Welcome to the resource topic for 2015/983
Title:
Fast, uniform, and compact scalar multiplication for elliptic curves and genus 2 Jacobians with applications to signature schemes
Authors: Ping Ngai Chung, Craig Costello, Benjamin Smith
Abstract:We give a general framework for uniform, constant-time one- and two-dimensional scalar multiplication algorithms for elliptic curves and Jacobians of genus~2 curves that operate by projecting to the (x)-line or Kummer surface, where we can exploit faster and more uniform pseudomultiplication, before recovering the proper ``signed’’ output back on the curve or Jacobian. This extends the work of López 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.
ePrint: https://eprint.iacr.org/2015/983
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