Extending Scalar Multiplication Using Double Bases

Abstract. It has been recently acknowledged [4, 6, 9] that the use of double bases representations of scalars n, that is an expression of the form n = e,s,t(-1)e As Bt can speed up significantly scalar multiplication on those elliptic curves where multiplication by one base (say B) is fast. This is the case in particular of Koblitz curves and supersingular curves, where scalar multiplication can now be achieved in o(log n) curve additions. Previous literature dealt basically with supersingular curves (in characteristic 3, although the methods can be easily extended to arbitrary characteristic), where A, B N. Only [4] attempted to provide a similar method for Koblitz curves, where at least one base must be non-real, although their method does not seem practical for cryptographic sizes (it is only asymptotic), since the constants involved are too large. We provide here a unifying theory by proposing an alternate recoding algorithm which works in all cases with optimal constants. Further...

• Type: Conference
• Year: 2006
• Where: ASIACRYPT
• Authors: Roberto Maria Avanzi, Vassil S. Dimitrov, Christophe Doche, Francesco Sica
• Keywords: ASIACRYPT 2006, Cryptology, Koblitz Curves, Scalar Multiplication, Supersingular Curves