Algebraic maps constant on isomorphism classes of unpolarized abelian varieties are constant

TL;DR

The paper proves that any rational map constant on isomorphism classes of unpolarized abelian varieties must be globally constant, providing insights relevant to cryptographic protocol construction.

Contribution

It establishes a fundamental property of rational maps on abelian varieties, linking algebraic geometry to cryptography.

Findings

Rational maps constant on isomorphism classes are globally constant.

Results have implications for cryptographic protocol design.

Provides a new perspective on the structure of abelian varieties.

Abstract

We show that if a rational map is constant on each isomorphism class of unpolarized abelian varieties of a given dimension, then it is a constant map. Our results are motivated by and shed light on a proposed construction of a cryptographic protocol for multiparty non-interactive key exchange.