NTCRJan 1, 2020

Isogenies of certain abelian varieties over finite fields with p-ranks zero

arXiv:2001.00210v13 citations
AI Analysis

This work addresses a foundational problem in isogeny-based cryptography, providing theoretical results that could enhance cryptographic constructions, though it appears incremental as it builds on existing mathematical frameworks.

The paper tackles the problem of understanding isogenies between abelian varieties over finite fields with non-commutative endomorphism algebras, showing that any two such varieties with maximal endomorphism rings are linked by a cyclic isogeny of prime degree.

We study the isogenies of certain abelian varieties over finite fields with non-commutative endomorphism algebras with a view to potential use in isogeny-based cryptography. In particular, we show that any two such abelian varieties with endomorphism rings maximal orders in the endomorphism algebra are linked by a cyclic isogeny of prime degree.

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