Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
An algorithm for modular exponentiation
Information Processing Letters
Concrete Mathematics: A Foundation for Computer Science
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Encyclopedia of Cryptography and Security
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Double-Base Number System for Multi-scalar Multiplications
EUROCRYPT '09 Proceedings of the 28th Annual International Conference on Advances in Cryptology: the Theory and Applications of Cryptographic Techniques
Efficient and secure elliptic curve point multiplication using double-base chains
ASIACRYPT'05 Proceedings of the 11th international conference on Theory and Application of Cryptology and Information Security
Handbook of Elliptic and Hyperelliptic Curve Cryptography, Second Edition
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During the past twenty years, elliptic curves have attracted more and more attention from the cryptography community. One of the core operations of elliptic curve cryptography protocols is the scalar multiplication. Any algorithm reducing the complexity of such multiplications will speed up cryptographic primitives based on these algebraic structures. In this paper, we study two recently introduced techniques for scalar multiplication: Double-Base Number System (DBNS) and Double-Base Chain (DBC). Our results are twofold. First, we demonstrate a theoretical bound @W(logn) on the length of any DBC used to decompose some (logn)-bit integers. Second, we present a new algorithm to obtain a {2,3}-integer expansion of n. The bound previously computed will imply the optimality of this algorithm. Our scheme represents a trade-off method between the DBNS approach and the DBC technique. Experimentally, our algorithm constructs shorter chains on average than both the binary/ternary method and the greedy algorithm approach.