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Commit 2f860b0

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Implement offsetting to previous internal states
1 parent 2ed391e commit 2f860b0

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4 files changed

+143
-9
lines changed

4 files changed

+143
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lines changed

‎README.md‎

Lines changed: 31 additions & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -27,7 +27,7 @@ This cracker works as the following way. It obtains first 624 32 bit numbers fro
2727
It is **important to feed cracker exactly 32-bit integers** generated by the generator due to the fact that they will be generated anyway, but dropped if you don't request for them.
2828
As well, you must feed the cracker exactly after new seed is presented, or after 624*32 bits are generated since every 624 32-bit numbers generator shifts it's state and cracker is designed to be fed from the begining of some state.
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30-
#### Implemented methods
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### Implemented methods
3131

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Cracker has one method for feeding: `submit(n)`. After submitting 624 integers it won't take any more and will be ready for predicting new numbers.
3333

@@ -54,3 +54,33 @@ print("Random result: {}\nCracker result: {}"
5454
Random result: 127160928
5555
Cracker result: 127160928
5656
```
57+
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As well as predicting future values, it can recover the *previous* states to predict earlier values, ones that came before the numbers you submit. After having submitted enough random numbers to clone the internal state (624), you can use the `offset(n)` method to offset the state by some number.
59+
60+
A positive number simply advances the RNG by `n`, as if you would ask for a number repeatedly `n` times. A **negative** number however will *untwist* the internal state (which can also be done manually with `untwist()`). Then after untwisting enough times it will set the internal state to exactly the point in the past where previous numbers were generated from. From then on, you can call the `predict_*()` methods again to get random numbers, now in the past.
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```python
63+
import random, time
64+
from randcrack import RandCrack
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66+
random.seed(time.time())
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unknown = [random.getrandbits(32) for _ in range(10)]
69+
70+
cracker = RandCrack()
71+
72+
for _ in range(624):
73+
cracker.submit(random.getrandbits(32))
74+
75+
cracker.offset(-624) # Go back -624 states from submitted numbers
76+
cracker.offset(-10) # Go back -10 states to the start of `unknown`
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print("Unknown:", unknown)
79+
print("Guesses:", [cracker.predict_getrandbits(32) for _ in range(10)])
80+
```
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> **Warning**: The `randint()`, `randrange()` and `choice()` methods all use `randbelow(n)`, which will internally may advance the state **multiple times** depending on the random number that comes from the generator. A number is generated with the number of bits `n` has, but it may still be above `n` the first time. In that case numbers keep being generated in this way until one is below `n`.
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>
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> This causes predicting **previous** values of these functions to become imprecise as it is not yet known how many numbers were generated with the single function call. You will still be able to generate all the numbers if you offset back further than expected to include all numbers, but there will be an amount of numbers before/after the target sequence (e.g. if the sequence is `[1, 2, 3]`, guesses may be `[123, 42, 1, 2, 3, 1337]`).
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>
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> This is not a problem with the `getrandbits()` method, as it always does exactly 1. And the `random()` method always does exactly 2

‎randcrack/randcrack.py‎

Lines changed: 46 additions & 2 deletions
Original file line numberDiff line numberDiff line change
@@ -211,6 +211,37 @@ def _regen(self):
211211

212212
self.counter = 0
213213

214+
def untwist(self):
215+
w, n, m = 32, 624, 397
216+
a = 0x9908B0DF
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# I like bitshifting more than these custom functions...
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MT = [self._to_int(x) for x in self.mt]
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for i in range(n-1, -1, -1):
222+
result = 0
223+
tmp = MT[i]
224+
tmp ^= MT[(i + m) % n]
225+
if tmp & (1 << w-1):
226+
tmp ^= a
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result = (tmp << 1) & (1 << w-1)
228+
tmp = MT[(i - 1 + n) % n]
229+
tmp ^= MT[(i + m-1) % n]
230+
if tmp & (1 << w-1):
231+
tmp ^= a
232+
result |= 1
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result |= (tmp << 1) & ((1 << w-1) - 1)
234+
MT[i] = result
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self.mt = [self._to_bitarray(x) for x in MT]
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def offset(self, n):
239+
if n >= 0:
240+
[self._predict_32() for _ in range(n)]
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else:
242+
[self.untwist() for _ in range(-n // 624 + 1)]
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[self._predict_32() for _ in range(624 - (-n % 624))]
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214245

215246
if __name__ == "__main__":
216247
import random
@@ -222,8 +253,21 @@ def _regen(self):
222253

223254
random.seed(time.time())
224255

256+
unknown = [random.getrandbits(32) for _ in range(1000)]
257+
225258
for i in range(624):
226259
cracker.submit(random.randint(0, 4294967294))
227260

228-
print("Guessing next 32000 random bits success rate: {}%"
229-
.format(sum([random.getrandbits(32) == cracker.predict_getrandbits(32) for x in range(1000)]) / 10))
261+
# Future values after syncing
262+
percentage = sum([random.getrandbits(32) == cracker.predict_getrandbits(32) for x in range(1000)]) / 10
263+
print(f"Guessing next 32000 random bits success rate: {percentage}%")
264+
assert percentage == 100
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# Previous values
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cracker.offset(-1000) # From guessing future
268+
cracker.offset(-624) # From submitting
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cracker.offset(-1000) # Back to start of unknown
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271+
percentage = sum([unknown[i] == cracker.predict_getrandbits(32) for i in range(1000)]) / 10
272+
print(f"Guessing previous 32000 random bits success rate: {percentage}%")
273+
assert percentage == 100

‎randcrack/test.py‎

Lines changed: 18 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -0,0 +1,18 @@
1+
import random
2+
import time
3+
from randcrack import RandCrack
4+
5+
random.seed(time.time())
6+
7+
unknown = [random.getrandbits(32) for _ in range(10)]
8+
9+
cracker = RandCrack()
10+
11+
for _ in range(624):
12+
cracker.submit(random.getrandbits(32))
13+
14+
cracker.offset(-624) # Go back -624 states from submitted numbers
15+
cracker.offset(-10) # Go back -10 states to the start of `unknown`
16+
17+
print("Unknown:", unknown)
18+
print("Guesses:", [cracker.predict_getrandbits(32) for _ in range(10)])

‎tests/test_randcrack.py‎

Lines changed: 48 additions & 6 deletions
Original file line numberDiff line numberDiff line change
@@ -11,7 +11,7 @@ def test_submit_not_enough():
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1212
cracker = RandCrack()
1313

14-
for i in range(623):
14+
for _ in range(623):
1515
cracker.submit(random.randint(0, 4294967294))
1616

1717
with pytest.raises(ValueError):
@@ -23,19 +23,19 @@ def test_submit_too_much():
2323

2424
cracker = RandCrack()
2525

26-
for i in range(624):
26+
for _ in range(624):
2727
cracker.submit(random.randint(0, 4294967294))
2828

2929
with pytest.raises(ValueError):
30-
cracker.submit(random.randint(0, 4294967294))
30+
cracker.submit(random.getrandbits(32))
3131

3232

3333
def test_predict_first_624():
3434
random.seed(time.time())
3535

3636
cracker = RandCrack()
3737

38-
for i in range(624):
38+
for _ in range(624):
3939
cracker.submit(random.randint(0, 4294967294))
4040

4141
assert sum([random.getrandbits(32) == cracker.predict_getrandbits(32) for _ in range(1000)]) == 1000
@@ -46,16 +46,58 @@ def test_predict_first_1000_close():
4646

4747
cracker = RandCrack()
4848

49-
for i in range(624):
49+
for _ in range(624):
5050
cracker.submit(random.randint(0, 4294967294))
5151

5252
assert sum([random.getrandbits(32) == cracker.predict_getrandbits(32) for _ in range(1000)]) == 1000
5353

54+
5455
def test_predict_random():
5556
random.seed(time.time())
5657

5758
cracker = RandCrack()
5859

59-
for i in range(624):
60+
for _ in range(624):
6061
cracker.submit(random.randint(0, 4294967294))
62+
6163
assert sum([random.random() == cracker.predict_random() for _ in range(1000)]) == 1000
64+
65+
66+
def test_predict_previous():
67+
random.seed(time.time())
68+
69+
unknown = [random.getrandbits(32) for _ in range(1000)]
70+
71+
cracker = RandCrack()
72+
73+
for _ in range(624):
74+
cracker.submit(random.getrandbits(32))
75+
76+
cracker.offset(-624)
77+
cracker.offset(-1000)
78+
79+
assert unknown == [cracker.predict_getrandbits(32) for _ in range(1000)]
80+
81+
82+
def test_predict_previous_randbelow():
83+
random.seed(time.time())
84+
85+
# randint() uses randbelow() internally
86+
unknown = [random.randint(1, 800) for _ in range(1000)]
87+
88+
cracker = RandCrack()
89+
90+
for _ in range(624):
91+
cracker.submit(random.getrandbits(32))
92+
93+
cracker.offset(-624)
94+
cracker.offset(-2000) # Go back too far to include everything
95+
96+
guesses = [cracker.predict_randint(1, 800) for _ in range(2000)]
97+
98+
def is_subseq(x, y):
99+
return all(any(c == ch for c in y) for ch in x)
100+
101+
# The sequence of unknown numbers should be in guesses, but there may be numbers before and after
102+
# (e.g. if the sequence is [1, 2, 3], guesses may be [123, 42, 1, 2, 3, 1337])
103+
assert is_subseq(unknown, guesses)

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