Trilinear maps for cryptography II
Cryptography and Security
2019-02-07 v6 Number Theory
Abstract
We continue to study the construction of cryptographic trilinear maps involving abelian varieties over finite fields. We introduce Weil descent as a tool to strengthen the security of a trilinear map. We form the trilinear map on the descent variety of an abelian variety of small dimension defined over a finite field of a large extension degree over a ground field. The descent bases, with respect to which the descents are performed, are trapdoor secrets for efficient construction of the trilinear map which pairs three trapdoor DDH-groups. The trilinear map also provides efficient public identity testing for the third group. We present a concrete construction involving the jacobian varieties of hyperelliptic curves.
Cite
@article{arxiv.1810.03646,
title = {Trilinear maps for cryptography II},
author = {Ming-Deh A. Huang},
journal= {arXiv preprint arXiv:1810.03646},
year = {2019}
}