From 5d86000231e634f6e057acdd7e99b51877396cca Mon Sep 17 00:00:00 2001 From: FallenSigh Date: Sat, 27 Jun 2026 03:53:53 +0800 Subject: [PATCH] add docs and test data --- docs/ML-KEM算法详解.md | 339 + docs/NIST.FIPS.202_SHA3哈希函数.pdf | Bin 0 -> 1551816 bytes docs/NIST.FIPS.203_ML-KEM密钥封装.pdf | Bin 0 -> 1245519 bytes docs/哈希函数文档.md | 376 + test_data/README.md | 85 + test_data/kat_MLKEM_1024.rsp | 11000 ++++++++++++++++++++++++ test_data/kat_MLKEM_512.rsp | 11000 ++++++++++++++++++++++++ test_data/kat_MLKEM_768.rsp | 11000 ++++++++++++++++++++++++ 8 files changed, 33800 insertions(+) create mode 100755 docs/ML-KEM算法详解.md create mode 100755 docs/NIST.FIPS.202_SHA3哈希函数.pdf create mode 100755 docs/NIST.FIPS.203_ML-KEM密钥封装.pdf create mode 100755 docs/哈希函数文档.md create mode 100644 test_data/README.md create mode 100644 test_data/kat_MLKEM_1024.rsp create mode 100644 test_data/kat_MLKEM_512.rsp create mode 100644 test_data/kat_MLKEM_768.rsp diff --git a/docs/ML-KEM算法详解.md b/docs/ML-KEM算法详解.md new file mode 100755 index 0000000..3956c4a --- /dev/null +++ b/docs/ML-KEM算法详解.md @@ -0,0 +1,339 @@ +# ML-KEM (FIPS 203) 算法详解 + +--- + +## 一、定位与层次 + +ML-KEM 是一种**后量子密钥封装机制**(KEM),基于 Module Learning With Errors(MLWE)困难问题。整个算法分两层: + +``` +┌──────────────────────────────────────────────┐ +│ ML-KEM 层 (§6-7) │ +│ KeyGen / Encaps / Decaps (Alg 19-21) │ +│ + 内部接口 (Alg 16-18, CAVP 测试用) │ +│ └─ FO 变换: G, H, J 哈希 + 隐式拒绝 │ +├──────────────────────────────────────────────┤ +│ K-PKE 层 (§5) │ +│ KeyGen / Encrypt / Decrypt (Alg 13-15) │ +│ └─ 格密码: A·s+e 噪声线性系统 │ +├──────────────────────────────────────────────┤ +│ 数学基础 (§4) │ +│ 环 R_q = Z_q[x]/(x²⁵⁶+1), q=3329 │ +│ NTT, 采样 (均匀/CBD), 编解码, 压缩 │ +├──────────────────────────────────────────────┤ +│ SHA-3 哈希层 (FIPS 202) │ +│ KECCAK-p[1600,24], SHA3-256/512, SHAKE128/256│ +└──────────────────────────────────────────────┘ +``` + +--- + +## 二、数学基础 + +### 2.1 环 `R_q = Z_q[x]/(x^256 + 1)` + +| 参数 | 值 | +|------|-----| +| 模数 `q` | **3329**(12 bit 素数) | +| 多项式次数 `n` | **256** | +| 环定义 | 系数在 `{0,1,...,3328}` 中,乘法模 `x^256+1` | + +### 2.2 NTT(数论变换) + +因为 `x^256 + 1` 在 `Z_q` 上分解为 128 个二次因式: + +``` +x^256 + 1 = Π_{i=0}^{127} (x² − ζ^{2·BitRev₇(i)+1}) +``` + +- **NTT**(正变换):系数表示 → NTT 域表示(128 对 (a₀, a₁)) +- **INTT**(逆变换):NTT 域 → 系数域 +- **MultiplyNTTs**:NTT 域中乘法 = 128 次独立的一次多项式乘法(Algorithm 12 `BaseCaseMultiply`) + +``` +NTT 域中: 多项式乘法 = O(128) 次 BaseCaseMultiply +系数域中: 多项式乘法 = O(256×256) 次模乘 ← NTT 加速 +``` + +### 2.3 采样分布 + +| 算法 | 分布 | 说明 | +|------|------|------| +| **SampleNTT** (Alg 7) | 均匀分布 | SHAKE128 可扩展输出 + 拒绝采样 | +| **SamplePolyCBD** (Alg 8) | 中心二项分布 CBD_η | 从 `64η` 字节比特串计算:`x = Σ(b_{2iη+j} − b_{2iη+η+j})`,结果 mod q | + +CBD_η 参数: + +| η | 每系数使用比特数 | 输出范围 | PRF 输出 | +|---|---------------|---------|---------| +| 2 | 4 bit | `[-2, 2]` → mod q 后 `{3327,3328,0,1,2}` | 128 字节 | +| 3 | 6 bit | `[-3, 3]` → mod q 后 `{3326,...,0,...,3}` | 192 字节 | + +CBD 的核心特性:输出值集中在 0 附近(小噪声),且无需高斯采样(硬件友好)。 + +### 2.4 编码与压缩 + +| 算法 | 功能 | 域映射 | +|------|------|--------| +| ByteEncode_d / ByteDecode_d | 整数数组 ↔ 字节数组 | `Z_m^256 ↔ B^{32d}`(d=12 时 m=q,否则 m=2^d)| +| Compress_d / Decompress_d | 压缩 / 解压 | `Z_q ↔ Z_{2^d}`,舍入到最近整数,**禁止浮点** | + +压缩的数学定义: + +``` +Compress_d(x) = ⌈(2^d / q) · x⌋ mod 2^d +Decompress_d(y) = ⌈(q / 2^d) · y⌋ +``` + +关键性质: + +``` +Compress_d(Decompress_d(y)) = y (对所有 y ∈ Z_{2^d}) +Decompress_d(Compress_d(x)) ≈ x (误差很小,当 d 接近 12) +``` + +--- + +## 三、K-PKE 层(非对称加密,不可单独使用) + +核心思想:**带噪声的线性方程组**。 + +``` +私钥: s ∈ R_q^k (k 个秘密多项式) +公钥: (A, t = A·s + e) + └─ A ∈ R_q^{k×k}: 伪随机生成(种子 ρ + XOF) + └─ e ∈ R_q^k: 噪声(CBD 采样) +``` + +### Algorithm 13: `K-PKE.KeyGen(d)` — 密钥生成 + +``` +输入: 随机种子 d (32 字节) +输出: ek_PKE (384k+32 B), dk_PKE (384k B) + +Step 1: (ρ, σ) ← G(d || k) G = SHA3-512, 域分离用 k +Step 3-7: Â[i][j] ← SampleNTT(ρ||j||i) × k² 次 + └─ Â 是 NTT 域中的矩阵(已在 NTT 域) +Step 8-11: s[i] ← SamplePolyCBD_η1(PRF_η1(σ, N++)) × k 次 +Step 12-15: e[i] ← SamplePolyCBD_η1(PRF_η1(σ, N++)) × k 次 +Step 16-17: ŝ ← NTT(s), ê ← NTT(e) +Step 18: t̂ ← Â ∘ ŝ + ê 矩阵乘 + 加噪声(全在 NTT 域) +Step 19-20: 序列化:ByteEncode₁₂(t̂) || ρ → ek + ByteEncode₁₂(ŝ) → dk +``` + +### Algorithm 14: `K-PKE.Encrypt(ek, m, r)` — 加密 + +``` +输入: ek, 明文 m (32B), 随机数 r (32B) +输出: 密文 c + +Step 2-3: 从 ek 解析 t̂ 和 ρ +Step 4-8: 用 ρ 重生成 Â(与 KeyGen 相同) +Step 9-12: y[i] ← CBD_η1(PRF_η1(r, N++)) × k +Step 13-16: e1[i] ← CBD_η2(PRF_η2(r, N++)) × k +Step 17: e2 ← CBD_η2(PRF_η2(r, N++)) +Step 18: ŷ ← NTT(y) +Step 19: u ← NTT⁻¹(Âᵀ ∘ ŷ) + e1 注意:Â 转置! +Step 20: μ ← Decompress₁(ByteDecode₁(m)) 明文编码为 Z_q 多项式 +Step 21: v ← NTT⁻¹(t̂ᵀ ∘ ŷ) + e2 + μ +Step 22-23: c₁ ← ByteEncode_du(Compress_du(u)) + c₂ ← ByteEncode_dv(Compress_dv(v)) +Step 24: c ← c₁ || c₂ +``` + +**为什么加密能解密?** + +``` +解密计算: v' − sᵀ·u' + = (tᵀ·y + e2 + μ) − sᵀ·(Aᵀ·y + e1) + = (A·s + e)ᵀ·y + e2 + μ − sᵀ·Aᵀ·y − sᵀ·e1 + = sᵀ·Aᵀ·y + eᵀ·y + e2 + μ − sᵀ·Aᵀ·y − sᵀ·e1 + = μ + (eᵀ·y + e2 − sᵀ·e1) + ≈ μ ← 噪声项很小,四舍五入恢复 +``` + +### Algorithm 15: `K-PKE.Decrypt(dk, c)` — 解密 + +``` +Step 5: ŝ ← ByteDecode₁₂(dk) +Step 6: w ← v' − NTT⁻¹(ŝᵀ ∘ NTT(u')) +Step 7: m ← ByteEncode₁(Compress₁(w)) +``` + +--- + +## 四、ML-KEM 层(CCA 安全 KEM) + +在 K-PKE(CPA 安全)基础上,通过 **Fujisaki-Okamoto 变换** 升级为 CCA 安全。 + +### 所用哈希函数 + +| 函数 | 底层 | 用途 | +|------|------|------| +| **G** | SHA3-512 | KeyGen: `(ρ,σ)←G(d‖k)`;Encaps: `(K,r)←G(m‖H(ek))`;Decaps: `(K',r')←G(m'‖h)` | +| **H** | SHA3-256 | `H(ek)` 存在 dk 中用于验证;Encaps 中参与 G 输入 | +| **J** | SHAKE256(_, 256) | **隐式拒绝**:`K̄←J(z‖c)`,当重加密密文不匹配时使用 | + +### Algorithm 16: `KeyGen_internal(d, z)` — 内部密钥生成 + +``` +dk_PKE ← K-PKE 的解密密钥 (384k B) +ek_PKE ← K-PKE 的加密密钥 (384k+32 B) +h ← H(ek_PKE) 32 B +z ← 随机 (32 B, 隐式拒绝用) + +dk = dk_PKE || ek_PKE || h || z 共 768k+96 B +ek = ek_PKE 共 384k+32 B +``` + +### Algorithm 17/20: `Encaps(ek)` — 封装 + +``` +Step 1: m ←$ B³² 随机 32 字节 +Step 2: (K, r) ← G(m || H(ek)) K = 共享密钥, r = 加密随机数 +Step 3: c ← K-PKE.Encrypt(ek, m, r) +Output: (K, c) +``` + +### Algorithm 18/21: `Decaps(dk, c)` — 解封装 + +``` +Step 1-4: 解析 dk → dk_PKE, ek_PKE, h, z +Step 5: m' ← K-PKE.Decrypt(dk_PKE, c) +Step 6: (K', r') ← G(m' || h) +Step 7: K̄ ← J(z || c) 隐式拒绝密钥 +Step 8: c' ← K-PKE.Encrypt(ek_PKE, m', r') +Step 9-11: if c ≠ c' then K' ← K̄ 隐式拒绝! +Output: K' +``` + +**隐式拒绝的作用**:如果攻击者篡改了密文: + +- 解密得到 `m' ≠ m`(噪声导致) +- 重加密得到 `c' ≠ c` +- 返回 `J(z || c)` 而非 `G(m' || h)` +- 攻击者**不知道**解密失败(无显式错误),无法利用侧信道 + +**通信流程(7 步)**: + +``` +Alice Bob +───── ─── +key_gen() → (ek, dk) + ──── ek ────▶ + encaps(ek) → (K, ct_kem) + xor_crypt(K, "hello world") → encrypted + ◀─ (ct_kem, encrypted) ── +decaps(dk, ct_kem) → K' +xor_crypt(K', encrypted) → "hello world" ✓ +``` + +--- + +## 五、参数集 + +| 参数 | ML-KEM-512 | ML-KEM-768 | ML-KEM-1024 | +|------|-----------|-----------|-------------| +| **k**(矩阵维度) | 2 | 3 | 4 | +| **η₁**(s, e, y 噪声) | 3 | 2 | 2 | +| **η₂**(e1, e2 噪声) | 2 | 2 | 2 | +| **du**(u 压缩) | 10 | 10 | 11 | +| **dv**(v 压缩) | 4 | 4 | 5 | +| NIST 安全类别 | 1 (≈AES-128) | 3 (≈AES-192) | 5 (≈AES-256) | + +### 密钥与密文大小 + +| 对象 | ML-KEM-512 | ML-KEM-768 | ML-KEM-1024 | +|------|-----------|-----------|-------------| +| ek(公钥) | 800 B | 1184 B | 1568 B | +| dk(私钥) | 1632 B | 2400 B | 3168 B | +| c(密文) | 768 B | 1088 B | 1568 B | +| K(共享密钥) | 32 B | 32 B | 32 B | + +--- + +## 六、输入检查(FIPS 203 §7) + +### Encaps(§7.2)— 封装密钥检查 + +``` +1. 类型检查: ek 长度 = 384k+32 +2. 模数检查: ByteEncode₁₂(ByteDecode₁₂(ek[0:384k])) == ek[0:384k] + 确保编码的值在 [0, q-1] 范围内,无模归约 +``` + +### Decaps(§7.3)— 解封装输入检查 + +``` +1. 密文类型检查: c 长度 = 32(du·k + dv) +2. 私钥类型检查: dk 长度 = 768k+96 +3. 哈希检查: H(dk[384k:768k+32]) == dk[768k+32:768k+64] + 确保 dk 中的 ek_PKE 未被篡改 +``` + +--- + +## 七、Const Generic 参数映射 + +| Rust 参数 | 含义 | 512 | 768 | 1024 | +|-----------|------|-----|-----|------| +| `K` | 矩阵维度 | 2 | 3 | 4 | +| `ETA_BYTES` | 64·η₁ | 192 | 128 | 128 | +| `ETA2_BYTES` | 64·η₂ | 128 | 128 | 128 | +| `DU` | u 压缩 | 10 | 10 | 11 | +| `DV` | v 压缩 | 4 | 4 | 5 | + +```rust +// Rust 调用示例 +ml_kem::key_gen::<2, 192>(&d, &z); // ML-KEM-512 +ml_kem::encaps::<2, 192, 128, 10, 4>(&ek, &m); // ML-KEM-512 +ml_kem::decaps::<2, 192, 128, 10, 4>(&dk, &c); // ML-KEM-512 +``` + +--- + +## 八、算法依赖关系图 + +``` +Algorithm 19 key_gen ──────────────┐ +Algorithm 20 encaps ───────────────┤ +Algorithm 21 decaps ───────────────┤ + ▼ +Algorithm 16 keygen_internal ──────┐ +Algorithm 17 encaps_internal ──────┤ +Algorithm 18 decaps_internal ──────┤ + ▼ +Algorithm 13 K-PKE.KeyGen ─────────┐ +Algorithm 14 K-PKE.Encrypt ────────┤ +Algorithm 15 K-PKE.Decrypt ────────┤ + ▼ +Algorithm 7 SampleNTT ────────────┐ +Algorithm 8 SamplePolyCBD ────────┤ +Algorithm 9 NTT ──────────────────┤ +Algorithm 10 INTT ─────────────────┤ +Algorithm 11 MultiplyNTTs ─────────┤ +Algorithm 12 BaseCaseMultiply ─────┤ +Algorithm 5 ByteEncode ───────────┤ +Algorithm 6 ByteDecode ───────────┤ +Algorithm 1 Compress ─────────────┤ +Algorithm 2 Decompress ───────────┤ +Algorithm 3 BitsToBytes ──────────┤ +Algorithm 4 BytesToBits ──────────┤ + ▼ + G / H / J / PRF (SHA-3) + │ + KECCAK-p[1600,24] +``` + +--- + +## 九、安全性概要 + +| 攻击类型 | K-PKE (CPA) | ML-KEM (CCA) | +|----------|------------|-------------| +| 选择明文攻击 (CPA) | ✓ 安全 | ✓ 安全 | +| 选择密文攻击 (CCA) | ✗ 不安全 | ✓ 安全(FO 变换) | +| 量子攻击 | 基于 MLWE 困难假设 | 同上 + FO 在 QROM 下安全 | + +**MLWE 安全性**:区分 `(A, A·s+e)` 和 `(A, u)`(u 均匀随机)的计算困难度 ≈ 格上最短向量问题(SVP),已知无高效量子算法。 diff --git a/docs/NIST.FIPS.202_SHA3哈希函数.pdf b/docs/NIST.FIPS.202_SHA3哈希函数.pdf new file mode 100755 index 0000000000000000000000000000000000000000..2d1eae880b705fda7052f2ac185ab26b8d3ae11c GIT binary patch literal 1551816 zcmZ^~WmHvBy9P?b1~%Od(%s$N-60_@-AH$LcO%jgN=bJ~DBXgT(n<(;r{8zZ9cSDz zu75;ad+oVqyidK0PE%H%jftSP~?ds}9#m&w4-)qz?Jzguh z*t&un{rl0znhIQKBQDONX5(dP4ekmq6%_pMwVDn#uWbHZOvTMB!2jRhX?S}%Ik^1$ zPF{ikUM4OMMYVCU{?G7uz(xN%PAL}`S1(T!Dz1Nn*QPS#ka2bKvT^YOALZfvpKnm` zaP@WrLy^(pkhSq~cx9ulAkCq}q3dDk;^}7TVdL`3|G&@sp9}vpN^1v8X;(iJa8FJu zelBh*0U>TPFb&{Z@Ra}gCJt>IPgie`S2mvD&hp?(|9t_sIp@D86Z-EJy1JZH0{{CX z7uEm!TW%_F$A6;*U#02c`bx*f%Y*|g28XVVpBIOcGnj1|GY&%yD@U7G|8A?~%t^(? 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