The number of rational points of hyperelliptic curves over subsets of finite fields

2017/10/08 by Nelson, Kristina, Solymosi, Jozsef, Tom, Foster +1
#Cryptography and Security (cs.CR) #FOS: Computer and information sciences #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1710.02781

Abstract

We prove two related concentration inequalities concerning the number of rational points of hyperelliptic curves over subsets of a finite field. In particular, we investigate the probability of a large discrepancy between the numbers of quadratic residues and non-residues in the image of such subsets over uniformly random hyperelliptic curves of given degrees. We find a constant probability of such a high difference and show the existence of sets with an exceptionally large discrepancy.

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