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Library consisting of explanation and implementation of all the existing attacks on various Encryption Systems, Digital Signatures, Key Exchange, Authentication methods along with example challenges from CTFs

License: MIT License

Python 99.78% Shell 0.07% Dockerfile 0.15%
crypto ctf cryptography cryptanalysis ctf-tools ctf-challenges ctf-solutions

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amoniaka-knabino avatar ashutosh1206 avatar sayoojsamuel avatar

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crypton's Issues

False positives in non-prime-suborder elem generation in Small Subgroup Confinement

In the step-3 of Attack in Practice section of Small Subgroup Confinement Attack, we generate elements that produce subgroup order p1e1.

This method can generate false positives in cases where the order of subgroup to be generated is non-prime. For example: if we want to generate elements having subgroup order 23, the method can generate elements having subgroup order 2, 22 other than elements having subgroup order 23.

PoC (sagemath):

q = 919
Zq = Zmod(q)
group_order = q-1
print(group_order)
assert group_order % (3^3) == 0

subgroup_order = 3^3
exp = group_order/subgroup_order
nfalse_positives = 0
for i in range(10000):
    elem = Zq(randint(1, q-1))
    res = elem**exp
    if res != 1:
        order = res.multiplicative_order()
        if Integer(order) != sub_order:
            nfalse_positives += 1
print("False positives: ", str(nfalse_positives))

Thanks to Vara Prasad for finding this issue and the PoC

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