On-the-Fly Multi-Base Recoding for ECC Scalar Multiplication without Pre-Computations

Thomas Chabrier (1) , Arnaud Tisserand (1)

1 CAIRN - Energy Efficient Computing ArchItectures with Embedded Reconfigurable Resources

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.

Mots clés: elliptic curve cryptography; scalar multiplication; DBNS; MBNS; divisibility test; exact division by constant

Domaines: Arithmétique des ordinateurs; Cryptographie et sécurité [cs.CR]; Micro et nanotechnologies/Microélectronique

Thomas Chabrier, Arnaud Tisserand. On-the-Fly Multi-Base Recoding for ECC Scalar Multiplication without Pre-Computations. ARITH - 21st IEEE International Symposium on Computer Arithmetic, Apr 2013, Austin, TX, United States. pp.219-228, ⟨10.1109/ARITH.2013.17⟩. ⟨hal-00772613⟩