    println!("Can you prove that 2+2=5?");
+
+    let (output, proof) = _prove_two_plus_two();
+    println!("output: {}", output);
+    // 写入文件:
+    std::fs::write("proof", hex::encode(proof.serialize_to_bytes().unwrap())).unwrap();
+    // println!(
+    //     "proof: {}",
+    //     hex::encode(proof.serialize_to_bytes().unwrap())
+    // );
+
+    // let line = std::io::stdin().lines().next().unwrap().unwrap();
+    // let proof = RV32IHyraxProof::deserialize_from_bytes(&hex::decode(line).unwrap()).unwrap();
+
+    let inputs = &proof.proof.program_io.inputs;
+    println!("inputs: {:?}", inputs);
+    assert_eq!(inputs.len(), 0);
+
+    let outputs = &proof.proof.program_io.outputs;
+    println!("outputs: {:?}", outputs);
+    assert_eq!(outputs.len(), 2);
+    assert_eq!(outputs[0], 5); // 2+2 is 5!
+
+    let panics = &proof.proof.program_io.panic;
+    println!("panics: {:?}", panics);
+    assert!(!panics);
+
+    println!("Verifying the proof...");
+    let is_valid = verify_two_plus_two(proof);
+    if is_valid {
+        println!("The proof is valid!");
+        println!("FLAG: {}", std::env::var("FLAG").unwrap());
+    } else {
+        println!("The proof is invalid! :(");
+    }
+}
diff --git a/docs/crypto/2+2=5/imgs/instruction-cycle.png b/docs/crypto/2+2=5/imgs/instruction-cycle.png
new file mode 100644
index 0000000..12071a9
Binary files /dev/null and b/docs/crypto/2+2=5/imgs/instruction-cycle.png differ
diff --git a/docs/crypto/2+2=5/imgs/jolt.png b/docs/crypto/2+2=5/imgs/jolt.png
new file mode 100644
index 0000000..8fb5e44
Binary files /dev/null and b/docs/crypto/2+2=5/imgs/jolt.png differ
diff --git a/docs/crypto/2+2=5/two_plus_two.md b/docs/crypto/2+2=5/two_plus_two.md
new file mode 100644
index 0000000..82e3c8b
--- /dev/null
+++ b/docs/crypto/2+2=5/two_plus_two.md
@@ -0,0 +1,196 @@
+---
+title: Crypto - 2+2=5
+description: 2024 | MOCA Italian Hacker Camp | Crypto
+---
+
+## 1. Background
+
+[Jolt](https://jolt.a16zcrypto.com/intro.html) 是由 A16Z 的密码学家们提出的一个针对 Risc-V ISA （未来将支持更多ISA）的 zkVM 框架，它底层使用了 sumcheck-based SNARK，这个 SNARK 充分利用多变量多项式及其多项式承诺的优势。Jolt zkVM 据说拥有非常出色的性能表现并且还存在优化空间。
+
+首先需要了解 Jolt zkVM 架构，分为 4 个组件。一个 Virtual Machine（VM）实质上是做两个事情：
+- 重复地执行“取指-译码-执行“逻辑（也叫 instruction cycle）。指令由 ISA 定义
+- 读写 RAM
+ 
+![](./imgs/jolt.png)
+
+结合 Jolt 论文中的图示，可以看到：CPU 从一个状态 $state_i$，（结合 PC）从storage 中读取程序代码的指令，读取源寄存器的值甚至读写 memory，然后通过 lookup query 译码执行返回结果，最终把结果写到目的寄存器，更新到CPU状态为 $CPU_{i+1}$ 。
+
+其中：
+- 读写 storage，regs，memory 中的数据需要用到 offline memory checking.
+- 译码执行需要使用 lasso
+- 前两者生成的约束表示为 R1CS 形式，然后证明。
+
+在 Jolt 代码实现中，把 storage 中存放的字节码指令（只读） 与 regs 和 memory 中存放的数据（可读写） 分离开，因而构成了四大组件。
+
+![](./imgs/instruction-cycle.png)
+
+- 字节码：也就是程序指令，使用 read-only memory checking argument 证明
+- 读写内存：使用 memory checking argument 去证明读写内存的正确性。对于 register，Jolt 将其实现为在特殊地址的内存。
+- 指令查询：在执行指令时，使用一种名为 Lasso 的 lookup argument 证明
+- R1CS：以上所有的 instruction cycle 都需要满足 R1CS 约束。它作为一种粘合剂，可以为跨组件的数据施加约束。
+
+Jolt zkVM 的使用与 RISC0 的 zkVM 类似，都是使用 guest program 来表示欲证明的 computation，host program 则是运行 zkVM 的程序，通过 host program 我们可以利用 jolt_sdk 来为 guest program 的正确运行生成证明，guest program 的输入也是在 host program 中构造并传递的。
+
+## 2. Puzzle Description
+
+> [Attachments](https://github.com/fibonhack/MOCA-2024-finals-challs/raw/refs/heads/main/crypto/two_plus_two/two_plus_two.zip)
+
+内容如下：
+
+```
+.
+├── Dockerfile
+├── diff.patch
+├── jolt
+├── readme.txt
+└── server
+```
+
+先看 readme：
+
+```
+# Author: @gio-d3141
+# Dockerfile should build fine (will take a while) but the setup is kind of cursed, DM me if necessary
+
+git clone git@github.com:a16z/jolt.git
+cd jolt
+
+# just the latest commit at time of writing
+git checkout 0cc7aa31981ff8503fe256706d2aa9c320abd1cd
+git apply ../diff.patch
+```
+
+这个题 clone 了 jolt 库，并打了一个 patch，补丁内容如下：
+
+```
+diff --git a/jolt-core/src/r1cs/jolt_constraints.rs b/jolt-core/src/r1cs/jolt_constraints.rs
+index 5fb0d871..295dce32 100644
+--- a/jolt-core/src/r1cs/jolt_constraints.rs
++++ b/jolt-core/src/r1cs/jolt_constraints.rs
+@@ -289,13 +289,8 @@ impl<F: JoltField> R1CSConstraintBuilder<F> for UniformJoltConstraints {
+ 
+         // if (rd != 0 && update_rd_with_lookup_output == 1) constrain(rd_val == LookupOutput)
+         // if (rd != 0 && is_jump_instr == 1) constrain(rd_val == 4 * PC)
+-        let rd_nonzero_and_lookup_to_rd =
++        let _rd_nonzero_and_lookup_to_rd =
+             cs.allocate_prod(JoltIn::Bytecode_RD, JoltIn::OpFlags_LookupOutToRd);
+-        cs.constrain_eq_conditional(
+-            rd_nonzero_and_lookup_to_rd,
+-            JoltIn::RD_Write,
+-            JoltIn::LookupOutput,
+-        );
+         let rd_nonzero_and_jmp = cs.allocate_prod(JoltIn::Bytecode_RD, JoltIn::OpFlags_IsJmp);
+         let lhs = JoltIn::Bytecode_ELFAddress + (PC_START_ADDRESS - PC_NOOP_SHIFT);
+         let rhs = JoltIn::RD_Write;
+```
+
+它变动了 `rd_nonzero_and_lookup_to_rd` 的内容，具体是删除了：
+
+```
+-        cs.constrain_eq_conditional(
+-            rd_nonzero_and_lookup_to_rd,
+-            JoltIn::RD_Write,
+-            JoltIn::LookupOutput,
+-        );
+```
+
+git 很好地帮我们定位到了所修改的文件 `jolt/src/r1cs/jolt_constraints.rs` 第 292 行。
+
+附件还给出了 host 中要运行的 guest 程序代码：
+
+```rust
+#![cfg_attr(feature = "guest", no_std)]
+#![no_main]
+
+#[jolt::provable]
+fn two_plus_two() -> u16 {
+    let mut n: u16 = 2;
+
+    #[cfg(any(target_arch = "riscv32", target_arch = "riscv64"))]
+    unsafe {
+        core::arch::asm!(
+            "li {n}, 2",
+            "add {n}, {n}, {n}",
+            n = inout(reg) n,
+        );
+    }
+
+    #[cfg(target_arch = "x86_64")]
+    unsafe {
+        core::arch::asm!(
+            "mov {n}, 2",
+            "add {n}, {n}, {n}",
+            n = inout(reg) n,
+        );
+    }
+    n
+}
+```
+
+出题人的意图应该在于利用修改之后的 jolt 库来证明 2 + 2 = 5.
+
+## 3. Alynasis
+
+我们需要深入理解 jolt zkVM 的 [R1CS 设计](https://jolt.a16zcrypto.com/how/r1cs_constraints.html)。
+
+jolt 的 R1CS 部分是通用的组件，意味着它适用于每一个 CPU step （也就是“取指-译码-执行”的 instruction cycle），每一个 step 只需要接近 60 个约束和 80 个变量。
+
+每一个 CPU step 需要的输入有：
+- 字节码相关（只读）：
+  - bytecode read address: 这一步中所需要取出的指令的 idx
+  - 预处理之后的指令表示：`(elf_address, bitflags, rs1, rs2, rd, imm)`
+- 读写内存相关：
+  - 指令所需要读写的内存地址，如果不是一个 load/store 指令，则置 0.
+  - 内存中读写的字节
+- 指令 lookup（执行）相关：
+  - 指令操作数 `x` 和 `y` 的 chunks
+  - lookup query. 一般是操作数的结合
+  - lookup output.
+
+单看 patch 所修改的那个变量名，可知：它约束了 rd（目的寄存器）非 0 且 rd 的值与 lookup 的 output 相等。从上面的注释也解释了这一点：
+
+```
+ // if (rd != 0 && update_rd_with_lookup_output == 1) constrain(rd_val == LookupOutput)
+
+ ...
+ cs.constrain_eq_conditional(
+    rd_nonzero_and_lookup_to_rd,
+    JoltIn::RD_Write,
+    JoltIn::LookupOutput,
+);
+...
+```
+
+`cs.constrain_eq_conditional` 目的是当第一个参数为 1，则第二、三个参数必须向灯。`JoltIn::RD_Write` 这个值来自于读写内存模块，表示写入目的寄存器的值，`JoltIn::LookupOutput` 这个值来自指令执行模块，表示指令 lookup 查询后返回的结果。
+
+因此，当补丁删除了这条约束后，zkVM将不再检查 rd 的输出与 lookup 的一致性，因此导致漏洞。也因此我们可以得到 `2 + 2 = 5` 的证明。
+
+## 4. EXP
+
+在写代码之前，我们应该梳理一下我们需要做哪些事情：
+1. 修改加法指令的逻辑，使得 `2 + 2 = 5`
+2. 调用 jolt_sdk 生成 proof
+
+对于第一点，我们需要修改 `jolt/tracer/src/emulator/cpu.rs`。这是 jolt 的 tracer 模块，用于模拟 CPU 生成 execution trace。
+
+```rust
+    Instruction {
+        mask: 0xfe00707f,
+        data: 0x00000033,
+        name: "ADD",
+        operation: |cpu, word, _address| {
+            let f = parse_format_r(word);
+            cpu.x[f.rd] = cpu.sign_extend(cpu.x[f.rs1].wrapping_add(cpu.x[f.rs2] + 1));
+            Ok(())
+        },
+        disassemble: dump_format_r,
+        trace: Some(trace_r),
+    },
+```
+
+如上，我把其中一个源寄存器加 1，即可得到 `2 + 2 = 5`。（只要能够使得 2+2=5逻辑成立都可）。
+
+在 host program 中打印 output 并生成 proof 即可。
+
+完整代码：见 [code](https://github.com/Xor0v0/ZK-Puzzle-Writeups/tree/main/docs/crypto/2+2=5/code) 文件夹.
+
diff --git a/docs/crypto/group-dynamics/code/exp.ipynb b/docs/crypto/group-dynamics/code/exp.ipynb
index bb83aa6..9c6c6ea 100644
--- a/docs/crypto/group-dynamics/code/exp.ipynb
+++ b/docs/crypto/group-dynamics/code/exp.ipynb
@@ -3,7 +3,11 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "metadata": {},
+   "metadata": {
+    "vscode": {
+     "languageId": "python"
+    }
+   },
    "outputs": [
     {
      "name": "stdout",
@@ -100,13 +104,6 @@
     "        print(s)\n",
     "        break"
    ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
   }
  ],
  "metadata": {
@@ -122,7 +119,7 @@
    },
    "file_extension": ".py",
    "mimetype": "text/x-python",
-   "name": "python",
+   "name": "sage",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
    "version": "3.11.9"
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
index 9a34447..5aac4f3 100644
--- a/docs/crypto/lets-hash-it-out/lets-hash-it-out.md
+++ b/docs/crypto/lets-hash-it-out/lets-hash-it-out.md
@@ -116,4 +116,4 @@ $$
 
 ## 4. Code
 
-见 `code/` 文件夹。
\ No newline at end of file
+见 [code](https://github.com/Xor0v0/ZK-Puzzle-Writeups/tree/main/docs/crypto/lets-hash-it-out/code) 文件夹。
\ No newline at end of file