An algorithm for modular exponentiation
Information Processing Letters
Theory and Applications of the Double-Base Number System
IEEE Transactions on Computers
Trading Inversions for Multiplications in Elliptic Curve Cryptography
Designs, Codes and Cryptography
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
FPGA implementation of point multiplication on koblitz curves using kleinian integers
CHES'06 Proceedings of the 8th international conference on Cryptographic Hardware and Embedded Systems
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
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Double base number systems (DBNS) provide an elegant way to represent numbers. These representations also have many interesting and useful properties, which have been exploited to find many applications in Cryptography and Signal Processing. In the current article we present a scheme to represent numbers in double (and multi-) base format by combinatorial objects like graphs and diagraphs. The combinatorial representation leads to proof of some interesting results about the double and multibase representation of integers. These proofs are based on simple combinatorial arguments. In this article we have provided a graph theoretic proof of the recurrence relation satisfied by the number of double base representations of a given integer. The result has been further generalized to more than 2 bases. Also, we have uncovered some interesting properties of the sequence representing the number of double base representation of a positive integer n. It is expected that the combinatorial representation can serve as a tool for a better understanding of the double (and multi-) base number systems.