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Fuzzy extractors: How to generate strong keys from biometrics and other noisy data. Technical Report 2003/235, Cryptology ePrint archive, http://eprint.iacr.org, 2006. Previous version appeared at EUROCRYPT 2004
 34 [DRS07] [DS05] [EHMS00] [FJ01] Yevgeniy Dodis, Leonid Reyzin, and Adam
, 2004
"... We provide formal definitions and efficient secure techniques for • turning noisy information into keys usable for any cryptographic application, and, in particular, • reliably and securely authenticating biometric data. Our techniques apply not just to biometric information, but to any keying mater ..."
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Cited by 470 (37 self)
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We provide formal definitions and efficient secure techniques for • turning noisy information into keys usable for any cryptographic application, and, in particular, • reliably and securely authenticating biometric data. Our techniques apply not just to biometric information, but to any keying material that, unlike traditional cryptographic keys, is (1) not reproducible precisely and (2) not distributed uniformly. We propose two primitives: a fuzzy extractor reliably extracts nearly uniform randomness R from its input; the extraction is errortolerant in the sense that R will be the same even if the input changes, as long as it remains reasonably close to the original. Thus, R can be used as a key in a cryptographic application. A secure sketch produces public information about its input w that does not reveal w, and yet allows exact recovery of w given another value that is close to w. Thus, it can be used to reliably reproduce errorprone biometric inputs without incurring the security risk inherent in storing them. We define the primitives to be both formally secure and versatile, generalizing much prior work. In addition, we provide nearly optimal constructions of both primitives for various measures of “closeness” of input data, such as Hamming distance, edit distance, and set difference.
On irregularities of distribution
 Mathematika
, 1954
"... constantweight codes, distance distribution, equidistant codes, linear programming bound New lower bounds are presented on the second moment of the distance distribution of binary codes, in terms of the first moment of the distribution. These bounds are used to obtain upper bounds on the size of co ..."
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Cited by 73 (0 self)
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constantweight codes, distance distribution, equidistant codes, linear programming bound New lower bounds are presented on the second moment of the distance distribution of binary codes, in terms of the first moment of the distribution. These bounds are used to obtain upper bounds on the size of codes whose maximum distance is close to their minimum distance. It is then demonstrated how such bounds can be applied to bound from below the smallest attainable ratio between the maximum distance and the minimum distance of codes. Finally, counterparts of the bounds are derived for the special case of constantweight codes.
Extractor Codes
, 2001
"... We de ne new error correcting codes based on extractors. Weshow that for certain choices of parameters these codes have better list decoding properties than are known for other codes, and are provably better than ReedSolomon codes. We further show that codes with strong list decoding properties ar ..."
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Cited by 50 (7 self)
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We de ne new error correcting codes based on extractors. Weshow that for certain choices of parameters these codes have better list decoding properties than are known for other codes, and are provably better than ReedSolomon codes. We further show that codes with strong list decoding properties are equivalent to slice extractors, a variant of extractors. Wegive an application of extractor codes to extracting many hardcore bits from a oneway function, using few auxiliary random bits. Finally,weshow that explicit slice extractors for certain other parameters would yield optimal bipartite Ramsey graphs.
A New Algorithm For The MaximumWeight Clique Problem
"... Given a graph, in the maximum clique problem one wants to find the largest number of vertices, any two of which are adjacent. In the maximumweight clique problem, the vertices have positive, integer weights, and one wants to find a clique with maximum weight. A recent algorithm for the maximum cliq ..."
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Cited by 31 (0 self)
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Given a graph, in the maximum clique problem one wants to find the largest number of vertices, any two of which are adjacent. In the maximumweight clique problem, the vertices have positive, integer weights, and one wants to find a clique with maximum weight. A recent algorithm for the maximum clique problem is here used as a basis for developing an algorithm for the weighted case. Computational experiments with random graphs show that this new algorithm is faster than earlier algorithms in many cases. A set of weighted graphs obtained from the problem of constructing good constant weight errorcorrecting codes are proposed as test cases for maximumweight clique algorithms
New List Decoding Algorithms for ReedSolomon and BCH Codes
 SUBMITTED TO IEEE TRANS. INFORM. THEORY
, 2007
"... In this paper we reduce a class of algebraic equation systems to a rational curvefitting problem by means of the BerlekampMassey algorithm, and present a novel algorithm to list all solutions in discrete space. The proposed algorithm, when applied to list decoding of ReedSolomon and BCH codes, • ..."
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Cited by 17 (1 self)
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In this paper we reduce a class of algebraic equation systems to a rational curvefitting problem by means of the BerlekampMassey algorithm, and present a novel algorithm to list all solutions in discrete space. The proposed algorithm, when applied to list decoding of ReedSolomon and BCH codes, • corrects up to 1 − √ 1 − D errors for (generalized) ReedSolomon codes, identical to that of the GuruswamiSudan algorithm which is built upon the BerlekampWelch algorithm, where D denote the normalized minimum distance, however, provides a much tighter bound on the list size. • outperforms the GuruswamiSudan algorithm when the multiple syndrome sequences are available, e.g., in decoding ReedSolomon codes in terms of phased error bursts and in decoding interleaved ReedSolomon codes under nonbinary symmetric channels. • with appropriate modifications, corrects up to 1 2 (1 − √ 1 − 2D) errors for binary BCH codes, which is the best known bound under polynomial complexity. • with trivial simplifications, corrects up to ⌊ d d+1 2 ⌋ errors for ReedSolomon codes or up to ⌊ 2 ⌋ errors for binary BCH codes (where d denotes the minimum distance), while maintaining the same computational complexity as the BerlekampMassey algorithm. • exhibits polynomial complexity in nature, in particular, requires O ( n 6 (1 − √ 1 − D) 7) field operations for (generalized) ReedSolomon codes and O ( n 6 (1 − √ 1 − 2D) 7) for binary BCH codes in achieving its maximum list error correction capability (n denotes code length), whereas the most efficient implementation of the GuruswamiSudan algorithm has complexity O(n 10 (1 − D) 4).
Extensions to the Johnson bound
, 2001
"... We present extensions of some recent geometric proofs of the wellknown Johnson bound. Our extensions apply to arbitrary alphabets (while previous proofs were given only for the binary case). Our extensions yield a "weighted " version of the Johnson bound equally easily  the weighted ver ..."
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Cited by 16 (4 self)
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We present extensions of some recent geometric proofs of the wellknown Johnson bound. Our extensions apply to arbitrary alphabets (while previous proofs were given only for the binary case). Our extensions yield a "weighted " version of the Johnson bound equally easily  the weighted version is of interest in light of the recent developments on softdecision list decoding algorithms.
A new Table of Constant Weight Codes of Length Greater than 28
 THE ELECTRONIC JOURNAL OF COMBINATORICS
, 2006
"... Existing tables of constant weight codes are mainly confined to codes of length n ≤ 28. This paper presents tables of codes of lengths 29 ≤ n ≤ 63. The motivation for creating these tables was their application to the generation of good sets of frequency hopping lists in radio networks. The complete ..."
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Cited by 12 (1 self)
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Existing tables of constant weight codes are mainly confined to codes of length n ≤ 28. This paper presents tables of codes of lengths 29 ≤ n ≤ 63. The motivation for creating these tables was their application to the generation of good sets of frequency hopping lists in radio networks. The complete generation of all relevant cases by a small number of algorithms is augmented in individual cases by miscellaneous constructions. These sometimes give a larger number of codewords than the algorithms.
Improved Upper Bounds on Sizes of Codes
 IEEE TRANS. INFORM. THEORY
, 2002
"... Let A(n, d) denote the maximum possible number of codewords in a binary code of length and minimum Hamming distance . For large values of , the best known upper bound, for fixed , is the Johnson bound. We give a new upper bound which is at least as good as the Johnson bound for all values of and , a ..."
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Cited by 7 (2 self)
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Let A(n, d) denote the maximum possible number of codewords in a binary code of length and minimum Hamming distance . For large values of , the best known upper bound, for fixed , is the Johnson bound. We give a new upper bound which is at least as good as the Johnson bound for all values of and , and for each there are infinitely many values of for which the new bound is better than the Johnson bound. For small values of and , the best known method to obtain upper bounds on ( ) is linear programming. We give new inequalities for the linear programming and show that with these new inequalities some of the known bounds on ( ) for 28 are improved.
Bounds for codes by semidefinite programming
, 2006
"... Delsarte’s method and its extensions allow to consider the upper bound problem for codes in 2pointhomogeneous spaces as a linear programming problem with perhaps infinitely many variables, which are the distance distribution. We show that using as variables power sums of distances this problem can ..."
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Cited by 6 (4 self)
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Delsarte’s method and its extensions allow to consider the upper bound problem for codes in 2pointhomogeneous spaces as a linear programming problem with perhaps infinitely many variables, which are the distance distribution. We show that using as variables power sums of distances this problem can be considered as a finite semidefinite programming problem. This method allows to improve some linear programming upper bounds. In particular we obtain new bounds of onesided kissing numbers. 1