Are there any ongoing or current practical attempts to solve instances of the discrete logarithm problem of the order of magnitude used in cryptographic applications, for example with a 256 bit modulus and 160 bit exponent? I am interested in efforts similar to the work of members of the Mersenne Prime forum and the RSA factoring challenge, but for the discrete logarithm problem.
What principles and techniques are involved? Do any of these solutions yet approach a realistic time frame? I am mainly looking for working software implementations of any attempts.
I also found a similar question: https://crypto.stackexchange.com/questions/100/modern-integer-factorization-software. Does this software also allow what I want?
Here is some test data (all in decimal form):
- base: 47
- modulus: 112624315653284427036559548610503669920632123929604336254260115573677366691719
- result: 107169838909122878937980510796152643759453843830224828060309998762431169006781
You have to find 160 bit exponent.