Optimizing Double-Base Elliptic-Curve Single-Scalar Multiplication

This paper analyzes the best speeds that can be obtained for single-scalar multiplication with variable base point by combining a huge range of options: – many choices of coordinate systems and formulas for individual group operations, including new formulas for tripling on Edwards curves; – double-base chains with many different doubling/tripling ratios, including standard base-2 chains as an extreme case; – many precomputation strategies, going beyond Dimitrov, Imbert, Mishra (Asiacrypt 2005) and Doche and Imbert (Indocrypt 2006). The analysis takes account of speedups such as S − M tradeoffs and includes recent advances such as inverted Edwards coordinates. The main conclusions are as follows. Optimized precomputations and triplings save time for single-scalar multiplication in Jacobian coordinates, Hessian curves, and tripling-oriented Doche/Icart/Kohel curves. However, even faster single-scalar multiplication is possible in Jacobi intersections, Edwards curves, extended ...

• Type: Conference
• Year: 2007
• Where: INDOCRYPT
• Authors: Daniel J. Bernstein, Peter Birkner, Tanja Lange, Christiane Peters
• Keywords: Edwards Curves, INDOCRYPT 2007, Inverted Edwards Coordinates, Single-scalar Multiplication