--- layout: post title: 如何制作一个“完整”的博客压缩包？ tags: [压缩包, Quine, LZMA2, 7-Zip] --- 让AI做出真正的“完整”将不再是难事…… # 起因 在上次[用AI制作了各种东西](/2026/09/01/vibe-coding2.html)之后，我已经完全理解了AI确实是无所不能的。既然如此，那就让它帮我解决曾经未能解决的事情吧？ 去年，我为了让下载全站压缩包的按钮不断链，让这个压缩包也包含它本身而研究了[ZIP Quine](/2025/09/01/quine.html)，但限于DEFLATE的回溯窗口大小没能做到……但那是人做的东西，人还是太弱小了，现在换AI来试试，也许一切将变得不一样？ # 制作基于LZMA2的博客压缩包 首先，我把[Ruben Van Mello](https://github.com/ruvmello)写的那篇论文《[A Generator for Recursive Zip Files](https://www.mdpi.com/2076-3417/14/21/9797)》以及生成器[zip-quine-generator](https://github.com/ruvmello/zip-quine-generator)发给了AI，问它这个限制是不是真的，是不是真的无法创造出超过32KiB的ZIP Quine？没过多久它分析完了，告诉我确实存在这样的问题，但并不是无法解决的，最简单的办法就是换个回溯窗口更大的压缩算法。我看了一下它给我列出的几个算法，看起来LZMA2和zstd比较符合要求。不过zstd感觉不是很知名，一般的解压软件应该处理不了，所以我就选择让它基于LZMA2来制作了。 不过LZMA2只是算法，还得选个容器，考虑到7z算是最出名，而且LZMA2本来就是7-Zip的作者开发的，所以就直接让它做7z版本的了。另外因为[Nate Choe](https://github.com/NateChoe1)做了通过扩展欧几里得求逆元来计算CRC32的[PR](https://github.com/ruvmello/zip-quine-generator/pull/3)，所以我也告诉它要用这种方法在多项式时间内解出CRC32的值，而不是爆破。就这样AI花了两个小时左右成功把代码写出来了，效果非常完美，另外它还偷懒地将计算CRC32的算法改成了高斯消元法😆，因为7z格式有3个相互影响的CRC32值，用扩展欧几里得会更复杂一点，不过对7z来说不写入文件的CRC32也不影响，只是会不校验罢了，至少它还是按我要求做了……但其实这个问题也并不是完全不能用扩展欧几里得算法，后来我又强烈要求了一下，AI还是给我写出来了。以下是代码片段，有兴趣的人可以参考一下（不过这个看起来写的就是很复杂，所以我自己只用了高斯消元法）： ```python RU_POLY = 0x104C11DB7 # x^32+x^26+x^23+...+1（含 x^32 首项） def _find_probe(p): ret = 0 for i in range(64): if (1 << i) & p: ret = i return ret def _mul_raw(p1, p2): """多项式乘法（无模）。""" ret = 0 probe = _find_probe(p1) for i in range(64): if p2 & (1 << i): assert probe + i < 64, "多项式乘法溢出" ret ^= p1 << i return ret def _poly_divmod(dividend, divisor): """多项式长除法，返回 (商, 余)。""" probe = _find_probe(divisor) probe_bit = 1 << probe quot = 0 rem = dividend for i in range(63 - probe, -1, -1): if rem & (probe_bit << i): quot |= 1 << i rem ^= divisor << i return quot, rem def _mul(p1, p2, mod): """p1*p2 % mod。""" return _poly_divmod(_mul_raw(p1, p2), mod)[1] def _xgcd(p1, p2): """扩展欧几里得：返回 (k1,k2,gcd)，满足 p1*k1+p2*k2=gcd。""" if _find_probe(p1) < _find_probe(p2): k1, k2, g = _xgcd(p2, p1) return k2, k1, g if p2 == 0: return p1, 0, p1 q, r = _poly_divmod(p1, p2) c1, c2, g = _xgcd(p2, r) return c2, c1 ^ _mul_raw(c2, q), g def _minv(p, mod): """p 在环上的乘法逆元；不存在时返回 0。""" k1, _, g = _xgcd(p, mod) if g != 1: return 0 return _poly_divmod(k1, mod)[1] def _bitrev32(x): """32 位比特反转。CRC 的输出循环冗余（binascii 反射）↔ 本环（非反射）互为 bit-reverse。""" return int(format(x & 0xFFFFFFFF, "032b")[::-1], 2) def _ring_pow_x(k): """环内 x^k mod P（P=RU_POLY），二进制幂 O(log k)。变量列就是单个环幂。""" res, base, mod, e = 1, 2, RU_POLY, k while e: if e & 1: res = _mul(res, base, mod) base = _mul(base, base, mod) e >>= 1 return res def solve_crc_system(files): """解析解 CRC 定点系统 - 常数列 ：对“变量清零”的数据做一次 binascii.crc32，再 bit-reverse 32 位 （binascii 反射 CRC 与本环非反射 CRC 互为 bit-reverse，见 _bitrev32）。 - 变量列 ：单个环幂 x^(32 + 8*(len-pos-4))，二进制幂 O(log N) 一步算出； 同一变量出现在多处时按位异或累加。 各自 O(#rows) 次 CRC + 少量环幂即可建出整矩阵，Gauss 消元不变。 """ n = len(files) mod = RU_POLY matrix = [[0] * (n + 1) for _ in range(n)] for file in range(n): data = files[file][0] offsets = files[file][1] N = len(data) zero = bytearray(data) for pos in offsets: # 未知量占 4 字节，清零后求常数项 zero[pos:pos + 4] = b"\x00\x00\x00\x00" matrix[file][n] = _bitrev32(crc32(bytes(zero))) for pos, vid in offsets.items(): rest = N - pos - 4 # 变量被 4 字节（x^32）+ 其后字节（x^8/个）推到底 matrix[file][vid] ^= _ring_pow_x(32 + 8 * rest) matrix[file][file] ^= 1 for sr in range(n): ex = sr while ex < n and matrix[ex][sr] == 0: ex += 1 if ex == n: raise RuntimeError("CRC 多项式系统奇异 @row%d" % sr) if ex != sr: matrix[sr], matrix[ex] = matrix[ex], matrix[sr] inv = _minv(matrix[sr][sr], mod) for er in range(sr + 1, n): mult = _mul(inv, matrix[er][sr], mod) for ec in range(n + 1): matrix[er][ec] ^= _mul(mult, matrix[sr][ec], mod) res = [0] * n for row in range(n - 1, -1, -1): v = matrix[row][n] for col in range(row + 1, n): v ^= _mul(res[col], matrix[row][col], mod) res[row] = _mul(v, _minv(matrix[row][row], mod), mod) return [_impl_val(res[i]) for i in range(n)] def _impl_val(math_val): imp = 0 for bit in range(32): if math_val & (1 << bit): imp |= 1 << (31 - bit) return imp class BlogQuine: def solve_crc(self, F, lay, seed): T, h, d = lay["T"], lay["h"], lay["d"] k, n_sub, crc_base = lay["k"], lay["n_sub"], lay["crc_base"] hoff = lay["total"] - h vout_f = lay["total"] - 2 * T hcopy = vout_f + (T - h) # 已知 CRC：seed + 各文件（quine 的是未知量 D） known = [crc32(seed)] + [crc32(data) for _, data in self.files] assert len(known) == n_sub - 1 for i, e in enumerate(known): struct.pack_into(" Show Code ```python #!/usr/bin/env python3 # -*- coding: utf-8 -*- import argparse import binascii import io import lzma import os import struct import sys import tarfile import time import ctypes import ctypes.util # ============================================================ # Part 1: 最小 LZMA1 range coder（只做编码） # ============================================================ kNumBitModelTotalBits = 11 kBitModelTotal = 1 << kNumBitModelTotalBits # 2048 kNumMoveBits = 5 kTopValue = 1 << 24 # 0x1000000 kNumStates = 12 kNumLitStates = 7 kNumPosBitsMax = 4 kNumLenToPosStates = 4 kNumAlignBits = 4 kEndPosModelIndex = 14 kNumFullDistances = 1 << (kEndPosModelIndex >> 1) # 128 kMatchMinLen = 2 kNumLowLenBits = 3 kNumMidLenBits = 3 kNumHighLenBits = 8 kNumLowLenSymbols = 1 << kNumLowLenBits # 8 kNumMidLenSymbols = 1 << kNumMidLenBits # 8 kNumPosSlotBits = 6 PROB_INIT = kBitModelTotal >> 1 # 1024 class RangeEncoder: """LZMA 的区间编码器。low 是 64 位（要容纳进位），range 是 32 位。""" def __init__(self): self.low = 0 self.range = 0xFFFFFFFF self.cache = 0 self.cache_size = 1 # 初值 1 -> 第一个输出字节恒为 0x00 self.buf = bytearray() def _shift_low(self): if (self.low & 0xFFFFFFFF) < 0xFF000000 or (self.low >> 32) != 0: temp = self.cache while True: self.buf.append((temp + (self.low >> 32)) & 0xFF) temp = 0xFF self.cache_size -= 1 if self.cache_size == 0: break self.cache = (self.low >> 24) & 0xFF self.cache_size += 1 self.low = ((self.low & 0xFFFFFFFF) << 8) & 0xFFFFFFFF def encode_bit(self, probs, idx, bit): p = probs[idx] bound = (self.range >> kNumBitModelTotalBits) * p if bit == 0: self.range = bound probs[idx] = p + ((kBitModelTotal - p) >> kNumMoveBits) else: self.low += bound self.range -= bound probs[idx] = p - (p >> kNumMoveBits) while self.range < kTopValue: self.range = (self.range << 8) & 0xFFFFFFFF self._shift_low() def encode_direct_bits(self, value, num_bits): for i in range(num_bits - 1, -1, -1): self.range >>= 1 if (value >> i) & 1: self.low += self.range while self.range < kTopValue: self.range = (self.range << 8) & 0xFFFFFFFF self._shift_low() def bittree_encode(self, probs, off, num_bits, symbol): m = 1 for i in range(num_bits - 1, -1, -1): bit = (symbol >> i) & 1 self.encode_bit(probs, off + m, bit) m = (m << 1) | bit def bittree_reverse_encode(self, probs, off, num_bits, symbol): m = 1 for i in range(num_bits): bit = symbol & 1 symbol >>= 1 self.encode_bit(probs, off + m, bit) m = (m << 1) | bit def finish(self): for _ in range(5): self._shift_low() return bytes(self.buf) def _pos_slot_and_bits(d): if d < 4: return d, 0, 0 for slot in range(4, 64): n = (slot >> 1) - 1 base = (2 | (slot & 1)) << n if d < base + (1 << n): return slot, n, d - base raise ValueError("distance too large: %d" % d) # pb 必须与写进每个 LZMA2 chunk 头的 PROPS_BYTE(0x5D) 一致。 # lc/lp 只影响 literal 编码的概率表索引，而本编码器不实现 literal 路径，故无需常量。 PB = 2 class LzmaEncoder: """只实现 quine 用到的两条路径：match 与 rep0-match。 literal / rep-g1 / rep-g2 三条分支从未被构造，因此它们对应的概率表 （p_lit、p_is_rep_g1、p_is_rep_g2）以及 prev_byte 都不必存在。 reps 同理：编码器从不回读（rep0 的距离由解码器自行维护），故不保存。 """ def __init__(self): self.pos_mask = (1 << PB) - 1 self.rc = RangeEncoder() self.pos = 0 self.state = 0 n = PROB_INIT self.p_is_match = [n] * (kNumStates << kNumPosBitsMax) self.p_is_rep = [n] * kNumStates self.p_is_rep_g0 = [n] * kNumStates self.p_rep0_long = [n] * (kNumStates << kNumPosBitsMax) self.p_pos_slot = [n] * (kNumLenToPosStates << kNumPosSlotBits) self.p_spec_pos = [n] * (kNumFullDistances - kEndPosModelIndex) self.p_align = [n] * (1 << kNumAlignBits) self.p_len_choice = [n] * 2 self.p_len_low = [n] * (16 * kNumLowLenSymbols) self.p_len_mid = [n] * (16 * kNumMidLenSymbols) self.p_len_high = [n] * (1 << kNumHighLenBits) self.p_rep_len_choice = [n] * 2 self.p_rep_len_low = [n] * (16 * kNumLowLenSymbols) self.p_rep_len_mid = [n] * (16 * kNumMidLenSymbols) self.p_rep_len_high = [n] * (1 << kNumHighLenBits) @property def pos_state(self): return self.pos & self.pos_mask def _encode_len(self, choice, low, mid, high, length): ps = self.pos_state l = length - kMatchMinLen if l < kNumLowLenSymbols: self.rc.encode_bit(choice, 0, 0) self.rc.bittree_encode(low, ps << kNumLowLenBits, kNumLowLenBits, l) else: self.rc.encode_bit(choice, 0, 1) l -= kNumLowLenSymbols if l < kNumMidLenSymbols: self.rc.encode_bit(choice, 1, 0) self.rc.bittree_encode(mid, ps << kNumMidLenBits, kNumMidLenBits, l) else: self.rc.encode_bit(choice, 1, 1) self.rc.bittree_encode(high, 0, kNumHighLenBits, l - kNumMidLenSymbols) def _write_dist(self, dist, lts): d = dist - 1 slot, n, low_bits = _pos_slot_and_bits(d) self.rc.bittree_encode(self.p_pos_slot, lts << kNumPosSlotBits, kNumPosSlotBits, slot) if slot >= 4: if slot < kEndPosModelIndex: base = (2 | (slot & 1)) << n off = base - slot - 1 self.rc.bittree_reverse_encode(self.p_spec_pos, off, n, low_bits) else: self.rc.encode_direct_bits(low_bits >> kNumAlignBits, n - kNumAlignBits) self.rc.bittree_reverse_encode(self.p_align, 0, kNumAlignBits, low_bits & ((1 << kNumAlignBits) - 1)) def match(self, dist, length): assert kMatchMinLen <= length <= 273, length ps = self.pos_state self.rc.encode_bit(self.p_is_match, (self.state << kNumPosBitsMax) + ps, 1) self.rc.encode_bit(self.p_is_rep, self.state, 0) lts = min(length - kMatchMinLen, kNumLenToPosStates - 1) self._encode_len(self.p_len_choice, self.p_len_low, self.p_len_mid, self.p_len_high, length) self._write_dist(dist, lts) self.state = 7 if self.state < kNumLitStates else 10 self.pos += length def rep_match(self, length): assert kMatchMinLen <= length <= 273, length ps = self.pos_state self.rc.encode_bit(self.p_is_match, (self.state << kNumPosBitsMax) + ps, 1) self.rc.encode_bit(self.p_is_rep, self.state, 1) self.rc.encode_bit(self.p_is_rep_g0, self.state, 0) self.rc.encode_bit(self.p_rep0_long, (self.state << kNumPosBitsMax) + ps, 1) self._encode_len(self.p_rep_len_choice, self.p_rep_len_low, self.p_rep_len_mid, self.p_rep_len_high, length) self.state = 8 if self.state < kNumLitStates else 11 self.pos += length def finish(self): return self.rc.finish() # ============================================================ # Part 2: tar + xz 格式原语 # ============================================================ MAX_MATCH = 273 # LZMA1 单个 match 长度上限 CHUNK = 65536 # LZMA2 单 chunk 解压上限 PROPS_BYTE = 0x5D # lc=3, lp=0, pb=2 SEED_NOTE = ("\nMayx's Blog!").encode("utf-8") # xz 格式常量 XZ_MAGIC = b"\xFD7zXZ\x00" XZ_FOOTER_MAGIC = b"YZ" XZ_CHECK_CRC64 = 0x04 LZMA2_FILTER_ID = 0x21 CHECK_SIZE = 8 # CRC64 占 8 字节 _XZ_FLAGS = bytes([0x00, XZ_CHECK_CRC64]) # Stream Flags: reserved + check_type # tar 格式常量 TAR_BLOCK = 512 def round_up_512(n): """长度按 tar 块 512 字节向上取整。""" return (n + TAR_BLOCK - 1) // TAR_BLOCK * TAR_BLOCK def crc32(b): return binascii.crc32(b) & 0xFFFFFFFF # ---------- CRC64 (ECMA-182, reflected) ---------- _CRC64_POLY = 0xC96C5795D7870F42 # reflected ECMA-182 _CRC64_INIT = 0xFFFFFFFFFFFFFFFF _CRC64_XOROUT = 0xFFFFFFFFFFFFFFFF _CRC64_NON_REFLECTED = 0x142F0E1EBA9EA3693 # 非反射多项式 (65 bit) _CRC64_MOD_BIT = 1 << 64 # x^64 对应的 bit _liblzma = None try: _lzma_name = ctypes.util.find_library('lzma') if _lzma_name: _liblzma = ctypes.CDLL(_lzma_name) _liblzma.lzma_crc64.argtypes = [ctypes.c_char_p, ctypes.c_size_t, ctypes.c_uint64] _liblzma.lzma_crc64.restype = ctypes.c_uint64 # 验证：CRC64("123456789") 应为 0x995dc9bbdf1939fa if _liblzma.lzma_crc64(b'123456789', 9, 0) != 0x995dc9bbdf1939fa: _liblzma = None except (OSError, AttributeError): _liblzma = None def _make_crc64_table(): table = [] for i in range(256): crc = i for _ in range(8): crc = (crc >> 1) ^ _CRC64_POLY if (crc & 1) else crc >> 1 table.append(crc) return table _CRC64_TABLE = _make_crc64_table() def _crc64_pure(data): """纯 Python CRC64（ECMA-182 反射，init/xorout = 0xFFFF...FFFF）。""" crc = _CRC64_INIT for byte in data: crc = (crc >> 8) ^ _CRC64_TABLE[(crc ^ byte) & 0xFF] return crc ^ _CRC64_XOROUT def _crc64_lib(data): """liblzma CRC64（init=0，内部处理 init/xorout）。""" return _liblzma.lzma_crc64(data, len(data), 0) crc64 = _crc64_lib if _liblzma else _crc64_pure # ---------- GF(2^64) 多项式运算 ---------- # 用于 CRC64 自引用求解。CRC64 的线性贡献可表示为 # bit_reverse(contribution(D)) = D_poly * P (mod G_non) # 其中 D_poly = bit_reverse(D)，P 是位置决定的多项式。 # 方程 D_poly * (1 ^ P1 ^ P2) = bit_reverse(CRC64(W)) 通过多项式逆元求解。 def _bit_reverse64(v): r = 0 for _ in range(64): r = (r << 1) | (v & 1) v >>= 1 return r def _poly_mul_mod(a, b): """GF(2) 多项式乘法 mod G（非反射）。""" result = 0 while b: if b & 1: result ^= a b >>= 1 a <<= 1 if a & _CRC64_MOD_BIT: a ^= _CRC64_NON_REFLECTED return result def _poly_pow(base, exp): """多项式幂：base^exp mod G。""" result = 1 while exp: if exp & 1: result = _poly_mul_mod(result, base) base = _poly_mul_mod(base, base) exp >>= 1 return result def _poly_minv(p): """多项式逆元 p^(-1) mod G，用扩展欧几里得算法。""" if p == 0: return 0 old_r, r = p, _CRC64_NON_REFLECTED old_s, s = 1, 0 while r: # poly divmod(old_r, r) -> (q, rem) probe_r = r.bit_length() - 1 rem = old_r q = 0 while rem.bit_length() - 1 >= probe_r and rem: shift = rem.bit_length() - 1 - probe_r q |= 1 << shift rem ^= r << shift old_r, r = r, rem # s = old_s ^ q*s (raw 多项式乘法) prod = 0 a, b = q, s while b: if b & 1: prod ^= a b >>= 1 a <<= 1 old_s, s = s, old_s ^ prod if old_r != 1: return 0 # old_s mod G probe_m = _CRC64_NON_REFLECTED.bit_length() - 1 rem = old_s while rem.bit_length() - 1 >= probe_m and rem: shift = rem.bit_length() - 1 - probe_m rem ^= _CRC64_NON_REFLECTED << shift return rem def store_hdr(payload_len, first=False): """LZMA2 uncompressed chunk 头（3 字节，大端 size-1）。""" assert 1 <= payload_len <= 65536 return bytes([0x01 if first else 0x02]) + (payload_len - 1).to_bytes(2, "big") def matches_for(dist, total): """dist 固定、总长 total 的 token 序列：首个 match + 后续 rep0。""" assert total >= 2 toks = [] first = min(MAX_MATCH, total) if total - first == 1: first -= 1 toks.append(("m", dist, first)) total -= first while total > 0: l = min(MAX_MATCH, total) if total - l == 1: l -= 1 toks.append(("r0", l)) total -= l return toks def _add_gear(chunks, o, f, q): """追加一组标准 gear：store 载荷 x = slip+3，紧跟一个 lzma 把那 x 字节复制一遍。 lzma chunk 解压出的字节数正好等于 x，所以齿轮转完之后 slip (f - (o-q)) 精确 归约为 len(cb)（很小的正数，x 被 CHUNK 截断时则按 CHUNK 缩减）。 _layout_iterate 反复套用把 slip 压到 <= 16，_trim_layouts 用它做相位微调。 返回追加后的 (o, f)。 """ x = min(f - (o - q) + 3, CHUNK) chunks.append({"kind": "store", "foff": f, "size": 3 + x, "ooff": o, "olen": x}) o += x f += 3 + x cb, cu = lzma_chunk(matches_for(x, x), o) chunks.append({"kind": "lzma", "foff": f, "size": len(cb), "ooff": o, "olen": cu, "bytes": cb}) return o + cu, f + len(cb) def _forward_vac(F, vac, q): """vac_store：把紧随其后的等长字节块前移覆盖自身。""" fo = vac["ooff"] - q olen = vac["olen"] F[fo:fo + olen] = F[fo + olen:fo + 2 * olen] def dict_prop_for(maxdist): """选最小的 LZMA2 dict prop 使字典 >= maxdist。""" for p in range(41): if (2 | (p & 1)) << (p // 2 + 11) >= maxdist: return p, (2 | (p & 1)) << (p // 2 + 11) raise ValueError("distance too large") def lzma_chunk(tokens, out_pos): """编一个 LZMA chunk（0xC0: state+props reset，无 dict reset，无 end marker）。""" enc = LzmaEncoder() enc.pos = out_pos total = 0 for t in tokens: if t[0] == "m": enc.match(t[1], t[2]) total += t[2] else: enc.rep_match(t[1]) total += t[1] data = enc.finish() assert total - 1 < 65536 and len(data) - 1 < 65536 hdr = bytes([0xC0]) + (total - 1).to_bytes(2, "big") + \ (len(data) - 1).to_bytes(2, "big") + bytes([PROPS_BYTE]) return hdr + data, total # ---------- tar 原语 ---------- def tar_header(name, size, mtime, mode=0o644, typeflag=b'0', uid=0, gid=0): """构建 512 字节 POSIX ustar tar header。 注意：tar 数值字段包含 null 终止符，slice 范围必须精确匹配字段宽度。 mode/uid/gid 各 8 字节（7 octal + NUL），size/mtime 各 12 字节（11 octal + NUL）。 """ h = bytearray(512) name_bytes = name.encode('utf-8')[:100] h[0:len(name_bytes)] = name_bytes h[100:108] = b'%07o\x00' % mode # 8 bytes (field 100-107) h[108:116] = b'%07o\x00' % uid # 8 bytes (field 108-115) h[116:124] = b'%07o\x00' % gid # 8 bytes (field 116-123) h[124:136] = b'%011o\x00' % size # 12 bytes (field 124-135) h[136:148] = b'%011o\x00' % mtime # 12 bytes (field 136-147) h[148:156] = b' ' # checksum placeholder (8 spaces) h[156:157] = typeflag h[257:263] = b'ustar\x00' h[263:265] = b'00' assert len(h) == 512, "header length %d != 512" % len(h) # 计算校验和：所有字节之和，checksum 字段视为空格 chksum = sum(h) & 0o7777777 h[148:156] = b'%06o\x00 ' % chksum # 6 octal + NUL + space = 8 bytes assert len(h) == 512, "header length %d != 512 after checksum" % len(h) return bytes(h) # ---------- xz 原语 ---------- def xz_varint(v): """xz 变长整数编码：每字节 7 位数据（LSB first），MSB 为续位。""" b = [] while v >= 0x80: b.append((v & 0x7F) | 0x80) v >>= 7 b.append(v & 0x7F) return bytes(b) def xz_stream_header(): """12 字节 xz stream header (CHECK_CRC64)。 Stream Flags = [reserved(0x00), check_type(CRC64=0x04)]。 """ flags = _XZ_FLAGS crc = crc32(flags) return XZ_MAGIC + flags + struct.pack(' data 映射，避免下面三处按 rel 回头线性搜索整个 files 列表 self.file_map = dict(self.files) self.dirs = [r for r, isd in self.walk_entries if isd] self.content = b"".join(data for _, data in self.files) def _prefixed(self, rel): return self.src_dir + "/" + rel if self.src_dir else rel def tar_entries(self, d_seed, xz_size): """计算 tar 归档中每个条目的 (header, data_size, is_dir)。 顺序：seed, walk_entries (interleaved files+dirs), quine。 """ entries = [] # seed 文件 seed_hdr = tar_header(self.seed_name, d_seed, self.mtime) entries.append({"name": self.seed_name, "hdr": seed_hdr, "data_size": d_seed, "is_dir": False}) # walk 顺序的文件和目录 for rel, isd in self.walk_entries: if isd: hdr = tar_header(rel, 0, self.mtime, mode=0o755, typeflag=b'5') entries.append({"name": rel, "hdr": hdr, "data_size": 0, "is_dir": True}) else: # file_map 与 walk_entries 在 __init__ 里同步构造，这里必有 data = self.file_map[rel] entries.append({"name": rel, "hdr": tar_header(rel, len(data), self.mtime), "data_size": len(data), "is_dir": False}) # quine 文件（放在最后） qhdr = tar_header(self.quine_name, xz_size, self.mtime) entries.append({"name": self.quine_name, "hdr": qhdr, "data_size": xz_size, "is_dir": False}) return entries # ---------- 结构计算 ---------- def _compute_q(self, d_seed): """计算 xz_bytes 在 tar 中的偏移 q。 q = seed + files + dirs 的 tar 占用 + quine tar header。 q 不依赖 xz_size（quine 的 data 在 q 之后）。""" q = 0 # seed 文件 q += TAR_BLOCK # seed tar header q += round_up_512(d_seed) # seed data + pad # walk 顺序的文件和目录 for rel, isd in self.walk_entries: q += TAR_BLOCK # tar header if not isd: q += round_up_512(len(self.file_map[rel])) # quine tar header q += TAR_BLOCK return q def _trim_layouts(self, base, o_g, f_g, q, w_plant_off, d_seed): """枚举 trim 配置，产出一批「相位」不同的候选布局。 trim = [可选的裸 store chunk，载荷长度 x0] + 一组标准 gear （store 载荷 x = s+3，紧接着一个 lzma 复制这 x 字节）。 裸 store 把 slip 抬高 3、把 f 抬高 3+x0；随后这组 gear 把 slip 重新归一到 len(cb)，jump 再归一到 -3。净效果是 (o_pre, f_pre) 被整体平移 δ ≈ s_g + 6 + len(cb) + 3 + x0，而 δ 决定了自洽方程的模 4 相位。 旧实现 δ 恒为 0，相位一旦不对就永远无解 —— 而 d_seed += 1 根本不改变 布局（q 只在跨 512 字节块时才变），所以那 80 次重试是纯粹的无效空转。 注意：不能只插一个裸的 lzma 复制块。lzma 复制块的输出必须等于 F[o-q : o-q+olen]，而这只能靠前面那个「载荷 = F[o-q : o-q+x] 且 x = s+3」 的 store chunk 把字节搬到正确位置来实现；裸插复制块解压出来和 F 对不上。 返回 [(chunks, o_before_jump, f_before_jump, y, jb), ...]，按文件体积升序。 """ s_g = f_g - (o_g - q) out = [] seen = set() for x0 in range(0, s_g + 4): chunks = list(base) o, f = o_g, f_g if x0: # 裸 store：载荷 = F[o-q : o-q+x0]，要求 x0 <= s+3 以免读到尚未定稿的字节 chunks.append({"kind": "store", "foff": f, "size": 3 + x0, "ooff": o, "olen": x0}) o += x0 f += 3 + x0 o, f = _add_gear(chunks, o, f, q) # 一组标准 gear # jump 不动点：y = s + 3 + len(jb) s = f - (o - q) y = max(2, s + 17) jb = ju = None for _ in range(64): try: jb, ju = lzma_chunk([("m", o - w_plant_off, y)], o) except AssertionError: jb = None break y2 = s + 3 + len(jb) if y2 == y: break if y2 < 2 or y2 > 273: jb = None break y = y2 if jb is None or ju != y: continue if y + w_plant_off - TAR_BLOCK > d_seed: continue key = (o + y, f + len(jb)) if key in seen: continue seen.add(key) out.append((chunks, o, f, y, jb)) out.sort(key=lambda t: t[2] + len(t[4])) return out def _solve_gadget(self, chunks_pre, o_j, f_j, y, jb, q, bh, FEW, block_hdr, dict_size, hdrA, hdrB, d_seed, k): """在一个给定相位的布局上求解 gadget（T / gb / suffix / tz / k）。 关键简化：tz 只依赖 u = gb + suffix 与 k；T = u + tz + 4 也只依赖 (u, k)； 而 gb 又由 T 唯一确定（len(lzma_chunk(matches_for(T, T))))。 因此只需一维枚举 u 即可遍历全部解，既不漏解也远快于原来的三重暴力。 """ o_pre = o_j + y f_pre = f_j + len(jb) if f_pre != (o_pre - q) - 3: # jump 应把 slip 归一到 -3 return None chunks = list(chunks_pre) chunks.append({"kind": "lzma", "foff": f_j, "size": len(jb), "ooff": o_j, "olen": y, "bytes": jb, "jump": True}) best = None for u in range(8, 512): # 512k 必须落在 [f_pre + 2u + 2059, f_pre + 2u + 3595) lo = f_pre + 2 * u + 2059 hi = f_pre + 2 * u + 3595 for k_cand in range(max(1, (lo - 512) // 512), (hi + 512) // 512 + 2): num = k_cand * 512 - (o_pre + 2 * u + 8 - q - 1024) if num % 3 != 0: continue tz_cand = num // 3 if tz_cand < 1024: continue T = u + tz_cand + 4 if T < 2: continue gb, gu = lzma_chunk(matches_for(T, T), o_pre + T) gb_len = len(gb) suffix = u - gb_len if suffix < 1: continue # 精确自检（不再用带 9 字节偏差的预筛公式） f_final = f_pre + 3 + T + gb_len + 3 + tz_cand + 1 n = f_final - (12 + bh) bp = (4 - (12 + bh + n) % 4) % 4 unpadded = bh + n + CHECK_SIZE idx = xz_index([(unpadded, q + k_cand * 512 + 1024)]) ix = len(idx) suffix_actual = bp + CHECK_SIZE + ix + 12 if suffix_actual != suffix: continue xz_size = 12 + bh + n + bp + CHECK_SIZE + ix + 12 xz_pad_actual = round_up_512(xz_size) if xz_pad_actual != k_cand * 512: continue total_w_actual = q + xz_pad_actual + 1024 o_final = o_pre + 2 * T + tz_cand if o_final != total_w_actual: continue if best is not None and xz_size >= best["xz_size"]: continue # 已找到更小的解，跳过 backward_size = ix // 4 - 1 final = list(chunks) final.append({"kind": "store", "foff": f_pre, "size": 3 + T, "ooff": o_pre, "olen": T, "vac": True}) final.append({"kind": "lzma", "foff": f_pre + 3 + T, "size": gb_len, "ooff": o_pre + T, "olen": gu, "bytes": gb}) final.append({"kind": "store", "foff": f_pre + 3 + T + gb_len, "size": 3 + tz_cand, "ooff": o_pre + 2 * T, "olen": tz_cand, "trailing": True}) final.append({"kind": "term", "foff": f_pre + 3 + T + gb_len + 3 + tz_cand, "size": 1, "ooff": o_final, "olen": 0, "bytes": b"\x00"}) best = { "q": q, "d_seed": d_seed, "k": k, "chunks": final, "block_hdr": block_hdr, "bh": bh, "n": n, "xz_size": xz_size, "T": T, "suffix": suffix_actual, "bp": bp, "ix": ix, "dict_size": dict_size, "FEW": FEW, "hdrA": hdrA, "hdrB": hdrB, "jump_y": y, "index": idx, "stream_hdr": xz_stream_header(), "footer": xz_stream_footer(backward_size), "entries": self.tar_entries(d_seed, xz_size), } return best def _layout_iterate(self, d_seed, maxdist_hint): """核心布局。 阶段 1a：C1 / repro / gears（只依赖 q，所有 trim 配置共用，只算一次） 阶段 1b：插入 trim 微调块，平移 (o_pre, f_pre) 改变模 4 相位 阶段 2 ：按 u = gb + suffix 一维搜索自洽解 """ block_hdr, dict_size = xz_block_header(maxdist_hint) bh = len(block_hdr) FEW = 12 + bh + 3 w_hdrA_off = TAR_BLOCK + 12 + bh w_hdrB_off = TAR_BLOCK + 12 + bh + 3 w_plant_off = TAR_BLOCK + 12 + bh + 6 q = self._compute_q(d_seed) # ---------- 阶段 1a：C1 + repro + gears ---------- base = [] o, f = 0, 12 + bh Ls = [] rem = q + FEW while rem > CHUNK: Ls.append(CHUNK) rem -= CHUNK Ls.append(rem) assert Ls[-1] >= 2, "末 C1 chunk 载荷 %d 太小" % Ls[-1] k = len(Ls) hdrA = store_hdr(CHUNK, first=False) hdrB = store_hdr(Ls[-1], first=False) S = 0 for j, L in enumerate(Ls): base.append({"kind": "store", "foff": f, "size": 3 + L, "ooff": o, "olen": L, "first": j == 0, "c1": True, "S": S}) o += L f += 3 + L S += L assert o == q + FEW S = 0 for j, L in enumerate(Ls): if j > 0: srcpos = w_hdrA_off if (j < k - 1 or L == CHUNK) else w_hdrB_off dist_h = (q + FEW + S + 3 * (j - 1)) - srcpos hb, hu = lzma_chunk([("m", dist_h, 3)], o) base.append({"kind": "lzma", "foff": f, "size": len(hb), "ooff": o, "olen": hu, "bytes": hb}) o += hu f += len(hb) cb, cu = lzma_chunk(matches_for(q + FEW + 3 * j, L), o) base.append({"kind": "lzma", "foff": f, "size": len(cb), "ooff": o, "olen": cu, "bytes": cb}) o += cu f += len(cb) S += L # gears：把 slip 压到 <= 16 while f - (o - q) > 16: o, f = _add_gear(base, o, f, q) o_g, f_g = o, f # ---------- 阶段 1b + 阶段 2 ---------- # 相位按文件体积升序枚举；第一个成功的相位通常已经足够好，但不同相位的 # (u, tz) 不同，xz_size 仍可能相差几百字节，所以再多看几个取最小的。 tried = 0 best = None since_hit = 0 for chunks_pre, o_j, f_j, y, jb in self._trim_layouts( base, o_g, f_g, q, w_plant_off, d_seed): lay = self._solve_gadget(chunks_pre, o_j, f_j, y, jb, q, bh, FEW, block_hdr, dict_size, hdrA, hdrB, d_seed, k) tried += 1 if lay is not None and (best is None or lay["xz_size"] < best["xz_size"]): best = lay if best is not None: since_hit += 1 if since_hit >= 10: break elif tried >= 80: # 一直无解，放弃后续相位 break if best is not None: return best raise RuntimeError("layout 不收敛: 无自洽解 (q=%d, f_pre=%d, o_pre=%d)" % (q, f_g, o_g)) # ---------- 装配 ---------- def assemble(self, lay): """构建 xz 文件 F 和 seed。""" F = bytearray(lay["xz_size"]) q = lay["q"] d_seed = lay["d_seed"] bh = lay["bh"] FEW = lay["FEW"] # bytearray 已全零初始化：block padding、CRC64 占位、trailing-zero 载荷 # 都不必再显式写 0（后面几处赋值只会写到各自独立的区间，不会交叉覆盖）。 # pass A: 写 xz stream header + block header + 所有 chunk bytes + suffix F[0:12] = lay["stream_hdr"] F[12:12+bh] = lay["block_hdr"] jump_c = None for c in lay["chunks"]: if c["kind"] == "store": F[c["foff"]:c["foff"] + 3] = store_hdr(c["olen"], first=c.get("first", False)) else: F[c["foff"]:c["foff"] + c["size"]] = c["bytes"] if c.get("jump"): jump_c = c # block padding + CRC64(pass D 填) + index + footer bp_off = 12 + bh + lay["n"] ix_off = bp_off + lay["bp"] + CHECK_SIZE F[ix_off:ix_off + lay["ix"]] = lay["index"] sf_off = ix_off + lay["ix"] F[sf_off:sf_off + 12] = lay["footer"] assert jump_c is not None # pass B: 构建 seed y = lay["jump_y"] plant = bytes(F[jump_c["ooff"] - q: jump_c["ooff"] - q + y]) seed = bytearray(d_seed) seed[0:12] = lay["stream_hdr"] seed[12:12+bh] = lay["block_hdr"] seed[12+bh:12+bh+3] = lay["hdrA"] seed[12+bh+3:12+bh+6] = lay["hdrB"] seed[12+bh+6:12+bh+6+y] = plant pad = (SEED_NOTE * (d_seed // len(SEED_NOTE) + 2))[:d_seed - 12 - bh - 6 - y] seed[12+bh+6+y:] = pad # 构建 tar 前缀 T（含 seed data） T = self._build_tar_prefix_with_seed(lay, seed) F_prefix = bytes(F[0:FEW]) P = T + F_prefix assert len(P) == q + FEW, "P 长度 %d != q+FEW %d" % (len(P), q + FEW) # pass C: 填充 store payloads for c in lay["chunks"]: if c["kind"] != "store": continue ooff, olen = c["ooff"], c["olen"] if c.get("c1"): F[c["foff"] + 3:c["foff"] + 3 + olen] = P[c["S"]:c["S"] + olen] elif c.get("trailing"): # 载荷是尾部零：F 全零初始化，且唯一会写到 chunk 之外的 vac_store # 目标是 [f_pre+3, f_pre+3+T)（f_pre == (o_pre-q)-3 已由 _solve_gadget # 断言），与本区块不重叠，因此无需写入。 continue elif c.get("vac"): _forward_vac(F, c, q) else: # 其余 store 的载荷 = 输出流自身对应位置的字节（自引用复制） fo = ooff - q F[c["foff"] + 3:c["foff"] + 3 + olen] = F[fo:fo + olen] # pass D: 求解 CRC64 自引用 self._solve_crc64(F, lay, T) return bytes(F), bytes(seed) def _build_tar_prefix_with_seed(self, lay, seed): """构建 tar 前缀 T（含 seed data）。""" entries = lay["entries"] T = bytearray() for e in entries[:-1]: T += e["hdr"] if not e["is_dir"] and e["data_size"] > 0: data = seed if e["name"] == self.seed_name else self.file_map[e["name"]] T += data T += b'\x00' * (round_up_512(e["data_size"]) - e["data_size"]) T += entries[-1]["hdr"] # quine tar header return bytes(T) def _solve_crc64(self, F, lay, T_prefix): """求解 CRC64 自引用。 CRC64 值 D = CRC64(W)，W = T + F + 尾部零。 D 在 W 中出现两次：F 的 CRC64 字段 + vac_store 副本。 解法（多项式逆元）： CRC64 的线性贡献可表示为 GF(2^64) 多项式乘法： bit_reverse(contribution(D)) = D_poly * P (mod G) 其中 D_poly = bit_reverse(D)，P = x^(64+trailing) mod G。 方程 D_poly * (1 ^ P1 ^ P2) = bit_reverse(CRC64(W)) (mod G) 用扩展欧几里得求 (1 ^ P1 ^ P2) 的逆元，一步求解。 """ q = lay["q"] bh = lay["bh"] n = lay["n"] bp = lay["bp"] xz_size = lay["xz_size"] T = lay["T"] # CRC64 位置 1：在 F 中（block padding 后） crc_f_off = 12 + bh + n + bp crc_w1 = q + crc_f_off # CRC64 位置 2：vac_store 副本 crc_f_copy = crc_f_off - T crc_w2 = q + crc_f_copy # 构造 W = T + F + 尾部零（先把两处 CRC64 置 0） xz_pad = round_up_512(xz_size) tz = xz_pad - xz_size + 1024 W = bytearray(T_prefix) + F + b'\x00' * tz W[crc_w1:crc_w1 + CHECK_SIZE] = b'\x00' * CHECK_SIZE W[crc_w2:crc_w2 + CHECK_SIZE] = b'\x00' * CHECK_SIZE # CRC64(W) 的多项式表示 crc_poly = _bit_reverse64(crc64(bytes(W))) # P1 = x^(64 + 位置1之后的bit数) mod G trailing1 = (len(W) - crc_w1 - 8) * 8 P1 = _poly_pow(2, 64 + trailing1) # P2 = x^(64 + 位置2之后的bit数) mod G trailing2 = (len(W) - crc_w2 - 8) * 8 P2 = _poly_pow(2, 64 + trailing2) # D_poly = crc_poly * inv(1 ^ P1 ^ P2) coeff = 1 ^ P1 ^ P2 inv = _poly_minv(coeff) if inv == 0: raise RuntimeError("CRC64 多项式无逆元") D_poly = _poly_mul_mod(crc_poly, inv) D = _bit_reverse64(D_poly) # 写入 D 到 F 的 CRC64 位置 struct.pack_into(' 不过对我来说，相比于TXZ格式我还是更喜欢7z一点，一是因为LZMA2本来就是7-Zip的作者发明的，XZ感觉像是摘桃子的，二是TXZ这个名字听起来有点怪，感觉不像压缩包，三是XZ Utils出过后门，尽管整个Linux社区都在使用XZ，但是我还是稍微有点偏见，所以这份TXZ的生成器我就粘贴出来给需要的人吧，我博客用7z格式就好了。 # 感想 以前总是有人说AI没有创新能力，只是对曾经在网络上出现的东西进行重组，但人何尝不是这样呢？像这次制作的7z/TXZ Quine生成器在整个网络上没有任何公开信息，当然我也知道这并不是理论上的创新，但谁说组合创新不是创新呢？再看看最近OpenAI又解决了一大堆数学难题，完全可以相信AI是真的拥有智能，所以我相信总有一天AI将能完成人类能做的所有事情，人类将不再需要额外的思考，只需要做自己想做的事情吧。