Public-Key Cryptography through the Lens of Monoid Actions

ePrint Report: Public-Key Cryptography through the Lens of Monoid Actions

Hart Montgomery, Sikhar Patranabis

We show that key exchange and two-party computation are exactly equivalent to monoid actions with certain structural and hardness properties. To the best of our knowledge, this is the first "natural" characterization of the mathematical structure inherent to any key exchange or two-party computation protocol, and the first explicit proof of the necessity of mathematical structure for public-key cryptography. We then utilize these characterizations to show …

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