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main.py
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1344 lines (1066 loc) · 47.7 KB
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#!/usr/bin/env python3
import os
import sys
import time
import hmac
import json
import zlib
import base64
import struct
import secrets
import hashlib
import threading
import argparse
import numpy as np
from typing import Tuple, Dict, List, Optional, Union, Any
from dataclasses import dataclass, field
from enum import IntEnum
from concurrent.futures import ThreadPoolExecutor, as_completed
import ctypes
from ctypes import c_uint64, c_uint32, c_uint8, POINTER, Structure
import platform
if platform.system() == 'Windows':
try:
kernel32 = ctypes.windll.kernel32
ntdll = ctypes.windll.ntdll
except:
kernel32 = ntdll = None
else:
kernel32 = ntdll = None
class SecurityLevel(IntEnum):
NIST_1 = 128
NIST_3 = 192
NIST_5 = 256
@dataclass
class CryptoParameters:
n: int
q: int
k: int
eta1: int
eta2: int
du: int
dv: int
noise_bound: float
xmss_height: int
wots_w: int
wots_len: int
poly_bytes: int
secret_key_bytes: int
public_key_bytes: int
ciphertext_bytes: int
class ConstantTime:
@staticmethod
def select_u32(a: int, b: int, c: int) -> int:
mask = (-c) & 0xFFFFFFFF
return (a & mask) | (b & (~mask))
@staticmethod
def compare_bytes(a: bytes, b: bytes) -> bool:
if len(a) != len(b):
return False
d = 0
for x, y in zip(a, b):
d |= x ^ y
return d == 0
@staticmethod
def cmov(r: bytearray, x: bytes, b: int):
mask = -b & 0xFF
for i in range(len(r)):
if i < len(x):
r[i] ^= mask & (r[i] ^ x[i])
class SHAKE256:
def __init__(self):
self.state = [0] * 25
self.pos = 0
self.rate = 136
def absorb(self, data: bytes):
for byte in data:
if self.pos >= self.rate:
self._keccak_f()
self.pos = 0
self.state[self.pos // 8] ^= byte << (8 * (self.pos % 8))
self.pos += 1
def finalize(self):
if self.pos < self.rate:
self.state[self.pos // 8] ^= 0x1F << (8 * (self.pos % 8))
self.state[(self.rate - 1) // 8] ^= 0x80 << (8 * ((self.rate - 1) % 8))
self._keccak_f()
self.pos = 0
def squeeze(self, length: int) -> bytes:
output = bytearray()
while len(output) < length:
if self.pos >= self.rate:
self._keccak_f()
self.pos = 0
remaining = min(length - len(output), self.rate - self.pos)
for i in range(remaining):
byte_idx = (self.pos + i) // 8
bit_offset = ((self.pos + i) % 8) * 8
if byte_idx < len(self.state):
output.append((self.state[byte_idx] >> bit_offset) & 0xFF)
else:
output.append(0)
self.pos += remaining
return bytes(output)
def _keccak_f(self):
RC = [0x01, 0x82, 0x8a, 0x00, 0x8b, 0x01, 0x81, 0x09,
0x8a, 0x88, 0x09, 0x03, 0x8b, 0x8b, 0x8b, 0x89,
0x03, 0x02, 0x80, 0x00, 0x0a, 0x0a, 0x81, 0x8a]
for round_idx in range(24):
C = [self.state[i] ^ self.state[i+5] ^ self.state[i+10] ^ self.state[i+15] ^ self.state[i+20] for i in range(5)]
D = [C[(i+4)%5] ^ self._rotl64(C[(i+1)%5], 1) for i in range(5)]
for i in range(25):
self.state[i] ^= D[i % 5]
B = [0] * 25
B[0] = self.state[0]
for i in range(1, 25):
j = (i * 6) % 25
rho = ((i-1) * i) // 2
B[j] = self._rotl64(self.state[i], rho % 64)
for i in range(0, 25, 5):
for j in range(5):
self.state[i+j] = B[i+j] ^ ((~B[i+(j+1)%5]) & B[i+(j+2)%5])
self.state[0] ^= RC[round_idx]
def _rotl64(self, x: int, n: int) -> int:
n = n % 64
if n == 0:
return x & 0xFFFFFFFFFFFFFFFF
return ((x << n) | (x >> (64 - n))) & 0xFFFFFFFFFFFFFFFF
def shake256(data: bytes, length: int) -> bytes:
shake = SHAKE256()
shake.absorb(data)
shake.finalize()
return shake.squeeze(length)
class SecureRandom:
def __init__(self):
self._pool = bytearray(8192)
self._idx = 0
self._counter = 0
self._last_reseed = time.time_ns()
self._lock = threading.Lock()
self._reseed()
def _reseed(self):
entropy = bytearray()
entropy.extend(secrets.token_bytes(2048))
entropy.extend(struct.pack('>Q', time.time_ns()))
entropy.extend(struct.pack('>Q', os.getpid()))
if hasattr(os, 'urandom'):
entropy.extend(os.urandom(1024))
try:
with open('/dev/urandom', 'rb') as f:
entropy.extend(f.read(512))
except:
pass
if kernel32:
try:
buf = ctypes.create_string_buffer(256)
kernel32.RtlGenRandom(buf, 256)
entropy.extend(buf.raw)
except:
pass
mixed = shake256(bytes(self._pool) + bytes(entropy), len(self._pool))
for i in range(len(mixed)):
self._pool[i] = mixed[i]
self._idx = 0
self._counter = 0
self._last_reseed = time.time_ns()
def bytes(self, length: int) -> bytes:
with self._lock:
if time.time_ns() - self._last_reseed > 300_000_000_000 or self._counter > 1000000:
self._reseed()
output = bytearray()
while len(output) < length:
if self._idx >= len(self._pool) - 64:
self._reseed()
chunk_size = min(64, length - len(output))
state = bytes(self._pool[self._idx:self._idx + 64])
chunk = shake256(state + struct.pack('>Q', self._counter), chunk_size)
output.extend(chunk)
self._idx = (self._idx + 17) % (len(self._pool) - 64)
self._counter += 1
return bytes(output)
def uniform_int(self, bound: int) -> int:
if bound <= 1:
return 0
byte_length = (bound.bit_length() + 7) // 8
while True:
candidate = int.from_bytes(self.bytes(byte_length), 'little')
if candidate < bound:
return candidate
class GaussianSampler:
def __init__(self, sigma: float, precision: int = 64):
self.sigma = sigma
self.precision = precision
self.tail_bound = max(1, int(6 * sigma))
self.rng = SecureRandom()
self._build_cdt()
def _build_cdt(self):
self.cdt = []
total = 0.0
for z in range(-self.tail_bound, self.tail_bound + 1):
prob = np.exp(-z * z / (2.0 * self.sigma * self.sigma))
total += prob
self.cdt.append((total, z))
if total > 0:
self.cdt = [(p / total, z) for p, z in self.cdt]
else:
self.cdt = [(1.0, 0)]
def sample(self) -> int:
u = int.from_bytes(self.rng.bytes(8), 'little') / (2**64)
for prob, value in self.cdt:
if u <= prob:
return value
return 0
def sample_vector(self, length: int) -> np.ndarray:
return np.array([self.sample() for _ in range(length)], dtype=np.int32)
class NTT:
def __init__(self, n: int, q: int):
self.n = n
self.q = q
self.ninv = pow(n, q - 2, q)
self.root = self._find_primitive_root()
self.zetas = self._compute_zetas()
self.zetas_inv = [pow(z, q - 2, q) for z in self.zetas]
def _find_primitive_root(self) -> int:
for g in range(2, min(self.q, 1000)):
if pow(g, self.n, self.q) == 1 and pow(g, self.n // 2, self.q) != 1:
return g
return 17
def _compute_zetas(self) -> List[int]:
zetas = []
k = 1
length = 2
while length <= self.n:
for start in range(0, self.n, 2 * length):
zeta = pow(self.root, k * (self.q - 1) // self.n, self.q)
zetas.append(zeta)
k += 2
length *= 2
return zetas
def forward(self, poly: np.ndarray) -> np.ndarray:
a = poly.copy().astype(np.int64)
k = 0
length = 2
while length <= self.n:
for start in range(0, self.n, 2 * length):
if k < len(self.zetas):
zeta = self.zetas[k]
k += 1
else:
zeta = 1
for j in range(start, start + length):
if j + length < len(a):
t = (zeta * a[j + length]) % self.q
a[j + length] = (a[j] - t) % self.q
a[j] = (a[j] + t) % self.q
length *= 2
return a.astype(np.int32)
def inverse(self, poly: np.ndarray) -> np.ndarray:
a = poly.copy().astype(np.int64)
k = len(self.zetas_inv) - 1
length = self.n // 2
while length >= 2:
for start in range(0, self.n, 2 * length):
if k >= 0 and k < len(self.zetas_inv):
zeta = self.zetas_inv[k]
k -= 1
else:
zeta = 1
for j in range(start, start + length):
if j + length < len(a):
t = a[j]
a[j] = (t + a[j + length]) % self.q
a[j + length] = (zeta * (t - a[j + length])) % self.q
length //= 2
for i in range(len(a)):
a[i] = (a[i] * self.ninv) % self.q
return a.astype(np.int32)
class Polynomial:
def __init__(self, coeffs: np.ndarray, q: int):
self.coeffs = np.array(coeffs, dtype=np.int32) % q
self.q = q
self.n = len(coeffs)
self.ntt = NTT(self.n, q) if self.n in [256, 512, 1024] and q > self.n else None
def __add__(self, other: 'Polynomial') -> 'Polynomial':
return Polynomial((self.coeffs + other.coeffs) % self.q, self.q)
def __sub__(self, other: 'Polynomial') -> 'Polynomial':
return Polynomial((self.coeffs - other.coeffs) % self.q, self.q)
def __mul__(self, other: 'Polynomial') -> 'Polynomial':
if self.ntt and other.ntt and len(self.coeffs) == len(other.coeffs):
try:
a_ntt = self.ntt.forward(self.coeffs)
b_ntt = self.ntt.forward(other.coeffs)
c_ntt = (a_ntt * b_ntt) % self.q
result = self.ntt.inverse(c_ntt)
return Polynomial(result, self.q)
except:
pass
result = np.zeros(self.n, dtype=np.int32)
for i in range(self.n):
for j in range(self.n):
idx = i + j
coeff_product = int(self.coeffs[i]) * int(other.coeffs[j])
if idx >= self.n:
result[idx - self.n] = (result[idx - self.n] - coeff_product) % self.q
else:
result[idx] = (result[idx] + coeff_product) % self.q
return Polynomial(result, self.q)
def compress(self, d: int) -> np.ndarray:
if d <= 0 or d >= 32:
return self.coeffs.copy()
scale = 1 << d
return np.array([((int(x) * scale + self.q // 2) // self.q) % scale for x in self.coeffs], dtype=np.int32)
def decompress(self, compressed: np.ndarray, d: int) -> 'Polynomial':
if d <= 0 or d >= 32:
return Polynomial(compressed, self.q)
scale = 1 << d
coeffs = np.array([int(x) * self.q // scale for x in compressed], dtype=np.int32)
return Polynomial(coeffs, self.q)
def to_bytes(self) -> bytes:
if self.q <= 1:
return bytes(len(self.coeffs))
bits_per_coeff = max(1, (self.q - 1).bit_length())
total_bits = self.n * bits_per_coeff
total_bytes = (total_bits + 7) // 8
result = bytearray(total_bytes)
bit_pos = 0
for coeff in self.coeffs:
coeff = int(coeff) % self.q
for bit in range(bits_per_coeff):
if bit >= 0 and coeff & (1 << bit):
byte_idx = bit_pos // 8
bit_idx = bit_pos % 8
if byte_idx < len(result) and bit_idx >= 0:
result[byte_idx] |= 1 << bit_idx
bit_pos += 1
return bytes(result)
@classmethod
def from_bytes(cls, data: bytes, n: int, q: int) -> 'Polynomial':
if q <= 1:
return cls(np.zeros(n, dtype=np.int32), max(q, 2))
bits_per_coeff = max(1, (q - 1).bit_length())
coeffs = np.zeros(n, dtype=np.int32)
bit_pos = 0
for i in range(n):
coeff = 0
for bit in range(bits_per_coeff):
byte_idx = bit_pos // 8
bit_idx = bit_pos % 8
if (byte_idx < len(data) and bit_idx >= 0 and
bit >= 0 and (data[byte_idx] & (1 << bit_idx))):
coeff |= 1 << bit
bit_pos += 1
coeffs[i] = coeff % q
return cls(coeffs, q)
class PolynomialVector:
def __init__(self, polys: List[Polynomial]):
self.polys = polys
self.k = len(polys)
self.q = polys[0].q if polys else 2
self.n = polys[0].n if polys else 0
def __add__(self, other: 'PolynomialVector') -> 'PolynomialVector':
return PolynomialVector([p1 + p2 for p1, p2 in zip(self.polys, other.polys)])
def __sub__(self, other: 'PolynomialVector') -> 'PolynomialVector':
return PolynomialVector([p1 - p2 for p1, p2 in zip(self.polys, other.polys)])
def dot(self, other: 'PolynomialVector') -> Polynomial:
if not self.polys or not other.polys:
return Polynomial(np.zeros(self.n, dtype=np.int32), self.q)
result = self.polys[0] * other.polys[0]
for i in range(1, min(len(self.polys), len(other.polys))):
result = result + (self.polys[i] * other.polys[i])
return result
def compress(self, d: int) -> List[np.ndarray]:
return [poly.compress(d) for poly in self.polys]
def decompress(self, compressed: List[np.ndarray], d: int) -> 'PolynomialVector':
polys = []
for comp in compressed:
base_poly = Polynomial(np.zeros(self.n, dtype=np.int32), self.q)
polys.append(base_poly.decompress(comp, d))
return PolynomialVector(polys)
def to_bytes(self) -> bytes:
return b''.join(poly.to_bytes() for poly in self.polys)
@classmethod
def from_bytes(cls, data: bytes, k: int, n: int, q: int) -> 'PolynomialVector':
base_poly = Polynomial(np.zeros(n, dtype=np.int32), q)
poly_size = len(base_poly.to_bytes())
polys = []
for i in range(k):
start = i * poly_size
end = (i + 1) * poly_size
if end <= len(data):
poly_data = data[start:end]
else:
poly_data = data[start:] + b'\x00' * (end - len(data))
polys.append(Polynomial.from_bytes(poly_data, n, q))
return cls(polys)
class PolynomialMatrix:
def __init__(self, matrix: List[List[Polynomial]]):
self.matrix = matrix
self.rows = len(matrix)
self.cols = len(matrix[0]) if matrix else 0
self.q = matrix[0][0].q if matrix and matrix[0] else 2
self.n = matrix[0][0].n if matrix and matrix[0] else 0
def multiply_vector(self, vec: PolynomialVector) -> PolynomialVector:
result_polys = []
for i in range(self.rows):
if self.cols > 0 and len(vec.polys) > 0:
poly_sum = self.matrix[i][0] * vec.polys[0]
for j in range(1, min(self.cols, len(vec.polys))):
poly_sum = poly_sum + (self.matrix[i][j] * vec.polys[j])
result_polys.append(poly_sum)
else:
result_polys.append(Polynomial(np.zeros(self.n, dtype=np.int32), self.q))
return PolynomialVector(result_polys)
def to_bytes(self) -> bytes:
return b''.join(b''.join(poly.to_bytes() for poly in row) for row in self.matrix)
@classmethod
def from_bytes(cls, data: bytes, rows: int, cols: int, n: int, q: int) -> 'PolynomialMatrix':
base_poly = Polynomial(np.zeros(n, dtype=np.int32), q)
poly_size = len(base_poly.to_bytes())
matrix = []
idx = 0
for i in range(rows):
row = []
for j in range(cols):
start = idx * poly_size
end = (idx + 1) * poly_size
if end <= len(data):
poly_data = data[start:end]
else:
poly_data = data[start:] + b'\x00' * (end - len(data))
row.append(Polynomial.from_bytes(poly_data, n, q))
idx += 1
matrix.append(row)
return cls(matrix)
class WOTS:
def __init__(self, n: int, w: int):
self.n = n
self.w = max(2, w)
self.log_w = max(1, (self.w - 1).bit_length())
self.len1 = (8 * n + self.log_w - 1) // self.log_w
self.len2 = max(1, (self.len1 * (self.w - 1)).bit_length() // self.log_w + 1)
self.len = self.len1 + self.len2
self.rng = SecureRandom()
def base_w(self, msg: bytes, out_len: int) -> List[int]:
result = []
total = 0
bits = 0
for byte in msg:
total = (total << 8) + byte
bits += 8
while bits >= self.log_w and len(result) < out_len:
shift_amount = max(0, bits - self.log_w)
if shift_amount < 64:
result.append((total >> shift_amount) & (self.w - 1))
else:
result.append(0)
bits -= self.log_w
while len(result) < out_len:
if bits >= self.log_w:
shift_amount = max(0, bits - self.log_w)
if shift_amount < 64:
result.append((total >> shift_amount) & (self.w - 1))
else:
result.append(0)
else:
result.append(0)
bits = max(0, bits - self.log_w)
return result[:out_len]
def chain(self, x: bytes, i: int, s: int, seed: bytes, addr: List[int]) -> bytes:
if s == 0:
return x
tmp = x
for j in range(i, i + s):
addr_copy = addr.copy()
if len(addr_copy) > 4:
addr_copy[4] = j
hash_input = seed + struct.pack('>32I', *(addr_copy + [0] * (32 - len(addr_copy)))[:32]) + tmp
tmp = shake256(hash_input, self.n)
return tmp
def keygen(self, seed: bytes, addr: List[int]) -> Tuple[List[bytes], List[bytes]]:
sk = []
pk = []
for i in range(self.len):
addr_copy = addr.copy()
if len(addr_copy) > 3:
addr_copy[3] = i
while len(addr_copy) < 32:
addr_copy.append(0)
sk_i = shake256(seed + struct.pack('>32I', *addr_copy[:32]), self.n)
sk.append(sk_i)
pk_i = self.chain(sk_i, 0, self.w - 1, seed, addr_copy)
pk.append(pk_i)
return sk, pk
def sign(self, msg: bytes, sk: List[bytes], seed: bytes, addr: List[int]) -> List[bytes]:
csum = 0
msg_base_w = self.base_w(msg, self.len1)
for i in range(self.len1):
csum += self.w - 1 - msg_base_w[i]
csum_bytes = csum.to_bytes(max(1, (self.len2 * self.log_w + 7) // 8), 'big')
csum_base_w = self.base_w(csum_bytes, self.len2)
sig = []
for i in range(self.len1):
addr_copy = addr.copy()
if len(addr_copy) > 3:
addr_copy[3] = i
sig.append(self.chain(sk[i], 0, msg_base_w[i], seed, addr_copy))
for i in range(self.len2):
addr_copy = addr.copy()
if len(addr_copy) > 3:
addr_copy[3] = self.len1 + i
sig.append(self.chain(sk[self.len1 + i], 0, csum_base_w[i], seed, addr_copy))
return sig
def verify(self, msg: bytes, sig: List[bytes], pk: List[bytes], seed: bytes, addr: List[int]) -> bool:
try:
csum = 0
msg_base_w = self.base_w(msg, self.len1)
for i in range(self.len1):
csum += self.w - 1 - msg_base_w[i]
csum_bytes = csum.to_bytes(max(1, (self.len2 * self.log_w + 7) // 8), 'big')
csum_base_w = self.base_w(csum_bytes, self.len2)
computed_pk = []
for i in range(self.len1):
if i < len(sig):
addr_copy = addr.copy()
if len(addr_copy) > 3:
addr_copy[3] = i
steps = self.w - 1 - msg_base_w[i]
computed_pk.append(self.chain(sig[i], msg_base_w[i], steps, seed, addr_copy))
else:
computed_pk.append(b'')
for i in range(self.len2):
if self.len1 + i < len(sig):
addr_copy = addr.copy()
if len(addr_copy) > 3:
addr_copy[3] = self.len1 + i
steps = self.w - 1 - csum_base_w[i]
computed_pk.append(self.chain(sig[self.len1 + i], csum_base_w[i], steps, seed, addr_copy))
else:
computed_pk.append(b'')
return len(computed_pk) == len(pk) and all(ConstantTime.compare_bytes(a, b) for a, b in zip(computed_pk, pk))
except:
return False
class XMSS:
def __init__(self, n: int, h: int, w: int):
self.n = n
self.h = max(1, min(h, 20))
self.w = max(2, w)
self.wots = WOTS(n, w)
self.rng = SecureRandom()
def keygen(self) -> Tuple[bytes, bytes]:
seed = self.rng.bytes(self.n)
sk_seed = self.rng.bytes(self.n)
sk_prf = self.rng.bytes(self.n)
pub_seed = self.rng.bytes(self.n)
leaves = []
max_leaves = min(1 << self.h, 1024)
for i in range(max_leaves):
addr = [i] + [0] * 31
try:
_, pk = self.wots.keygen(sk_seed, addr)
leaf = shake256(pub_seed + b''.join(pk), self.n)
leaves.append(leaf)
except:
leaves.append(shake256(pub_seed + struct.pack('>I', i), self.n))
if len(leaves) == 0:
leaves = [shake256(pub_seed, self.n)]
tree = self._build_tree(leaves, pub_seed)
root = tree[0] if tree else shake256(pub_seed, self.n)
sk = {
'sk_seed': base64.b64encode(sk_seed).decode(),
'sk_prf': base64.b64encode(sk_prf).decode(),
'pub_seed': base64.b64encode(pub_seed).decode(),
'root': base64.b64encode(root).decode(),
'idx': 0,
'h': self.h,
'w': self.w,
'n': self.n,
'max_signatures': max_leaves
}
pk = {
'root': base64.b64encode(root).decode(),
'pub_seed': base64.b64encode(pub_seed).decode(),
'h': self.h,
'w': self.w,
'n': self.n
}
return (json.dumps(pk).encode(), json.dumps(sk).encode())
def _build_tree(self, leaves: List[bytes], pub_seed: bytes) -> List[bytes]:
if not leaves:
return [shake256(pub_seed, self.n)]
tree = [leaves]
level = leaves
while len(level) > 1:
next_level = []
for i in range(0, len(level), 2):
left = level[i]
right = level[i + 1] if i + 1 < len(level) else left
parent = shake256(pub_seed + left + right, self.n)
next_level.append(parent)
tree.insert(0, next_level)
level = next_level
return tree
def sign(self, msg: bytes, sk: bytes) -> bytes:
try:
sk_data = json.loads(sk)
max_sigs = sk_data.get('max_signatures', 1 << self.h)
if sk_data['idx'] >= max_sigs:
raise ValueError("Signature capacity exceeded")
sk_seed = base64.b64decode(sk_data['sk_seed'])
sk_prf = base64.b64decode(sk_data['sk_prf'])
pub_seed = base64.b64decode(sk_data['pub_seed'])
idx = sk_data['idx']
r = shake256(sk_prf + msg + struct.pack('>Q', idx), self.n)
msg_hash = shake256(r + msg, self.n)
addr = [idx] + [0] * 31
wots_sk, _ = self.wots.keygen(sk_seed, addr)
wots_sig = self.wots.sign(msg_hash, wots_sk, pub_seed, addr)
auth_path = self._compute_auth_path(idx, sk_seed, pub_seed, max_sigs)
signature = {
'idx': idx,
'r': base64.b64encode(r).decode(),
'wots_sig': [base64.b64encode(s).decode() for s in wots_sig],
'auth_path': [base64.b64encode(p).decode() for p in auth_path]
}
sk_data['idx'] += 1
return json.dumps(signature).encode()
except Exception as e:
raise ValueError(f"Signing failed: {e}")
def _compute_auth_path(self, idx: int, sk_seed: bytes, pub_seed: bytes, max_leaves: int) -> List[bytes]:
leaves = []
for i in range(max_leaves):
addr = [i] + [0] * 31
try:
_, pk = self.wots.keygen(sk_seed, addr)
leaf = shake256(pub_seed + b''.join(pk), self.n)
leaves.append(leaf)
except:
leaves.append(shake256(pub_seed + struct.pack('>I', i), self.n))
if not leaves:
return [shake256(pub_seed, self.n)]
tree = self._build_tree(leaves, pub_seed)
auth_path = []
current_idx = idx
for level in range(len(tree) - 1, 0, -1):
sibling_idx = current_idx ^ 1
if sibling_idx < len(tree[level]):
auth_path.append(tree[level][sibling_idx])
else:
auth_path.append(tree[level][current_idx])
current_idx >>= 1
return auth_path
def verify(self, msg: bytes, sig: bytes, pk: bytes) -> bool:
try:
sig_data = json.loads(sig)
pk_data = json.loads(pk)
idx = sig_data['idx']
r = base64.b64decode(sig_data['r'])
wots_sig = [base64.b64decode(s) for s in sig_data['wots_sig']]
auth_path = [base64.b64decode(p) for p in sig_data['auth_path']]
root = base64.b64decode(pk_data['root'])
pub_seed = base64.b64decode(pk_data['pub_seed'])
msg_hash = shake256(r + msg, self.n)
addr = [idx] + [0] * 31
_, wots_pk = self.wots.keygen(shake256(pub_seed, self.n), addr)
if not self.wots.verify(msg_hash, wots_sig, wots_pk, pub_seed, addr):
return False
leaf = shake256(pub_seed + b''.join(wots_pk), self.n)
computed_root = self._verify_auth_path(leaf, idx, auth_path, pub_seed)
return ConstantTime.compare_bytes(computed_root, root)
except:
return False
def _verify_auth_path(self, leaf: bytes, idx: int, auth_path: List[bytes], pub_seed: bytes) -> bytes:
current = leaf
current_idx = idx
for sibling in auth_path:
if current_idx & 1:
current = shake256(pub_seed + sibling + current, self.n)
else:
current = shake256(pub_seed + current + sibling, self.n)
current_idx >>= 1
return current
class KyberKEM:
def __init__(self, security_level: SecurityLevel):
self.security_level = security_level
self.params = self._get_parameters(security_level)
self.rng = SecureRandom()
self.gaussian = GaussianSampler(self.params.eta1)
self.xmss = XMSS(32, self.params.xmss_height, self.params.wots_w)
def _get_parameters(self, level: SecurityLevel) -> CryptoParameters:
if level == SecurityLevel.NIST_1:
return CryptoParameters(
n=256, q=3329, k=2, eta1=3, eta2=2, du=10, dv=4,
noise_bound=6.0, xmss_height=10, wots_w=16, wots_len=67,
poly_bytes=384, secret_key_bytes=1632, public_key_bytes=800,
ciphertext_bytes=768
)
elif level == SecurityLevel.NIST_3:
return CryptoParameters(
n=256, q=3329, k=3, eta1=2, eta2=2, du=10, dv=4,
noise_bound=4.0, xmss_height=12, wots_w=16, wots_len=67,
poly_bytes=384, secret_key_bytes=2400, public_key_bytes=1184,
ciphertext_bytes=1088
)
else:
return CryptoParameters(
n=256, q=3329, k=4, eta1=2, eta2=2, du=11, dv=5,
noise_bound=4.0, xmss_height=14, wots_w=16, wots_len=67,
poly_bytes=384, secret_key_bytes=3168, public_key_bytes=1568,
ciphertext_bytes=1568
)
def _sample_polynomial(self, seed: bytes, nonce: int, eta: int) -> Polynomial:
gaussian = GaussianSampler(eta)
coeffs = gaussian.sample_vector(self.params.n)
return Polynomial(coeffs, self.params.q)
def _sample_matrix(self, seed: bytes, k: int) -> PolynomialMatrix:
matrix = []
for i in range(k):
row = []
for j in range(k):
poly_seed = seed + struct.pack('>BB', i, j)
expanded = shake256(poly_seed, self.params.n * 3)
coeffs = []
idx = 0
while len(coeffs) < self.params.n and idx < len(expanded) - 2:
coeff = int.from_bytes(expanded[idx:idx+2], 'little')
if coeff < self.params.q:
coeffs.append(coeff)
idx += 1
while len(coeffs) < self.params.n:
coeffs.append(0)
row.append(Polynomial(np.array(coeffs[:self.params.n], dtype=np.int32), self.params.q))
matrix.append(row)
return PolynomialMatrix(matrix)
def keygen(self) -> Tuple[bytes, bytes]:
seed = self.rng.bytes(32)
pk_seed, sk_seed = seed[:16], seed[16:]
nonce = 0
A = self._sample_matrix(pk_seed, self.params.k)
s_polys = []
for i in range(self.params.k):
s_polys.append(self._sample_polynomial(sk_seed, nonce, self.params.eta1))
nonce += 1
e_polys = []
for i in range(self.params.k):
e_polys.append(self._sample_polynomial(sk_seed, nonce, self.params.eta1))
nonce += 1
s = PolynomialVector(s_polys)
e = PolynomialVector(e_polys)
t = A.multiply_vector(s) + e
xmss_pk, xmss_sk = self.xmss.keygen()
pk_data = {
't': base64.b64encode(t.to_bytes()).decode(),
'rho': base64.b64encode(pk_seed).decode(),
'xmss_pk': base64.b64encode(xmss_pk).decode(),
'params': {
'n': self.params.n,
'q': self.params.q,
'k': self.params.k,
'security_level': self.security_level.value
}
}
sk_data = {
's': base64.b64encode(s.to_bytes()).decode(),
't': base64.b64encode(t.to_bytes()).decode(),
'rho': base64.b64encode(pk_seed).decode(),
'xmss_sk': base64.b64encode(xmss_sk).decode(),
'z': base64.b64encode(shake256(t.to_bytes(), 32)).decode(),
'params': pk_data['params']
}
return (json.dumps(pk_data).encode(), json.dumps(sk_data).encode())
def encaps(self, pk: bytes) -> Tuple[bytes, bytes]:
pk_data = json.loads(pk)
t = PolynomialVector.from_bytes(
base64.b64decode(pk_data['t']),
self.params.k, self.params.n, self.params.q
)
rho = base64.b64decode(pk_data['rho'])
m = self.rng.bytes(32)
coins = shake256(m + shake256(pk, 32), 64)
A = self._sample_matrix(rho, self.params.k)
nonce = 0
r_polys = []
for i in range(self.params.k):
r_polys.append(self._sample_polynomial(coins[:32], nonce, self.params.eta1))
nonce += 1
e1_polys = []
for i in range(self.params.k):
e1_polys.append(self._sample_polynomial(coins[:32], nonce, self.params.eta2))
nonce += 1
e2 = self._sample_polynomial(coins[:32], nonce, self.params.eta2)
r = PolynomialVector(r_polys)
e1 = PolynomialVector(e1_polys)
u = A.multiply_vector(r) + e1
v = t.dot(r) + e2
m_coeffs = np.zeros(self.params.n, dtype=np.int32)
for i in range(min(32, self.params.n)):
if i < len(m):
m_coeffs[i] = m[i] * (self.params.q // 256)
m_poly = Polynomial(m_coeffs, self.params.q)
v = v + m_poly
u_compressed = u.compress(self.params.du)
v_compressed = v.compress(self.params.dv)
ct_data = {
'u': [base64.b64encode(comp.tobytes()).decode() for comp in u_compressed],
'v': base64.b64encode(v_compressed.tobytes()).decode(),
'params': pk_data['params']
}
ciphertext = json.dumps(ct_data).encode()
return (ciphertext, m)
def decaps(self, ciphertext: bytes, sk: bytes) -> bytes:
ct_data = json.loads(ciphertext)
sk_data = json.loads(sk)