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math.NT2011
An Improvement to the Number Field Sieve
Qizhi Zhang
We improve the "sieve" part of the number field sieve used in factoring integer and computing discrete logarithm. The runtime of our method is shorter than that of existing methods…
math.NT2011
On the ramification of non-abelian Galois coverings of degree
Qizhi Zhang
The refined Swan conductor is defined by K.\ Kato \cite{KK2}, and generalized by T.\ Saito \cite{wild}. In this part, we consider some smooth -adic étale sheaves of rank suc…
math.NT2011
On the Signature Calculus for finite fields of order square of prime numbers
Qizhi Zhang
In [Huang-Raskind 2009], the authors proved that the discrete logarithm problem in a prime finite field is random polynomial time equivalent to computing the ramification signature…