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855
Cryptanalysis of block ciphers with overdefined systems of equations
, 2002
"... Abstract. Several recently proposed ciphers, for example Rijndael and Serpent, are built with layers of small Sboxes interconnected by linear keydependent layers. Their security relies on the fact, that the classical methods of cryptanalysis (e.g. linear or differential attacks) are based on proba ..."
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Cited by 251 (22 self)
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on probabilistic characteristics, which makes their security grow exponentially with the number of rounds Nr. In this paper we study the security of such ciphers under an additional hypothesis: the Sbox can be described by an overdefined system of algebraic equations (true with probability 1). We show
Designing Against the `Overdefined System of Equations' Attack
, 2004
"... Recently, Courtois and Pieprzyk proposed an attack on symmetric ciphers that takes advantage of a previouslyunexploited property of substitution boxes, or sboxes, in the round function. This paper gives a brief overview of this "overdefined system of equations" attack and shows how the a ..."
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Cited by 1 (0 self)
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Recently, Courtois and Pieprzyk proposed an attack on symmetric ciphers that takes advantage of a previouslyunexploited property of substitution boxes, or sboxes, in the round function. This paper gives a brief overview of this "overdefined system of equations" attack and shows how
Efficient Algorithms for Solving Overdefined Systems of Multivariate Polynomial Equations
 IN ADVANCES IN CRYPTOLOGY, EUROCRYPTâ€™2000, LNCS 1807
, 2000
"... The security of many recently proposed cryptosystems is based on the difficulty of solving large systems of quadratic multivariate polynomial equations. This problem is NPhard over any field. When the number of equations m is the same as the number of unknowns n the best known algorithms are exhaus ..."
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Cited by 183 (20 self)
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of this algorithm is not known, but for sufficiently overdefined systems it was expected to run in polynomial time. In this paper we analyze the theoretical and practical aspects of relinearization. We ran a large number of experiments for various values of n and m, and analysed which systems of equations were
Sketchpad: A manmachine graphical communication system
, 2003
"... The Sketchpad system uses drawing as a novel communication medium for a computer. The system contains input, output, and computation programs which enable it to interpret information drawn directly on a computer display. It has been used to draw electrical, mechanical, scientific, mathematical, and ..."
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Cited by 702 (6 self)
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The Sketchpad system uses drawing as a novel communication medium for a computer. The system contains input, output, and computation programs which enable it to interpret information drawn directly on a computer display. It has been used to draw electrical, mechanical, scientific, mathematical
Bilattices and the Semantics of Logic Programming
, 1989
"... Bilattices, due to M. Ginsberg, are a family of truth value spaces that allow elegantly for missing or conflicting information. The simplest example is Belnap's fourvalued logic, based on classical twovalued logic. Among other examples are those based on finite manyvalued logics, and on prob ..."
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Cited by 444 (13 self)
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Bilattices, due to M. Ginsberg, are a family of truth value spaces that allow elegantly for missing or conflicting information. The simplest example is Belnap's fourvalued logic, based on classical twovalued logic. Among other examples are those based on finite manyvalued logics, and on probabilistic valued logic. A fixed point semantics is developed for logic programming, allowing any bilattice as the space of truth values. The mathematics is little more complex than in the classical twovalued setting, but the result provides a natural semantics for distributed logic programs, including those involving confidence factors. The classical twovalued and the Kripke/Kleene threevalued semantics become special cases, since the logics involved are natural sublogics of Belnap's logic, the logic given by the simplest bilattice. 1 Introduction Often useful information is spread over a number of sites ("Does anybody know, did Willie wear a hat when he left this morning?") that can be speci...
Robust Positioning Algorithms for Distributed AdHoc Wireless Sensor Networks
, 2002
"... A distributed algorithm for determining the positions of nodes in an adhoc, wireless sensor network is explained in detail. Details regarding the implementation of such an algorithm are also discussed. Experimentation is performed on networks containing 400 nodes randomly placed within a square are ..."
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Cited by 383 (9 self)
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A distributed algorithm for determining the positions of nodes in an adhoc, wireless sensor network is explained in detail. Details regarding the implementation of such an algorithm are also discussed. Experimentation is performed on networks containing 400 nodes randomly placed within a square area, and resulting error magnitudes are represented as percentages of each node's radio range. In scenarios with 5% errors in distance measurements, 5% anchor node population (nodes with known locations), and average connectivity levels between neighbors of 7 nodes, the algorithm is shown to have errors less than 33% on average. It is also shown that, given an average connectivity of at least 12 nodes and 10% anchors, the algorithm performs well with up to 40% errors in distance measurements.
Thesis PreProposal: An Efficient Solver of Sparse Overdefined Multivariate Quadratic Equation Systems Over Galois Field 2 8
, 2006
"... Ever since its introduction to the cryptography scene as the official Advanced Encryption Standard in 2001, the security of Rijndael [4] has been open to ..."
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Ever since its introduction to the cryptography scene as the official Advanced Encryption Standard in 2001, the security of Rijndael [4] has been open to
Algebraic Attacks on Stream Ciphers with Linear Feedback
, 2003
"... A classical construction of stream ciphers is to combine several LFSRs and a highly nonlinear Boolean function f . Their security is usually studied in terms of correlation attacks, that can be seen as solving a system of multivariate linear equations, true with some probability. At ICISC'0 ..."
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Cited by 260 (21 self)
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A classical construction of stream ciphers is to combine several LFSRs and a highly nonlinear Boolean function f . Their security is usually studied in terms of correlation attacks, that can be seen as solving a system of multivariate linear equations, true with some probability. At ICISC
Higher Order Correlation Attacks, XL algorithm and Cryptanalysis of Toyocrypt
, 2002
"... Abstract. A popular technique to construct stream ciphers is to use a linear sequence generator with a very large period and good statistical properties and a nonlinear filter. There is abundant literature on how to use linear approximations of this nonlinear function to attack the cipher, which i ..."
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Cited by 67 (8 self)
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is known as (fast) correlation attacks. In this paper we explore nonlinear approximations, much less well known. We will reduce the cryptanalysis of a stream cipher to solving an overdefined system of multivariate equations. At Eurocrypt 2000, Courtois, Klimov, Patarin and Shamir have introduced the XL
NoiseFree Symmetric Fully Homomorphic Encryption Based on NonCommutative Rings
"... A framework of noisefree symmetric fully homomorphic encryption (FHE) is proposed in this work. Different from the frameworks that are defined over noncommutative groups, our framework is constructed from matrices over noncommutative rings. The scheme is oneway secure against chosen plaintext ..."
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attacks (OWCPA) based on the factorization problem of matrices over noncommutative rings as well as the hardness of an overdefined system of multivariate polynomial equations over the given noncommutative algebraic structure. On the basis of this framework, a verifiable FHE is proposed, where
Results 1  10
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