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STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
A course in number theory and cryptography
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Exponentiating faster with addition chains
EUROCRYPT '90 Proceedings of the workshop on the theory and application of cryptographic techniques on Advances in cryptology
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
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A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
New Public-Key Schemes Based on Elliptic Curves over the Ring Zn
CRYPTO '91 Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology
CRYPTO '89 Proceedings of the 9th Annual International Cryptology Conference on Advances in Cryptology
Fast exponentiation with precomputation
EUROCRYPT'92 Proceedings of the 11th annual international conference on Theory and application of cryptographic techniques
Efficient Arithmetic on Koblitz Curves
Designs, Codes and Cryptography - Special issue on towards a quarter-century of public key cryptography
On String Replacement Exponentiation
Designs, Codes and Cryptography
Elliptic Curve Cryptography on a Palm OS Device
ACISP '01 Proceedings of the 6th Australasian Conference on Information Security and Privacy
Fast Elliptic Curve Multiplications with SIMD Operations
ICICS '02 Proceedings of the 4th International Conference on Information and Communications Security
Improved Algorithms for Elliptic Curve Arithmetic in GF(2n)
SAC '98 Proceedings of the Selected Areas in Cryptography
An Improved Implementation of Elliptic Curves over GF(2) when Using Projective Point Arithmetic
SAC '01 Revised Papers from the 8th Annual International Workshop on Selected Areas in Cryptography
On the Power of Multidoubling in Speeding Up Elliptic Scalar Multiplication
SAC '01 Revised Papers from the 8th Annual International Workshop on Selected Areas in Cryptography
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
Elliptic Curve Arithmetic Using SIMD
ISC '01 Proceedings of the 4th International Conference on Information Security
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
Resistance against Differential Power Analysis for Elliptic Curve Cryptosystems
CHES '99 Proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems
Software Implementation of Elliptic Curve Cryptography over Binary Fields
CHES '00 Proceedings of the Second International Workshop on Cryptographic Hardware and Embedded Systems
Fast Implementation of Elliptic Curve Defined over GF(pm) on CalmRISC with MAC2424 Coprocessor
CHES '00 Proceedings of the Second International Workshop on Cryptographic Hardware and Embedded Systems
An analysis of exponentiation based on formal languages
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
Generic GF(2m) arithmetic in software and its application to ECC
ACISP'03 Proceedings of the 8th Australasian conference on Information security and privacy
CT-RSA'03 Proceedings of the 2003 RSA conference on The cryptographers' track
Fast elliptic curve arithmetic and improved weil pairing evaluation
CT-RSA'03 Proceedings of the 2003 RSA conference on The cryptographers' track
Speeding up scalar multiplication using a new signed binary representation for integers
MCAM'07 Proceedings of the 2007 international conference on Multimedia content analysis and mining
wNAF, an efficient left-to-right signed digit recoding algorithm
ACNS'08 Proceedings of the 6th international conference on Applied cryptography and network security
A note on signed binary window algorithm for elliptic curve cryptosystems
CANS'05 Proceedings of the 4th international conference on Cryptology and Network Security
Advances in alternative non-adjacent form representations
INDOCRYPT'04 Proceedings of the 5th international conference on Cryptology in India
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The basic operation in elliptic cryptosystems is the computation of a multiple d驴P of a point P on the elliptic curve modulo n. We propose a fast and systematic method of reducing the number of operations over elliptic curves. The proposed method is based on pre-computation to generate an adequate addition-subtraction chain for multiplier the d. By increasing the average length of zero runs in a signed binary representation of d, we can speed up the window method. Formulating the time complexity of the proposed method makes clear that the proposed method is faster than other methods. For example, for d with length 512 bits, the proposed method requires 602.6 multiplications on average. Finally, we point out. that each addition/subtraction over the elliptic curve using homogeneous coordinates can be done in 3 multiplications if parallel processing is allowed.