On the elliptic curve endomorphism generator
L\'aszl\'o M\'erai

TL;DR
This paper investigates the properties of sequences generated by elliptic curve endomorphisms, focusing on their distribution and linear complexity, which are crucial for cryptographic applications.
Contribution
It introduces a new framework for analyzing sequences generated by elliptic curve endomorphisms and studies their distribution and linear complexity properties.
Findings
Sequences exhibit certain distribution patterns.
Linear complexity of sequences is characterized.
Implications for cryptographic security are discussed.
Abstract
For an elliptic curve over a finite field we define the point sequence recursively by with an endomorphism and with some initial point on . We study the distribution and the linear complexity of sequences obtained from .
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Taxonomy
TopicsCoding theory and cryptography · Cryptography and Residue Arithmetic · Algebraic Geometry and Number Theory
