IACR News item: 12 October 2015
Ping Ngai Chung, Craig Costello, Benjamin Smith
ePrint ReportThis extends the work of L\\\'opez and Dahab, Okeya and Sakurai, and Brier and Joye to genus~2, and also to two-dimensional scalar multiplication.
Our results show that many existing fast pseudomultiplication implementations (hitherto limited to applications in Diffie--Hellman key exchange) can be wrapped with simple and efficient pre- and post-computations to yield competitive full scalar multiplication algorithms, ready for use in more general discrete logarithm-based cryptosystems, including signature schemes. This is especially interesting for genus~2, where Kummer surfaces can outperform comparable elliptic curve systems.
As an example, we construct an instance of the Schnorr signature scheme driven by Kummer surface arithmetic.
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