Cryptology ePrint Archive: Report 2014/379

Hyper-and-elliptic-curve cryptography

Daniel J. Bernstein and Tanja Lange

Abstract: This paper introduces "hyper-and-elliptic-curve cryptography", in which a single high-security group supports fast genus-2-hyperelliptic-curve formulas for variable-base-point single-scalar multiplication (e.g., Diffie--Hellman shared-secret computation) and at the same time supports fast elliptic-curve formulas for fixed-base-point scalar multiplication (e.g., key generation) and multi-scalar multiplication (e.g., signature verification).

Category / Keywords: public-key cryptography / performance, Diffie--Hellman, elliptic curves, hyperelliptic curves, Weil restriction, isogenies, Scholten curves, Kummer surfaces, Edwards curves

Original Publication (in the same form): Eleventh Algorithmic Number Theory Symposium (archiving authorized by London Mathematical Society Journal of Computation and Mathematics)

Date: received 27 May 2014

Contact author: authorcontact-hyperand at box cr yp to

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Version: 20140528:163944 (All versions of this report)

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