Smaller keys for code-based cryptography: QC-MDPC mceliece implementations on embedded devices
CHES'13 Proceedings of the 15th international conference on Cryptographic Hardware and Embedded Systems
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Elliptic curve scalar multiplication is the central operation in elliptic curve cryptography. The paper presents a parallel architecture to accelerate scalar multiplications on Koblitz curves. The scalar multiplier architecture converts the scalar into $\tau-$NAF representation and processes the zero digits of the scalar in parallel to point additions. Since the conversion from integer to $\tau-$NAF is a time consuming operation, the proposed architecture uses recently developed \emph{double lazy reduction} algorithm for conversion of scalar. The scalar multiplier processes two consecutive $\tau-$NAF digits in every iteration. This facilitates parallel processing of large number of consecutive zero digits during a single point addition and practically no time is spent for processing the zero digits of the scalar. The proposed techniques are incorporated in a scalar multiplier and validated on Xilinx Virtex IV FPGA. Experimental results show that our architecture in $F_{2^{163}}$ has the best performance and has the computation time comparable with the fastest known implementation, which uses window based scalar multiplication algorithm.