A Literature Review on Scalar Recoding Algorithms in Elliptic Curve Cryptography

Elliptic Curve Cryptosystem (ECC) is a type of public key cryptography (PKC) based on the algebraic structure of elliptic curve over finite fields. In mid 80s Neal Koblitz and Victor Miller independently proposed the use of elliptic curves in cryptography. For a smaller key size, ECC is able to provide same level of security with RSA. This feature made ECC one of the most popular PKC algorithms today. Scalar multiplication is known as the fundamental operation in ECC algorithm and protocols. The efficiency of ECC is critically depends on efficiency of scalar multiplication operation. Scalar multiplication involves with three levels of computations: scalar arithmetic, point arithmetic and field arithmetic. Improving the first two levels will lead to significant increment in efficiency of scalar multiplication. Scalar arithmetic level can improve by employing an enhanced scalar recoding algorithm that can reduce the Hamming weight or de-crease the number of operations in the scalar representation process. This paper reviews some of the recoding algorithms and techniques.