Trilinear maps for cryptography II
This work addresses cryptographic security for applications requiring multilinear maps, but it appears incremental as it builds on prior studies of trilinear maps.
The paper tackles the problem of constructing secure cryptographic trilinear maps by using Weil descent on abelian varieties over finite fields, resulting in a concrete implementation with jacobian varieties of hyperelliptic curves that enables efficient public identity testing.
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.