The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Efficient Arithmetic on Koblitz Curves
Designs, Codes and Cryptography - Special issue on towards a quarter-century of public key cryptography
Optimal Left-to-Right Binary Signed-Digit Recoding
IEEE Transactions on Computers - Special issue on computer arithmetic
Guide to Elliptic Curve Cryptography
Guide to Elliptic Curve Cryptography
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Minimal Weight Digit Set Conversions
IEEE Transactions on Computers
Analysis of linear combination algorithms in cryptography
ACM Transactions on Algorithms (TALG)
A New Minimal Average Weight Representation for Left-to-Right Point Multiplication Methods
IEEE Transactions on Computers
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
New minimal weight representations for left-to-right window methods
CT-RSA'05 Proceedings of the 2005 international conference on Topics in Cryptology
Fractional windows revisited: improved signed-digit representations for efficient exponentiation
ICISC'04 Proceedings of the 7th international conference on Information Security and Cryptology
A Simple Left-to-Right Algorithm for Minimal Weight Signed Radix-r Representations
IEEE Transactions on Information Theory
Fast elliptic curve cryptography using minimal weight conversion of d integers
AISC '12 Proceedings of the Tenth Australasian Information Security Conference - Volume 125
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An algorithm is presented that produces an optimal radix-2 representation of an input integer n using digits from the set $${D_{\ell,u}=\{a\in{\mathbb{Z}}:\ell \le a\le u\}}$$ , where 驴 驴 0 and u 驴 1. The algorithm works by scanning the digits of the binary representation of n from left-to-right (i.e., from most-significant to least-significant); further, the algorithm is of the online variety in that it needs to scan only a bounded number of input digits before giving an output digit (i.e., the algorithm produces output before scanning the entire input). The output representation is optimal in the sense that, of all radix-2 representations of n with digits from D 驴,u , it has as few nonzero digits as possible (i.e., it has minimal weight). Such representations are useful in the efficient implementation of elliptic curve cryptography. The strategy the algorithm utilizes is to choose an integer of the form d 2 i , where $${d \in D_{\ell,u}}$$ , that is closest to n with respect to a particular distance function. It is possible to choose values of 驴 and u so that the set D 驴,u is unbalanced in the sense that it contains more negative digits than positive digits, or more positive digits than negative digits. Our distance function takes the possible unbalanced nature of D 驴,u into account.