Exponentiating faster with addition chains
EUROCRYPT '90 Proceedings of the workshop on the theory and application of cryptographic techniques on Advances in cryptology
CRYPTO '89 Proceedings on Advances in cryptology
An introduction to the analysis of algorithms
An introduction to the analysis of algorithms
Redundant Integer Representations and Fast Exponentiation
Designs, Codes and Cryptography - Special issue dedicated to Gustavus J. Simmons
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
Handbook of Applied Cryptography
Handbook of Applied Cryptography
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
CM-Curves with Good Cryptographic Properties
CRYPTO '91 Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology
Speeding up Elliptic Cryptosystems by Using a Signed Binary Window Method
CRYPTO '92 Proceedings of the 12th Annual International Cryptology Conference on Advances in Cryptology
An Improved Algorithm for Arithmetic on a Family of Elliptic Curves
CRYPTO '97 Proceedings of the 17th Annual International Cryptology Conference on Advances in Cryptology
Minimal Weight k-SR Representations
Proceedings of the 5th IMA Conference on Cryptography and Coding
An analysis of exponentiation based on formal languages
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
Minimal Weight Digit Set Conversions
IEEE Transactions on Computers
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The string replacement (SR) method was recently proposed as a methodfor exponentiation a^e in a group G. The canonicalk-SR method operates by replacing a run of i onesin a binary exponent,0, with i-1 zeroes followedby the single digit b=2^i-1. After recoding, it was shown in[5] that the expected weight of e tends to n/4 forn-bit exponents. In this paper we show that the canonicalk-SR recoding process can be described as a regular language andthen use generating functions to derive the exact probability distribution ofrecoded exponent weights. We also show that the canonical 2-SR recodingproduces weight distributions very similar to (optimal) signed-digitrecodings, but no group inversions are required.