d-complete sequences of integers
Mathematics of Computation
An algorithm for modular exponentiation
Information Processing Letters
Digital Arithmetic Using Analog Arrays
GLS '98 Proceedings of the Great Lakes Symposium on VLSI '98
Some Optimizations of Hardware Multiplication by Constant Matrices
IEEE Transactions on Computers
EURASIP Journal on Applied Signal Processing
Improving 2D-log-number-system representations by use of an optimal base
EURASIP Journal on Advances in Signal Processing
A graph theoretic analysis of double base number systems
INDOCRYPT'07 Proceedings of the cryptology 8th international conference on Progress in cryptology
A novel architecture for conversion of binary to single digit double base numbers
ACM SIGARCH Computer Architecture News
Extended double-base number system with applications to elliptic curve cryptography
INDOCRYPT'06 Proceedings of the 7th international conference on Cryptology in India
Conversion of binary to single-term triple base numbers for DSP applications
ACM SIGARCH Computer Architecture News
ACM SIGARCH Computer Architecture News
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
Efficient scalar multiplication by isogeny decompositions
PKC'06 Proceedings of the 9th international conference on Theory and Practice of Public-Key Cryptography
ACM SIGARCH Computer Architecture News
ISC'07 Proceedings of the 10th international conference on Information Security
A new algorithm for computing triple-base number system
ACM SIGARCH Computer Architecture News
Performance analysis of a FPGA based novel binary and DBNS multiplier
ACM SIGARCH Computer Architecture News
High performance MAC unit for DSP and cryptographic applications
ACM SIGARCH Computer Architecture News
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In this paper, we analyze some of the main properties of a double base number system, using bases 2 and 3; in particular, we emphasize the sparseness of the representation. A simple geometric interpretation allows an efficient implementation of the basic arithmetic operations and we introduce an index calculus for logarithmic-like arithmetic with considerable hardware reductions in look-up table size. We discuss the application of this number system in the area of digital signal processing; we illustrate the discussion with examples of finite impulse response filtering.