derivepassphrase.git

1) # SPDX-FileCopyrightText: 2024 Marco Ricci <m@the13thletter.info>
2) #
3) # SPDX-License-Identifier: MIT
4) 
5) """A Python reimplementation of James Coglan's "sequin" Node.js module.
6) 
7) James Coglan's "sequin" Node.js module provides a pseudorandom number
8) generator (using rejection sampling on a stream of input numbers) that
9) attempts to minimize the amount of information it throws away:
10) (non-degenerate) rejected samples are fed into a stream of higher-order
11) numbers from which the next random number generation request will be
12) served.  The sequin module is used in Coglan's "vault" module (a
13) deterministic, stateless password manager that recomputes passwords
14) instead of storing them), and this reimplementation is used for
15) a similar purpose.
16) 
17) The main API is the [`Sequin`] [sequin.Sequin] class, which is
18) thoroughly documented.
19) 
20) """
21) 

22) # ruff: noqa: RUF002,RUF003
23) 

24) from __future__ import annotations
25) 
26) import collections

27) from typing import TYPE_CHECKING

28) 

29) from typing_extensions import assert_type

30) 

31) if TYPE_CHECKING:
32)     from collections.abc import Iterator, Sequence
33) 

34) __all__ = ('Sequin', 'SequinExhaustedError')

35) __author__ = 'Marco Ricci <m@the13thletter.info>'
36) __version__ = '0.1.1'
37) 

38) 
39) class Sequin:
40)     """Generate pseudorandom non-negative numbers in different ranges.
41) 
42)     Given a (presumed high-quality) uniformly random sequence of input
43)     bits, generate pseudorandom non-negative integers in a certain range
44)     on each call of the `generate` method.  (It is permissible to
45)     specify a different range per call to `generate`; this is the main
46)     use case.)  We use a modified version of rejection sampling, where
47)     rejected values are stored in "rejection queues" if possible, and
48)     these rejection queues re-seed the next round of rejection sampling.
49) 
50)     This is a Python reimplementation of James Coglan's [Node.js sequin
51)     module][JS_SEQUIN], as introduced in [his blog post][BLOG_POST].  It
52)     uses a [technique by Christian Lawson-Perfect][SEQUIN_TECHNIQUE].
53)     I do not know why the original module is called "sequin"; I presume
54)     it to be a pun on "sequence".
55) 
56)     [JS_SEQUIN]: https://www.npmjs.com/package/sequin
57)     [BLOG_POST]: https://blog.jcoglan.com/2012/07/16/designing-vaults-generator-algorithm/
58)     [SEQUIN_TECHNIQUE]: https://checkmyworking.com/2012/06/converting-a-stream-of-binary-digits-to-a-stream-of-base-n-digits/
59) 
60)     """

61) 

62)     def __init__(
63)         self,
64)         sequence: str | bytes | bytearray | Sequence[int],

65)         /,
66)         *,
67)         is_bitstring: bool = False,

68)     ):
69)         """Initialize the Sequin.
70) 
71)         Args:
72)             sequence:
73)                 A sequence of bits, or things convertible to bits, to
74)                 seed the pseudorandom number generator.  Byte and text
75)                 strings are converted to 8-bit integer sequences.
76)                 (Conversion will fail if the text string contains
77)                 non-ISO-8859-1 characters.)  The numbers are then
78)                 converted to bits.

79)             is_bitstring:
80)                 If true, treat the input as a bitstring.  By default,
81)                 the input is treated as a string of 8-bit integers, from
82)                 which the individual bits must still be extracted.
83) 
84)         Raises:
85)             ValueError:
86)                 The sequence contains values outside the permissible
87)                 range.

88) 
89)         """

90)         msg = 'sequence item out of range'

91) 

92)         def uint8_to_bits(value):
93)             """Yield individual bits of an 8-bit number, MSB first."""
94)             for i in (0x80, 0x40, 0x20, 0x10, 0x08, 0x04, 0x02, 0x01):
95)                 yield 1 if value | i == value else 0

96) 

97)         if isinstance(sequence, str):

98)             try:
99)                 sequence = tuple(sequence.encode('iso-8859-1'))
100)             except UnicodeError as e:

101)                 raise ValueError(msg) from e

102)         else:
103)             sequence = tuple(sequence)
104)         assert_type(sequence, tuple[int, ...])

105)         self.bases: dict[int, collections.deque[int]] = {}

106) 

107)         def gen() -> Iterator[int]:
108)             for num in sequence:
109)                 if num not in range(2 if is_bitstring else 256):

110)                     raise ValueError(msg)

111)                 if is_bitstring:
112)                     yield num
113)                 else:
114)                     yield from uint8_to_bits(num)

115) 

116)         self.bases[2] = collections.deque(gen())

117) 
118)     def _all_or_nothing_shift(
119)         self, count: int, /, *, base: int = 2
120)     ) -> Sequence[int]:
121)         """Shift and return items if and only if there are enough.
122) 
123)         Args:
124)             count: Number of items to shift/consume.
125)             base: Use the base `base` sequence.
126) 
127)         Returns:
128)             If there are sufficient items in the sequence left, then
129)             consume them from the sequence and return them.  Otherwise,
130)             consume nothing, and return nothing.
131) 
132)         Notes:
133)             We currently remove now-empty sequences from the registry of
134)             sequences.
135) 
136)         Examples:

137)             >>> seq = Sequin([1, 0, 1, 0, 0, 1, 0, 0, 0, 1], is_bitstring=True)

138)             >>> seq.bases
139)             {2: deque([1, 0, 1, 0, 0, 1, 0, 0, 0, 1])}
140)             >>> seq._all_or_nothing_shift(3)
141)             (1, 0, 1)
142)             >>> seq._all_or_nothing_shift(3)
143)             (0, 0, 1)
144)             >>> seq.bases[2]
145)             deque([0, 0, 0, 1])
146)             >>> seq._all_or_nothing_shift(5)
147)             ()
148)             >>> seq.bases[2]
149)             deque([0, 0, 0, 1])
150)             >>> seq._all_or_nothing_shift(4)
151)             (0, 0, 0, 1)
152)             >>> 2 in seq.bases  # now-empty sequences are removed
153)             False
154) 
155)         """
156)         try:
157)             seq = self.bases[base]
158)         except KeyError:
159)             return ()

160)         stash: collections.deque[int] = collections.deque()
161)         try:

162)             for _ in range(count):

163)                 stash.append(seq.popleft())
164)         except IndexError:
165)             seq.extendleft(reversed(stash))

166)             return ()

167)         # Clean up queues.
168)         if not seq:
169)             del self.bases[base]
170)         return tuple(stash)

171) 
172)     @staticmethod

173)     def _big_endian_number(digits: Sequence[int], /, *, base: int = 2) -> int:

174)         """Evaluate the given integer sequence as a big endian number.
175) 
176)         Args:
177)             digits: A sequence of integers to evaluate.
178)             base: The number base to evaluate those integers in.
179) 
180)         Raises:
181)             ValueError: `base` is an invalid base.
182)             ValueError: Not all integers are valid base `base` digits.
183) 
184)         Examples:
185)             >>> Sequin._big_endian_number([1, 2, 3, 4, 5, 6, 7, 8], base=10)
186)             12345678

187)             >>> Sequin._big_endian_number([1, 2, 3, 4, 5, 6, 7, 8], base=100)
188)             102030405060708

189)             >>> Sequin._big_endian_number([0, 0, 0, 0, 1, 4, 9, 7], base=10)
190)             1497
191)             >>> Sequin._big_endian_number([1, 0, 0, 1, 0, 0, 0, 0], base=2)
192)             144
193)             >>> Sequin._big_endian_number([1, 7, 5, 5], base=8) == 0o1755
194)             True
195) 
196)         """

197)         if base < 2:  # noqa: PLR2004
198)             msg = f'invalid base: {base!r}'
199)             raise ValueError(msg)

200)         ret = 0
201)         allowed_range = range(base)
202)         n = len(digits)
203)         for i in range(n):
204)             i2 = (n - 1) - i
205)             x = digits[i]
206)             if not isinstance(x, int):

207)                 msg = f'not an integer: {x!r}'
208)                 raise TypeError(msg)

209)             if x not in allowed_range:

210)                 msg = f'invalid base {base!r} digit: {x!r}'
211)                 raise ValueError(msg)

212)             ret += (base**i2) * x

213)         return ret
214) 
215)     def generate(self, n: int, /) -> int:
216)         """Generate a base `n` non-negative integer.
217) 
218)         We attempt to generate a value using rejection sampling.  If the
219)         generated sample is outside the desired range (i.e., is
220)         rejected), then attempt to reuse the sample by seeding
221)         a "higher-order" input sequence of uniformly random numbers (for
222)         a different base).
223) 
224)         Args:
225)             n:
226)                 Generate numbers in the range 0, ..., `n` - 1.

227)                 (Inclusive.)  Must be larger than 0.

228) 
229)         Returns:
230)             A pseudorandom number in the range 0, ..., `n` - 1.
231) 
232)         Raises:

233)             ValueError:
234)                 The range is empty.

235)             SequinExhaustedError:

236)                 The sequin is exhausted.
237) 

238)         Examples:

239)             >>> seq = Sequin(
240)             ...     [1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1],
241)             ...     is_bitstring=True,
242)             ... )
243)             >>> seq2 = Sequin(
244)             ...     [1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1],
245)             ...     is_bitstring=True,
246)             ... )

247)             >>> seq.generate(5)
248)             3
249)             >>> seq.generate(5)
250)             3
251)             >>> seq.generate(5)
252)             1

253)             >>> seq.generate(5)  # doctest: +IGNORE_EXCEPTION_DETAIL

254)             Traceback (most recent call last):
255)                 ...

256)             SequinExhaustedError: Sequin is exhausted

257) 
258)             Using `n = 1` does not actually consume input bits:
259) 
260)             >>> seq2.generate(1)
261)             0
262) 
263)             But it still won't work on exhausted sequins:
264) 

265)             >>> seq.generate(1)  # doctest: +IGNORE_EXCEPTION_DETAIL

266)             Traceback (most recent call last):
267)                 ...

268)             SequinExhaustedError: Sequin is exhausted

269) 

270)         """

271)         if 2 not in self.bases:  # noqa: PLR2004
272)             raise SequinExhaustedError

273)         value = self._generate_inner(n, base=2)
274)         if value == n:

275)             raise SequinExhaustedError

276)         return value
277) 

278)     def _generate_inner(self, n: int, /, *, base: int = 2) -> int:

279)         """Recursive call to generate a base `n` non-negative integer.
280) 
281)         We first determine the correct exponent `k` to generate base `n`
282)         numbers from a stream of base `base` numbers, then attempt to
283)         take `k` numbers from the base `base` sequence (or bail if not
284)         possible).  If the resulting number `v` is out of range for
285)         base `n`, then push `v - n` onto the rejection queue for
286)         base `r` = `base` ** `k` - `n`, and attempt to generate the
287)         requested base `n` integer from the sequence of base `r` numbers
288)         next.  (This recursion is not attempted if `r` = 1.)  Otherwise,
289)         return the number.
290) 
291)         Args:
292)             n:
293)                 Generate numbers in the range 0, ..., `n` - 1.

294)                 (Inclusive.)  Must be larger than 0.

295)             base:
296)                 Use the base `base` sequence as a source for
297)                 pseudorandom numbers.
298) 
299)         Returns:
300)             A pseudorandom number in the range 0, ..., `n` - 1 if
301)             possible, or `n` if the stream is exhausted.
302) 

303)         Raises:
304)             ValueError:
305)                 The range is empty.
306) 

307)         Examples:

308)             >>> seq = Sequin(
309)             ...     [1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1],
310)             ...     is_bitstring=True,
311)             ... )
312)             >>> seq2 = Sequin(
313)             ...     [1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1],
314)             ...     is_bitstring=True,
315)             ... )

316)             >>> seq._generate_inner(5)
317)             3
318)             >>> seq._generate_inner(5)
319)             3
320)             >>> seq._generate_inner(5)
321)             1
322)             >>> seq._generate_inner(5)  # error condition: sequin exhausted
323)             5
324) 
325)             Using `n = 1` does not actually consume input bits, and
326)             always works, regardless of sequin exhaustion:
327) 
328)             >>> seq2._generate_inner(1)
329)             0
330)             >>> seq._generate_inner(1)
331)             0
332) 
333)             Using an unsuitable range will raise:
334) 

335)             >>> seq2._generate_inner(0)  # doctest: +IGNORE_EXCEPTION_DETAIL

336)             Traceback (most recent call last):
337)                 ...
338)             ValueError: invalid target range
339) 

340)         """

341)         if n < 1:

342)             msg = 'invalid target range'
343)             raise ValueError(msg)
344)         if base < 2:  # noqa: PLR2004
345)             msg = f'invalid base: {base!r}'
346)             raise ValueError(msg)

347)         # p = base ** k, where k is the smallest integer such that
348)         # p >= n.  We determine p and k inductively.
349)         p = 1
350)         k = 0
351)         while p < n:
352)             p *= base
353)             k += 1
354)         # The remainder r of p and n is used as the base for rejection
355)         # queue.
356)         r = p - n
357)         # The generated number v is initialized to n because of the
358)         # while loop below.
359)         v = n
360)         while v > n - 1:
361)             list_slice = self._all_or_nothing_shift(k, base=base)
362)             if not list_slice:

363)                 if n != 1:
364)                     return n

365)                 v = 0

366)             v = self._big_endian_number(list_slice, base=base)
367)             if v > n - 1:
368)                 # If r is 0, then p == n, so v < n, or rather
369)                 # v <= n - 1.
370)                 assert r > 0
371)                 if r == 1:
372)                     continue
373)                 self._stash(v - n, base=r)
374)                 v = self._generate_inner(n, base=r)
375)         return v
376) 
377)     def _stash(self, value: int, /, *, base: int = 2) -> None:
378)         """Stash `value` on the base `base` sequence."""
379)         if base not in self.bases:
380)             self.bases[base] = collections.deque()
381)         self.bases[base].append(value)
382) 

383) 

384) class SequinExhaustedError(Exception):

385)     """The sequin is exhausted.
386) 
387)     No more values can be generated from this sequin.
388) 
389)     """

390)