How to practically find solutions to a discrete logarithm? 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 checked some links given in Wikipeda's Discrete Logarithm records page, in particular GGNFS. Can someone help compiling and testing it?

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.
256-bit discrete logarithms on a prime field are definitely not of the order of magnitude used in cryptographic applications. Secure sizes for this problem are in the thousands of bits, very much like integer factorization.

To break that example discrete logarithm, you probably want to use Index Calculus, more specifically the Linear Sieve. Resorting to the Number Field Sieve is probably overkill for such a small prime field, and GGNFS is not prepared to solve discrete logarithms, although much of it could be reused to do so.

Note that 256-bit sizes are OK for problems with less structure, where only generic discrete logarithm algorithms, like Pollard's Rho, work --- such as elliptic curves over a 256-bit prime.