Commutativity, Associativity, and Public Key Cryptography
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In this paper, we will study some possible generalizations of the famous Diffie-Hellman algorithm. As we will see, at the end, most of these generalizations will not be secure or will be equivalent to some classical schemes. However, these results are not always obvious and moreover our analysis will present some interesting connections between the concepts of commutativity, associativity, and public key cryptography.
KeywordsDiffie-Hellman algorithms Chebyshev polynomials New public key algorithms
The authors want to thank Jérôme Plût, Gerhard Frey and Gérard Maze for very useful comments and particularly Gerhard Frey for his help to improve the presentation of this paper. We have met Gerhard Frey and Gérard Maze at NuTMiC 2017 in Poland.
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