An Analysis of Double Base Number Systems and a Sublinear Scalar Multiplication Algorithm

In this paper we produce a practical and efficient algorithm to find a decomposition of type n = kˆ i=1 2si 3ti , si, ti ∈ N ∪ {0} with k ≤   c + o(1) ¡ log n log log n . It is conjectured that one can take c = 2 above. Then this decomposition is refined into an effective scalar multiplication algorithm to compute nP on some supersingular elliptic curves of characteristic 3 with running time bounded by O  log n log log n  and essentially no storage. To our knowledge, this is the first instance of a scalar multiplication algorithm that requires o(log n) curve operations on an elliptic curve over Fq with log q ≈ log n and uses comparable storage as in the standard double-and-add algorithm. This leads to an efficient algorithm very useful for cryptographic protocols based on supersingular curves. This is for example the case of the well-studied (in the past four years) identity based schemes. The method carries over to any supersingular curve of fixed characteristic. Key...

• Type: Conference
• Year: 2005
• Where: MYCRYPT
• Authors: Mathieu Ciet, Francesco Sica
• Keywords: Cryptology, Elliptic Curve, Efficient Algorithm, MYCRYPT 2005, Scalar Multiplication Algorithm