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…r eqaution is handled with care, small cosmetic changes + python 3 code
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Hi Laurent, thanks very much for your input. Much appreciated. :) Please allow some time for me to review this. Many thanks, Markus |
lucaselblanc
approved these changes
Jul 1, 2024
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Hello Markus,
Thanks for reviewing the PR. Though, I don't see the modifications on the
master branch. Did you merge the pull request ?
Regards,
Laurent
Le lun. 1 juil. 2024 à 02:59, No Clip Studio ***@***.***> a
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Thank you for this nice code.
I made some modifications to make the code work with any prime number p. The main idea is that Q = P-1 and that before solving the linear equation denum*x = num % Q, we must first calculate the gcd between denum, num and Q. If this gcd is equal to 1, it is good. Otherwise, solve (denum/thegcd) = (num/thegcd) mod (Q/thegcd) gives res0 and check all solutions of the form res0+k (Q/thegcd), for k in [0, thegcd[.
The code now works with Python 3.
I also use the package gmpy2 for the computation of the modular inverse and the gcd. This package can handle very large integers. If you want to avoid dependencies, you can put the extended Euclid algorithm in another file than pollard_rho.py for more clarity.
Finally, I made some cosmetic changes and added a test.py file with a non safe prime number.