Is there any report on comparing quadratic and number field sieve performance in theory vs actual data for discrete logarithm over primes?
Is actual data better than theory in any way unexplained (I think I read this somewhere and cannot recollect)?
My query was more about distinction between theory and practice of quadratic sieve and distinction between theory and practice of number field sieve and not between distinction between quadratic and number field sieve.
To my knowledge, there are two reports that deal with the crossover point between the Gaussian integer sieve—which is the rough analogous of the quadratic sieve for discrete logarithms—and the number field sieve over prime fields:
Weber (1998) computed discrete logarithms over a 85-digit (~283 bits) prime, and concluded that at that size point the Gaussian integer sieve was faster.
Joux and Lercier (2003) not only compared the two algorithms, but made some improvements of their own to the number field sieve for discrete logarithms. They concluded that the number field sieve was faster already at the 100-digit (~332 bits) range.
