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
Elliptic curves in cryptography
Elliptic curves in cryptography
Elliptic Curves: Number Theory and Cryptography
Elliptic Curves: Number Theory and Cryptography
Guide to Elliptic Curve Cryptography
Guide to Elliptic Curve Cryptography
Advances in Elliptic Curve Cryptography (London Mathematical Society Lecture Note Series)
Advances in Elliptic Curve Cryptography (London Mathematical Society Lecture Note Series)
Trading Inversions for Multiplications in Elliptic Curve Cryptography
Designs, Codes and Cryptography
Optimizing double-base elliptic-curve single-scalar multiplication
INDOCRYPT'07 Proceedings of the cryptology 8th international conference on Progress in cryptology
AAECC'07 Proceedings of the 17th international conference on Applied algebra, algebraic algorithms and error-correcting codes
Extending scalar multiplication using double bases
ASIACRYPT'06 Proceedings of the 12th international conference on Theory and Application of Cryptology and Information Security
Extended double-base number system with applications to elliptic curve cryptography
INDOCRYPT'06 Proceedings of the 7th international conference on Cryptology in India
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
An analysis of double base number systems and a sublinear scalar multiplication algorithm
Mycrypt'05 Proceedings of the 1st international conference on Progress in Cryptology in Malaysia
Efficient scalar multiplication by isogeny decompositions
PKC'06 Proceedings of the 9th international conference on Theory and Practice of Public-Key Cryptography
ISC'07 Proceedings of the 10th international conference on Information Security
Fast Multibase Methods and Other Several Optimizations for Elliptic Curve Scalar Multiplication
Irvine Proceedings of the 12th International Conference on Practice and Theory in Public Key Cryptography: PKC '09
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
A new algorithm for computing triple-base number system
ACM SIGARCH Computer Architecture News
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We introduce a tree-based method to find short Double-Base chains. As compared to the classical greedy approach, this new method is not only simpler to implement and faster, experimentally it also returns shorter chains on average. The complexity analysis shows that the average length of a chain returned by this tree-based approach is $\frac{\log_2 n }{4.6419}\cdotp$ This tends to suggest that the average length of DB-chains generated by the greedy approach is not O(logn/loglogn). We also discuss generalizations of this method, namely to compute Step Multi-Base Representation chains involving more than 2 bases and extended DB-chains having nontrivial coefficients.