Discrete log problem over special primes

Sanu

2/12/24, 1:46 AM

I am trying to find discrete log over $GF(P)$ using Cado-NFS (https://gitlab.inria.fr/cado-nfs/cado-nfs/-/blob/master/README.dlp). It works well for random primes. But if I take primes that are divisor of numbers of the form $2^n-1$ for some positive integer $n$, it gives error. I use this in terminal:

./cado-nfs.py -dlp -ell factor of P-1 target=a P

I am getting error as follows:

Traceback (most recent call last):
  File "Prime_5.sage.py", line 245, in <module>
    y =  DLP(a,b, PRIME_FACTORS[j]) #gp.znlog(a, gp.Mod(b, PRIME_FACTORS[j])) #DLP(a,b, PRIME_FACTORS[j])
  File "Prime_5.sage.py", line 90, in DLP
    w = NFS(y,x,z)
  File "Prime_5.sage.py", line 28, in NFS
    x1 = ZZ(x1)
  File "sage/structure/parent.pyx", line 898, in sage.structure.parent.Parent.__call__ (build/cythonized/sage/structure/parent.c:9339)
  File "sage/structure/coerce_maps.pyx", line 161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_ (build/cythonized/sage/structure/coerce_maps.c:4628)
  File "sage/structure/coerce_maps.pyx", line 156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_ (build/cythonized/sage/structure/coerce_maps.c:4520)
  File "sage/rings/integer.pyx", line 713, in sage.rings.integer.Integer.__init__ (build/cythonized/sage/rings/integer.c:6568)
  File "sage/rings/integer.pyx", line 7097, in sage.rings.integer.mpz_set_str_python (build/cythonized/sage/rings/integer.c:43422)
TypeError: unable to convert '' to an integer

0 + 3

discrete-logarithm

Maarten Bodewes

2/12/24, 2:00 AM

What gives you what error exactly? We don't allow programming questions here, but if you don't fully get the math then including the source code and error is basically a requirement.

poncho

2/12/24, 2:20 AM

Actually, all primes (other than 2) is a divisor of $2^n-1$ for *some* $n$

Sanu

2/12/24, 2:31 AM

I have included error. Yes, all primes (other than 2) is a divisor of $2^n -1$. But I am facing problem for prime factors of $2^{197}-1, 2^{223}-1$ etc. Let P be a prime factor of $2^{197}-1$. For P, I am getting error. But if I take any other prime near P, it is giving result.

Elon Musk

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EN: Discrete log problem over special primes

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