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415,005
Signed binary representations revisited
 Proceedings of CRYPTO’04
, 2004
"... Abstract. The most common method for computing exponentiation of random elements in Abelian groups are sliding window schemes, which enhance the efficiency of the binary method at the expense of some precomputation. In groups where inversion is easy (e.g. elliptic curves), signed representations of ..."
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Cited by 17 (1 self)
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Abstract. The most common method for computing exponentiation of random elements in Abelian groups are sliding window schemes, which enhance the efficiency of the binary method at the expense of some precomputation. In groups where inversion is easy (e.g. elliptic curves), signed representations
Properties of Gray and binary representations
 Evolutionary Computation
"... Representations are formalized as encodings that map the search space to the vertex set of a graph. We define the notion of bit equivalent encodings and show that for such encodings the corresponding Walsh coefficients are also conserved. We focus on Gray codes as particular types of encoding and pr ..."
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Cited by 11 (1 self)
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Representations are formalized as encodings that map the search space to the vertex set of a graph. We define the notion of bit equivalent encodings and show that for such encodings the corresponding Walsh coefficients are also conserved. We focus on Gray codes as particular types of encoding
A Primer on Balanced Binary Representations
, 1992
"... We discuss balanced binary representations. 1 Introduction and Definitions Every nonnegative integer n can be represented essentially uniquely in base 2, as follows: n = � ei2 i ..."
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Cited by 1 (0 self)
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We discuss balanced binary representations. 1 Introduction and Definitions Every nonnegative integer n can be represented essentially uniquely in base 2, as follows: n = � ei2 i
Binary Representations for General CSPs
 In Proceedings of 14th Florida AI Research Symposium (FLAIRS2001), Key West, FL
, 2001
"... It is well known that a nonbinary constraint satisfaction problem (CSP) can be transformed into an equivalent binary CSP using the dual graph transformation. It is also known that the dual graph transformation is impractical in some cases where the CSP has a large number of constraints and/or ..."
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Cited by 1 (1 self)
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It is well known that a nonbinary constraint satisfaction problem (CSP) can be transformed into an equivalent binary CSP using the dual graph transformation. It is also known that the dual graph transformation is impractical in some cases where the CSP has a large number of constraints and
Binary Representations of ABCD Matrices
, 2000
"... The ABCD matrix is one of the essential mathematical instruments in optics. It is the twobytwo representation of the group Sp(2), which is applicable to many branches of physics, including squeezed states of light, special relativity and coupled oscillators. It is pointed out that the shear repres ..."
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representation is oriented to binary logic which may be friendly to computer applications. While this is a future possibility, it is known that paraaxial lens optics is based on the shear representation of the Sp(2) group. It is pointed out that the most general form of the ABCD matrix can be written in terms
LowWeight Binary Representations for Pairs of Integers
, 2001
"... . Shamir's method speeds up the computation of the product of powers of two elements of a group, a common object in publickey algorithms. Shamir's method is based on binary expansions and was designed for modular and nite eld arithmetic. Elliptic curve arithmetic uses signed binary ex ..."
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Cited by 67 (0 self)
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expansions rather than the ordinary binary expansions of modular arithmetic. This note extends Shamir's method to the elliptic curve setting by specifying an optimal signed binary representation for a pair of positive integers. 1 Shamir Methods Shamir suggested [4] a simple but powerful trick
Improving the Locality Properties of Binary Representations
"... Abstract. Choosing representations and operators that preserve locality between genotype and phenotype space is an important goal in EA design. In the GA literature there has been considerable discussion of this issue with respect to the choice between standard binary encoding and Gray codes. In thi ..."
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Abstract. Choosing representations and operators that preserve locality between genotype and phenotype space is an important goal in EA design. In the GA literature there has been considerable discussion of this issue with respect to the choice between standard binary encoding and Gray codes
Search, binary representations, and counting optima
 In Evolutionary Computing: AISB Workshop
, 1998
"... Choosing a good representation is a vital component of solving any search problem. However, choosing a good representation for a problem is as difficult as choosing a good search algorithm for a problem. Wolpert and Macready's No Free Lunch theorem proves that no search algorithm is better than ..."
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Cited by 3 (1 self)
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representations commonly used in genetic algorithms: Binary Reflected Gray coding and standard Binary encoding.
Symbolic Boolean manipulation with ordered binarydecision diagrams
 ACM COMPUTING SURVEYS
, 1992
"... Ordered BinaryDecision Diagrams (OBDDS) represent Boolean functions as directed acyclic graphs. They form a canonical representation, making testing of functional properties such as satmfiability and equivalence straightforward. A number of operations on Boolean functions can be implemented as grap ..."
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Cited by 1022 (13 self)
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Ordered BinaryDecision Diagrams (OBDDS) represent Boolean functions as directed acyclic graphs. They form a canonical representation, making testing of functional properties such as satmfiability and equivalence straightforward. A number of operations on Boolean functions can be implemented
LCF: A lexicographic binary representation of the rationals
 J. Universal Comput. Sci
, 1995
"... Abstract: A binary representation of the rationals derived from their continued fraction expansions is described and analysed. The concepts \adjacency", \mediant " and \convergent " from the literature on Farey fractions and continued fractions are suitably extended to pro ..."
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Cited by 8 (0 self)
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Abstract: A binary representation of the rationals derived from their continued fraction expansions is described and analysed. The concepts \adjacency", \mediant " and \convergent " from the literature on Farey fractions and continued fractions are suitably extended
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