Comments (2)
That's correct! If p is unsafe, then ALL keys k are vulnerable to quick recovery using Pohlig-Hellman, even if the order of the generator g is large
from blog.
Thank you for your quickly reply. I have a few other questions I want to ask.
- I'm trying to implement a small subgroup attack, and I've been stuck in this for a few days. So, can you tell me how to implement a small subgroup attack with the small group defined by small prime factor?
- In your article : Hacking private keys from unsafe primes using the Pohlig-Hellman discrete logarithm. I can not understan this step:
> .\find-generator.ps1 -p 100000008359681
2^((100000008359681 - 1)/2) mod 100000008359681 = 1, rejecting 2
3^((100000008359681 - 1)/5) mod 100000008359681 = 1, rejecting 3
4^((100000008359681 - 1)/2) mod 100000008359681 = 1, rejecting 4
5^((100000008359681 - 1)/2) mod 100000008359681 = 1, rejecting 5
6 passes all checks
> $g = [bigint]::Parse("6")
> $g
6
why 3^((100000008359681 - 1)/5)
the divisor is 5
and other case the divisor is 2
? And there are general method to find the generator?
from blog.
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