Faster initial splitting for small characteristic composite extension degree fields

Article Type

Research Article

Publication Title

Finite Fields and their Applications


Let p be a small prime and n=n1n2>1 be a composite integer. For the function field sieve algorithm applied to Fpn, Guillevic (2019) had proposed an algorithm for initial splitting of the target in the individual logarithm phase. This algorithm generates polynomials and tests them for B-smoothness for some appropriate value of B. The amortised cost of generating each polynomial is O(n22) multiplications over Fpn1. In this work, we propose a new algorithm for performing the initial splitting which also generates and tests polynomials for B-smoothness. The advantage over Guillevic splitting is that in the new algorithm, the cost of generating a polynomial is O(nlogp⁡(1/π)) multiplications in Fp, where π is the relevant smoothness probability.



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