Fast Algorithm Research On Scalar Decomposition Of Elliptic Curve Cryptography

Elliptic curve cryptography (ECC), as proposed by Koblitz and Miller indepen-dently in 1985, is a public-key cryptographic scheme. In recent years, it has been usedwidely in the field of cryptology because of its smaller key-length and higher securitylevel.Scalar multiplication is the most basic and computationally costliest operation inthe elliptic curve cryptography, and the scalar decomposition is the core issue of thescalar multiplication. Based on the research of former researchers, we have proposedthe following ideas.Firstly, a scalar representation in the form of d(1/2)a3b is proposed, where d isan odd integer belonging to a given set S. This is a combination of the extendeddouble-base number system (DBNS) and the double-base chain representation. Exper-imental results show that our approach leads to a shorter DBNS expansion and a lowercomplexity in elliptic curve scalar multiplication when compared with other existinge?cient algorithms, with the cost of only a few pre-computations and storages. Thiscontributes to the e?cient implementation of elliptic curve cryptography.Then a extended scalar representation and the corresponding scalar multiplicationusing the Multibase Number Representation are obtained which based on the resultsof our former research. Experimental results show that our new approach leads to ashorter expansion.Finally, a new scalar representation is given with the application of joint sparsefrom to the two adjacent coe?cients, and the results show that our approach leadsto a lower complexity in elliptic curve scalar multiplication at the cost of a few pre-computations and storages, and improve the e?ciency of elliptic curve cryptography.