Vol. 15, No. 3, 2021
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Algebraic maps constant on isomorphism classes of unpolarized abelian varieties are constant

Eric Rains, Karl Rubin, Travis Scholl, Shahed Sharif and Alice Silverberg
Vol. 15 (2021), No. 3, 711–727
DOI: 10.2140/ant.2021.15.711
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 shed light on a question raised by Boneh et al. (J. Math. Cryptol. 14:1 (2020), 5–14) concerning a proposal for multiparty noninteractive key exchange.

Keywords
abelian varieties, polarizations
Mathematical Subject Classification 2010
Primary: 14K10
Secondary: 11G10, 11G15
Milestones
Received: 16 December 2019
Revised: 10 July 2020
Accepted: 17 October 2020
Published: 20 May 2021
Authors
Eric Rains
Department of Mathematics
California Institute of Technology
Pasadena, CA
United States
Karl Rubin
Department of Mathematics
University of California
Irvine, CA
United States
Travis Scholl
Department of Mathematics
University of California
Irvine, CA
United States
Shahed Sharif
Department of Mathematics
California State University San Marcos
San Marcos, CA
United States
Alice Silverberg
Department of Mathematics
University of California
Irvine, CA
United States