Fast point multiplication on Koblitz curves: Parallelization method and implementations
Microprocessors & Microsystems
A modified low complexity digit-level Gaussian normal basis multiplier
WAIFI'10 Proceedings of the Third international conference on Arithmetic of finite fields
Sublinear scalar multiplication on hyperelliptic koblitz curves
SAC'11 Proceedings of the 18th international conference on Selected Areas in Cryptography
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Hi-index | 14.98 |
We describe algorithms for point multiplication on Koblitz curves using multiple-base expansions of the form $k = \sum \pm \tau^a (\tau-1)^b$ and $k= \sum \pm \tau^a (\tau-1)^b (\tau^2 - \tau - 1)^c.$ We prove that the number of terms in the second type is sublinear in the bit length of $k$, which leads to the first provably sublinear point multiplication algorithm on Koblitz curves. For the first type, we conjecture that the number of terms is sublinear and provide numerical evidence demonstrating that the number of terms is significantly less than that of $\tau$-adic non-adjacent form expansions. We present details of an innovative FPGA implementation of our algorithm and performance data demonstrating the efficiency of our method. We also show that implementations with very low computation latency are possible with the proposed method because parallel processing can be exploited efficiently.