Trilinear maps for cryptography II
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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. More specifically, we prepare a trilinear map by starting with an abelian variety of small dimension defined over a finite field K of large extension degree over a finite field k. The points and maps and functions involved in the trilinear maps are encoded using Weil descent. However the original abelian variety as well as the descent basis and descent table will be kept secret. We present a concrete construction involving the jacobian varieties of hyperelliptic curves. The idea of using Weil descent to strengthen security raises some interesting computational problems from a cryptanalytic perspective.
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