Pseudorandomness of Sato-Tate Distributions for Elliptic Curves
Chung Pang Mok, Huimin Zheng
TL;DR
This paper conjectures that the Frobenius angles of non-CM elliptic curves over rationals are statistically independent and follow the Sato-Tate distribution, supported by numerical evidence.
Contribution
It introduces conjectures on the pseudorandomness of Frobenius angles for elliptic curves without complex multiplication, backed by numerical data.
Findings
Numerical evidence supports the conjectures.
Frobenius angles appear statistically independent.
Angles follow the Sato-Tate measure.
Abstract
In this paper we propose conjectures that assert that, the sequence of Frobenius angles of a given elliptic curve over without complex multiplication is pseudorandom, in other words that the Frobenius angles are statistically independently distributed with respect to the Sato-Tate measure. Numerical evidences are presented to support the conjectures.
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Taxonomy
TopicsCryptography and Residue Arithmetic · Advanced Algebra and Geometry · Coding theory and cryptography