Redundant Integer Representations and Fast Exponentiation
Designs, Codes and Cryptography - Special issue dedicated to Gustavus J. Simmons
Efficient Exponentiation of a Primitive Root in GF(2m)
IEEE Transactions on Computers
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Signed Digit Representations of Minimal Hamming Weight
IEEE Transactions on Computers
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
Multiplierless multiple constant multiplication
ACM Transactions on Algorithms (TALG)
A loopless gray code for minimal signed-binary representations
ESA'05 Proceedings of the 13th annual European conference on Algorithms
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In radix-$r$ number system, the minimal weight signed-digit (SD) representation hasminimal number of nonzero signed-digits which belong to the set $\{\pm{1},\pm{2},\ldots,\pm{(r-1)}\}$. In this article, we derive closed form expressions for the average number of nonzero digits in the minimal weight SD representation and for the average length of the canonical SD representation, a special case of the minimal weight SD form,of a positive integer whose radix-$r$ form is of length $\schmi{n}$, $\schmi{n}\geq 1$.