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On-the-Fly Multi-Base Recoding for ECC Scalar Multiplication without Pre-Computations
Abstract : Scalar recoding is popular to speed up ECC scalar multiplication: non-adjacent form, double-base number system, multi-base number system. But fast recoding methods require pre-computations: multiples of base point or off-line conversion. In this paper, we present a multi-base recoding method for ECC scalar multiplication based on i) a greedy algorithm starting least significant terms first, ii) cheap divisibility tests by multi-base elements and iii) fast exact divisions by multibase elements. Multi-base terms are obtained on-the-fly using a special recoding unit which operates in parallel to curve-level operations and at very high speed. This ensures that all recoding steps are performed fast enough to schedule the next curve-level operations without interruptions. The proposed method can be fully implemented in hardware without pre-computations. We report FPGA implementation details and very good performances compared to state-of-art results.
Cited literature [29 references]
https://hal.inria.fr/hal-00772613
Contributor : Arnaud Tisserand <>
Submitted on : Thursday, January 10, 2013 - 6:22:40 PM
Last modification on : Friday, July 10, 2020 - 4:06:22 PM
Document(s) archivé(s) le : Thursday, April 11, 2013 - 4:08:52 AM
Contributor : Arnaud Tisserand <>
Submitted on : Thursday, January 10, 2013 - 6:22:40 PM
Last modification on : Friday, July 10, 2020 - 4:06:22 PM
Document(s) archivé(s) le : Thursday, April 11, 2013 - 4:08:52 AM
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PID2635353.pdf
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