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Survey and Benchmark of Block Ciphers for Wireless Sensor Networks
 ACM Transactions on Sensor Networks
, 2004
"... Choosing the most storage and energye#cient block cipher specifically for wireless sensor networks (WSNs) is not as straightforward as it seems. To our knowledge so far, there is no systematic evaluation framework for the purpose. In this paper, we have identified the candidates of block ciphe ..."
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Choosing the most storage and energye#cient block cipher specifically for wireless sensor networks (WSNs) is not as straightforward as it seems. To our knowledge so far, there is no systematic evaluation framework for the purpose. In this paper, we have identified the candidates of block ciphers suitable for WSNs based on existing literature.
Essential algebraic structure within the AES
, 2002
"... Abstract. One difficulty in the cryptanalysis of the Advanced Encryption Standard AES is the tension between operations in the two fields GF (2 8) and GF (2). This paper outlines a new approach that avoids this conflict. We define a new block cipher, the BES, that uses only simple algebraic operatio ..."
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Cited by 77 (7 self)
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Abstract. One difficulty in the cryptanalysis of the Advanced Encryption Standard AES is the tension between operations in the two fields GF (2 8) and GF (2). This paper outlines a new approach that avoids this conflict. We define a new block cipher, the BES, that uses only simple algebraic operations in GF (2 8). Yet the AES can be regarded as being identical to the BES with a restricted message space and key space, thus enabling the AES to be realised solely using simple algebraic operations in one field GF (2 8). This permits the exploration of the AES within a broad and rich setting. One consequence is that AES encryption can be described by an extremely sparse overdetermined multivariate quadratic system over GF (2 8), whose solution would recover an AES key.
Most tensor problems are NP hard
 CORR
, 2009
"... The idea that one might extend numerical linear algebra, the collection of matrix computational methods that form the workhorse of scientific and engineering computing, to numerical multilinear algebra, an analogous collection of tools involving hypermatrices/tensors, appears very promising and has ..."
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Cited by 45 (6 self)
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The idea that one might extend numerical linear algebra, the collection of matrix computational methods that form the workhorse of scientific and engineering computing, to numerical multilinear algebra, an analogous collection of tools involving hypermatrices/tensors, appears very promising and has attracted a lot of attention recently. We examine here the computational tractability of some core problems in numerical multilinear algebra. We show that tensor analogues of several standard problems that are readily computable in the matrix (i.e. 2tensor) case are NP hard. Our list here includes: determining the feasibility of a system of bilinear equations, determining an eigenvalue, a singular value, or the spectral norm of a 3tensor, determining a best rank1 approximation to a 3tensor, determining the rank of a 3tensor over R or C. Hence making tensor computations feasible is likely to be a challenge.
Building secure tamelike multivariate publickey cryptosystems: The new TTS
 In ACISP 2005, volume 3574 of LNCS
, 2005
"... Abstract. Multivariate publickey cryptosystems (sometimes polynomialbased PKC’s or just multivariates) handle polynomials of many variables over relatively small fields instead of elements of a large ring or group. The “tamelike ” or “sparse ” class of multivariates are distinguished by the relat ..."
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Cited by 13 (3 self)
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Abstract. Multivariate publickey cryptosystems (sometimes polynomialbased PKC’s or just multivariates) handle polynomials of many variables over relatively small fields instead of elements of a large ring or group. The “tamelike ” or “sparse ” class of multivariates are distinguished by the relatively few terms that they have per central equation. We explain how they differ from the “bigfield ” type of multivariates, represented by derivatives of C ∗ and HFE, how they are better, and give basic security criteria for them. The last is shown to be satisfied by efficient schemes called “Enhanced TTS ” which is built on a combination of the OilandVinegar and Triangular ideas. Their security levels are estimated. In this process we summarize and in some cases, improve rankbased attacks, which seek linear combinations of certain matrices at given ranks. These attacks are responsible for breaking many prior multivariate designs. 1 Introduction: Multivariate
A more secure and efficacious TTS signature scheme
 ICISC, LECTURE NOTES IN COMPUTER SCIENCE
, 2003
"... In 2002 the authors introduced the new genre of digital signature scheme TTS (Tame Transformation Signatures) along with a sample scheme TTS/2. TTS is from the family of multivariate cryptographic schemes to which the NESSIE primitive SFLASH also belongs. It is a realization of T. Moh’s theory ([31 ..."
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Cited by 10 (1 self)
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In 2002 the authors introduced the new genre of digital signature scheme TTS (Tame Transformation Signatures) along with a sample scheme TTS/2. TTS is from the family of multivariate cryptographic schemes to which the NESSIE primitive SFLASH also belongs. It is a realization of T. Moh’s theory ([31]) for digital signatures, based on Tame Transformations or Tame Maps. Properties of multivariate cryptosystems are determined mainly by their central maps. TTS uses Tame Maps as their central portion for even greater speed than ¥§ ¦derived SFLASH family of schemes, which uses monomials in a large field for the central portion, previously usually acknowledged as fastest. We show a small flaw in TTS/2 and present an improved TTS implementation which we call TTS/4. We will examine in some detail how well TTS/4 performs, how it stands up to previously known attacks, and why it represents an advance over TTS/2. Based on this topical assessment, we consider TTS in general and TTS/4 in particular to be competitive or superior in several aspects to other schemes, partly because the theoretical roots of TTS induce many good traits. One specific area in which TTS/4 should excel is in lowcost smartcards. It seems that the genre has great potential for practical deployment and deserves further attention by the cryptological community.
Multivariate polynomials for hashing
 In Inscrypt, Lecture Notes in Computer Science
, 2007
"... Abstract. We propose the idea of building a secure hash using quadratic or higher degree multivariate polynomials over a finite field as the compression function. We analyze some security properties and potential feasibility, where the compression functions are randomly chosen highdegree polynomials ..."
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Abstract. We propose the idea of building a secure hash using quadratic or higher degree multivariate polynomials over a finite field as the compression function. We analyze some security properties and potential feasibility, where the compression functions are randomly chosen highdegree polynomials, and show that under some plausible assumptions, highdegree polynomials as compression functions has good properties. Next, we propose to improve on the efficiency of the system by using some specially designed polynomials generated by a small number of random parameters, where the security of the system would then relies on stronger assumptions, and we give empirical evidence for the validity of using such polynomials.
Learning Fuzzy Rules with Evolutionary Algorithms — an Analytic Approach
"... Abstract. This paper provides an analytical approach to fuzzy rule base optimization. While most research in the area has been done experimentally, our theoretical considerations give new insights to the task. Using the symmetry that is inherent in our formulation, we show that the problem of findin ..."
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Abstract. This paper provides an analytical approach to fuzzy rule base optimization. While most research in the area has been done experimentally, our theoretical considerations give new insights to the task. Using the symmetry that is inherent in our formulation, we show that the problem of finding an optimal rule base can be reduced to solving a set of quadratic equations that generically have a one dimensional solution space. This alternate problem specification can enable new approaches for rule base optimization. 1
HFhash: Hash Functions Using Restricted HFE
 Challenge1”, in International Journal of Advanced Science and Technology
, 2011
"... Vulnerability of dedicated hash functions to various attacks has made the task of designing hash function much more challenging. This provides us a strong motivation to design a new cryptographic hash function viz. HFhash. This is a hash function, whose compression function is designed by using fir ..."
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Vulnerability of dedicated hash functions to various attacks has made the task of designing hash function much more challenging. This provides us a strong motivation to design a new cryptographic hash function viz. HFhash. This is a hash function, whose compression function is designed by using first 32 polynomials of HFE Challenge1 [8] with 64 variables by forcing remaining 16 variables as zero. HFhash gives 256 bits message digest and is as efficient as SHA256. It is secure against the differential attack proposed by Chabaud and Joux in [6] as well as by Wang et. al. in [25] applied to SHA0 and SHA1. We have also compared the efficiency of our HFhash with SHA256.
Secure and Efficient LCMQ Entity Authentication Protocol
"... The simple, computationally efficient HBlike entity authentication protocols based on the learning parity with noise (LPN) problem have attracted a great deal of attention in the past few years due to the broad application prospect in lowcost RFID tags. However, all previous protocols are vulnerab ..."
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The simple, computationally efficient HBlike entity authentication protocols based on the learning parity with noise (LPN) problem have attracted a great deal of attention in the past few years due to the broad application prospect in lowcost RFID tags. However, all previous protocols are vulnerable to a maninthemiddle attack discovered by Ouafi, Overbeck, and Vaudenay. In this paper, we propose a lightweight authentication protocol named LCMQ and prove it secure in a general maninthemiddle model. The technical core in our proposal is a special type of circulant matrix, for which we prove the linear independence of matrix vectors, present efficient algorithms on matrix operations, and describe a secure encryption against ciphertextonly attack. By combining all of those with LPN and related to the multivariate quadratic problem, the LCMQ protocol not only is provably secure against all probabilistic polynomialtime adversaries, but also outperforms all HBlike protocols, in terms of tag’s computation overhead, storage expense, and communication cost.
Algorithms
"... to solve massively underdefined systems of multivariate quadratic equations ..."
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to solve massively underdefined systems of multivariate quadratic equations