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Why PRNGs are not the same as CSPRNGs
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import z3 | |
def sym_xoroshiro128plus(solver, sym_s0, sym_s1, mask, result): | |
s0 = sym_s0 | |
s1 = sym_s1 | |
sym_r = (sym_s0 + sym_s1) | |
condition = z3.Bool('c0x%0.16x' % result) | |
solver.add(z3.Implies(condition, (sym_r & mask) == result & mask)) | |
s1 ^= s0 | |
sym_s0 = z3.RotateLeft(s0, 55) ^ s1 ^ (s1 << 14) | |
sym_s1 = z3.RotateLeft(s1, 36) | |
return sym_s0, sym_s1, condition | |
def find_seed(results_with_masks): | |
start_s0, start_s1 = z3.BitVecs('start_s0 start_s1', 64) | |
sym_s0 = start_s0 | |
sym_s1 = start_s1 | |
solver = z3.Solver() | |
conditions = [] | |
for result, mask in results_with_masks: | |
sym_s0, sym_s1, condition = sym_xoroshiro128plus(solver, sym_s0, sym_s1, mask, result) | |
conditions.append(condition) | |
if solver.check(conditions) == z3.sat: | |
model = solver.model() | |
return (model[start_s0].as_long(), model[start_s1].as_long()) | |
else: | |
return None | |
find_seed([(0x0, 0x0), (0x206e6172614b2020, 0xffffffffffffffff), (0x2020736e6f794c, 0xffffffffffffff)]) | |
# Output: (12030599390342465081, 17190518429081885642) |
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def bin2chr(data): | |
result = '' | |
while data: | |
char = data & 0xff | |
result += chr(char) | |
data >>= 8 | |
return result | |
class Xoroshiro128Plus(object): | |
def __init__(self, seed): | |
self.seed = seed | |
@staticmethod | |
def rotl(x, k): | |
return ((x << k) & 0xffffffffffffffff) | (x >> 64 - k) | |
def next(self): | |
s0 = self.seed[0] | |
s1 = self.seed[1] | |
result = (s0 + s1) & 0xffffffffffffffff | |
s1 ^= s0 | |
self.seed[0] = self.rotl(s0, 55) ^ s1 ^ ((s1 << 14) & 0xffffffffffffffff) | |
self.seed[1] = self.rotl(s1, 36) | |
return result | |
generator = Xoroshiro128Plus([0xb4581c52b5a611f1, 0x849afd73bea7cce9]) | |
print(repr(''.join(bin2chr(generator.next()) for i in range(4)))) | |
# Output: 'ÚÞMtÆ\x19ó8 Karan Lyons 3A?â\x11)ÐÑ{' |
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