Algebraic Maps Constant On Isomorphism Classes Of Unpolarized Abelian Varieties Are Constant

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.