Optimal left-to-right binary signed-digit recoding

Joye, Marc; Yen, Sung-Ming

doi:10.1109/12.863044

Cited by 114 publications

(55 citation statements)

References 24 publications

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“…Joye and Yen [5] give a surprisingly elegant left-to-right algorithm for computing the digits of a {0, ±1}-radix 2 representation of an integer. They also prove that the representations constructed by this algorithm have a minimal number of nonzero digits.…”

Section: Window Methodsmentioning

confidence: 99%

New Minimal Weight Representations for Left-to-Right Window Methods

Muir

Stinson

2005

Lecture Notes in Computer Science

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Abstract. For an integer w ≥ 2, a radix 2 representation is called a width-w nonadjacent form (w-NAF, for short) if each nonzero digit is an odd integer with absolute value less than 2 w−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.

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Section: Window Methodsmentioning

confidence: 99%

New Minimal Weight Representations for Left-to-Right Window Methods

Muir

Stinson

2005

Lecture Notes in Computer Science

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“…Many algorithms can be used to recode the binary representation or any BSD representa-tion to minimum weight BSD representation [20,11,12]. Notice that an integer may have many minimal weight BSD representations, the most famous one is called the sparse form since no two consecutive digits are both nonzeros.…”

Section: The Basic Bsd Methods For Multi-scalar Multiplicationsmentioning

confidence: 99%

Fast Multi-computations with Integer Similarity Strategy

Yang

Guan

Laih

2005

Public Key Cryptography - PKC 2005

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Abstract. Multi-computations in finite groups, such as multiexponentiations and multi-scalar multiplications, are very important in ElGamallike public key cryptosystems. Algorithms to improve multi-computations can be classified into two main categories: precomputing methods and recoding methods. The first one uses a table to store the precomputed values, and the second one finds a better binary signed-digit (BSD) representation. In this article, we propose a new integer similarity strategy for multi-computations. The proposed strategy can aid with precomputing methods or recoding methods to further improve the performance of multi-computations. Based on the integer similarity strategy, we propose two efficient algorithms to improve the performance for BSD sparse forms. The performance factor can be improved from 1.556 to 1.444 and to 1.407, respectively.

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“…In the cryptographic literature, the first left-to-right algorithm for minimal weight radix-2 representations using the digits {0, ±1} was proposed by Joye and Yen [6]. Several authors later proposed left-to-right constructions using the digits {0, ±1, ±3, .…”

Section: Algorithm 2 Scalar Multiplication Via Horner's Rulementioning

confidence: 99%

Unbalanced digit sets and the closest choice strategy for minimal weight integer representations

Heuberger

Muir

2009

Des. Codes Cryptogr.

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An online algorithm is presented that produces an optimal radix-2 representation of an input integer n using digits from the set D ,u = {a ∈ Z : ≤ a ≤ u}, where ≤ 0 and u ≥ 1. The algorithm works by scanning the digits of the binary representation of n from leftto-right (i.e., from most-significant to least-significant). The output representation is optimal in the sense that, of all radix-2 representations of n with digits from D ,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 d2 i , where d ∈ D ,u , that is closest to n with respect to a particular distance function. It is possible to choose values of and u so that the set D ,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 ,u into account.

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Optimal left-to-right binary signed-digit recoding

Cited by 114 publications

References 24 publications

New Minimal Weight Representations for Left-to-Right Window Methods

New Minimal Weight Representations for Left-to-Right Window Methods

Fast Multi-computations with Integer Similarity Strategy

Unbalanced digit sets and the closest choice strategy for minimal weight integer representations

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