A survey of fast exponentiation methods
Journal of Algorithms
Efficient Arithmetic on Koblitz Curves
Designs, Codes and Cryptography - Special issue on towards a quarter-century of public key cryptography
Elliptic curves in cryptography
Elliptic curves in cryptography
Optimal Left-to-Right Binary Signed-Digit Recoding
IEEE Transactions on Computers - Special issue on computer arithmetic
Efficient Elliptic Curve Exponentiation Using Mixed Coordinates
ASIACRYPT '98 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
Guide to Elliptic Curve Cryptography
Guide to Elliptic Curve Cryptography
Analysis of linear combination algorithms in cryptography
ACM Transactions on Algorithms (TALG)
Theoretical Computer Science
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
A New Minimal Average Weight Representation for Left-to-Right Point Multiplication Methods
IEEE Transactions on Computers
Analysis of Fractional Window Recoding Methods and Their Application to Elliptic Curve Cryptosystems
IEEE Transactions on Computers
Theoretical Computer Science
Faster Multi-exponentiation through Caching: Accelerating (EC)DSA Signature Verification
SCN '08 Proceedings of the 6th international conference on Security and Cryptography for Networks
New left-to-right minimal weight signed-digit radix-r representation
Computers and Electrical Engineering
Unbalanced digit sets and the closest choice strategy for minimal weight integer representations
Designs, Codes and Cryptography
Secure signed radix-r recoding methods for constrained-embedded devices
ISPEC'07 Proceedings of the 3rd international conference on Information security practice and experience
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
Affine precomputation with sole inversion in elliptic curve cryptography
ACISP'07 Proceedings of the 12th Australasian conference on Information security and privacy
Scalar multiplication on koblitz curves using double bases
VIETCRYPT'06 Proceedings of the First international conference on Cryptology in Vietnam
A note on signed binary window algorithm for elliptic curve cryptosystems
CANS'05 Proceedings of the 4th international conference on Cryptology and Network Security
Fractional windows revisited: improved signed-digit representations for efficient exponentiation
ICISC'04 Proceedings of the 7th international conference on Information Security and Cryptology
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For an integer w ≥ 2, a radix 2 representation is called a width-wnonadjacent form (w-NAF, for short) if each nonzero digit is an odd integer with absolute value less than 2w−−1, and, of any w consecutive digits, at most one is nonzero. In elliptic curve cryptography, the w-NAF window method is used to efficiently compute nP where n is an integer and P is an elliptic curve point. We introduce a new family of radix 2 representations which use the same digits as the w-NAF but have the advantage that they result in a window method which uses less memory. This memory savings results from the fact that these new representations can be deduced using a very simple left-to-right algorithm. Further, we show that like the w-NAF, these new representations have a minimal number of nonzero digits.