Scalar multiplication on elliptic curves

Thesis Type: Postgraduate

Institution Of The Thesis: Orta Doğu Teknik Üniversitesi, Institute of Applied Mathematics, Turkey

Approval Date: 2006




Elliptic curve cryptography has gained much popularity in the past decade and has been challenging the dominant RSA/DSA systems today. This is mainly due to elliptic curves offer cryptographic systems with higher speed, less memory and smaller key sizes than older ones. Among the various arithmetic operations required in implementing public key cryptographic algorithms based on elliptic curves, the elliptic curve scalar multiplication has probably received the maximum attention from the research community in the past a few years. Many methods for efficient and secure implementation of scalar multiplication have been proposed by many researchers. In this thesis, many scalar multiplication methods are studied in terms of their mathematical, computational and implementational points.