Abstract
We propose a new identification system based on algorithmic problems related to computing isomorphisms between central simple algebras. We design a statistical zero knowledge protocol which relies on the hardness of computing isomorphisms between orders in division algebras which generalizes a protocol by Hartung and Schnorr, which relies on the hardness of integral equivalence of quadratic forms.
Highlights
In this paper we propose an identification system based on an algorithmic problem related to the following problem from computational algebra
We will refer to this problem as the explicit isomorphism problem
In a sense our scheme can be thought of as a higher degree generalization of the protocol in [15] as the equivalence problem of rational quadratic forms is similar to the isomorphism problem of quaternion algebras
Summary
In this paper we propose an identification system based on an algorithmic problem related to the following problem from computational algebra. We will refer to this problem as the explicit isomorphism problem This is a well studied problem in computational algebra [5, 19, 20, 22, 24]. The algorithm of [20] can be used to compute isomorphisms between division algebras by a reduction to the original explicit isomorphism problem. This reduction on the other hand comes at the cost of squaring the dimension. In a sense our scheme can be thought of as a higher degree generalization of the protocol in [15] as the equivalence problem of rational quadratic forms is similar to the isomorphism problem of quaternion algebras.
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