A course in computational algebraic number theory
A course in computational algebraic number theory
A survey of fast exponentiation methods
Journal of Algorithms
Optimal Left-to-Right Binary Signed-Digit Recoding
IEEE Transactions on Computers - Special issue on computer arithmetic
Signed Digit Representations of Minimal Hamming Weight
IEEE Transactions on Computers
Efficient Algorithms for Pairing-Based Cryptosystems
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
New Minimal Modified Radix-r Representation with Applications to Smart Cards
PKC '02 Proceedings of the 5th International Workshop on Practice and Theory in Public Key Cryptosystems: Public Key Cryptography
The Weil and Tate Pairings as Building Blocks for Public Key Cryptosystems
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
Hardware Implementation of Finite Fields of Characteristic Three
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
Minimal Weight Digit Set Conversions
IEEE Transactions on Computers
A New Minimal Average Weight Representation for Left-to-Right Point Multiplication Methods
IEEE Transactions on Computers
Left-to-right Generalized Non-adjacent Form Recoding for Elliptic Curve Cryptosystems
ICHIT '06 Proceedings of the 2006 International Conference on Hybrid Information Technology - Volume 01
Efficient pairing computation on supersingular Abelian varieties
Designs, Codes and Cryptography
Efficient GF(pm) arithmetic architectures for cryptographic applications
CT-RSA'03 Proceedings of the 2003 RSA conference on The cryptographers' track
New left-to-right radix-r signed-digit recoding algorithm for pairing-based cryptosystems
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
A note on the signed sliding window integer recoding and a left-to-right analogue
SAC'04 Proceedings of the 11th international conference on Selected Areas in Cryptography
New minimal weight representations for left-to-right window methods
CT-RSA'05 Proceedings of the 2005 international conference on Topics in Cryptology
A Simple Left-to-Right Algorithm for Minimal Weight Signed Radix-r Representations
IEEE Transactions on Information Theory
A prefix-based approach for managing hybrid specifications in complex packet filtering
Computer Networks: The International Journal of Computer and Telecommunications Networking
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Recently, signed-digit radix-r (r=2) representation is used to speed up the scalar multiplication of pairing based cryptosystems. One such representation is wrNAF proposed by Takagi et al. at the international conference on information security 2004 (ISC 2004). This representation is obtained from right to left. In this paper, we present a new signed-digit radix-r representation with the same average weight, that is r-1w(r-1)+1 as the wrNAF. The new representation uses the same digits as the wrNAF but has the advantage that it can be deduced using a left-to-right algorithm. Further, we show that like the wrNAF, the new representation has a minimal number of non-zero digits. Interleaved with the left-to-right scalar multiplication, the new representation can reduce both the time and space complexity of the computation compared to the right-to-left wrNAF.