Fast Probabilistic Algorithms for Verification of Polynomial Identities
Journal of the ACM (JACM)
Small generic hardcore subsets for the discrete logarithm: short secret DL-keys
Information Processing Letters
On The Complexity Of Matrix Group Problems I
SFCS '84 Proceedings of the 25th Annual Symposium onFoundations of Computer Science, 1984
Lower bounds for discrete logarithms and related problems
EUROCRYPT'97 Proceedings of the 16th annual international conference on Theory and application of cryptographic techniques
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We propose a Diffie-Hellman-like key agreement protocol based on the computational intractability of reversing group action. The concept of a group action generalizes exponentiation and provides an algorithmic problem harder than the discrete logarithm problem. Using the action of the general linear group on the direct product of two cyclic groups, we invent a key agreement protocol secure against an attacker who has power to solve the discrete logarithm problem. We discuss a semantic secure asymmetric encryption scheme as well. Its security is evaluated in terms of a generic algorithm, which is a model of probabilistic algorithms over black box groups (similar to a straight-line program) and does not depend on any specific property of the group representation.