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On Fast and Provably Secure Message Authentication Based on Universal Hashing
 In Advances in Cryptology – CRYPTO ’96
, 1996
"... There are wellknown techniques for message authentication using universal hash functions. This approach seems very promising, as it provides schemes that are both efficient and provably secure under reasonable assumptions. This paper contributes to this line of research in two ways. First, it analy ..."
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There are wellknown techniques for message authentication using universal hash functions. This approach seems very promising, as it provides schemes that are both efficient and provably secure under reasonable assumptions. This paper contributes to this line of research in two ways. First, it analyzes the basic construction and some variants under more realistic and practical assumptions. Second, it shows how these schemes can be efficiently implemented, and it reports on the results of empirical performance tests that demonstrate that these schemes are competitive with other commonly employed schemes whose security is less wellestablished. 1 Introduction Message Authentication. Message authentication schemes are an important security tool. As more and more data is being transmitted over networks, the need for secure, highspeed, softwarebased message authentication is becoming more acute. The setting for message authentication is the following. Two parties A and B agree on a secre...
Efficient Computation of Minimal Polynomials in Algebraic Extensions of Finite Fields
 In Proceedings of the 1999 International Symposium on Symbolic and Algebraic Computation (Vancouver, BC
, 1999
"... New algorithms are presented for computing the minimal polynomial over a finite field K of a given element in an algebraic extension of K of the form K[ff] or K[ff][fi]. The new algorithms are explicit and can be implemented rather easily in terms of polynomial multiplication, and are much more effi ..."
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New algorithms are presented for computing the minimal polynomial over a finite field K of a given element in an algebraic extension of K of the form K[ff] or K[ff][fi]. The new algorithms are explicit and can be implemented rather easily in terms of polynomial multiplication, and are much more efficient than other algorithms in the literature. 1 Introduction In this paper, we consider the problem of computing the minimal polynomial over a finite field K of a given element oe in an algebraic extension of K of the form K[ff] or K[ff][fi]. The minimal polynomial of oe is defined to be the unique monic polynomial OE oe=K 2 K[x] of least degree such that OE oe=K (oe) = 0. In the first case, we assume that the ring K[ff] is given as K[x]=(f) where f 2 K[x] is a monic polynomial of degree n, and that elements in K[ff] are represented in the natural way as elements of K[x] !n (the set of polynomials of degree less than n). Similarly, in the second case, we assume that K[ff] is given as a...
Modular Rational Sparse Multivariate Polynomial Interpolation
 In ISSAC ’90: Proceedings of the international symposium on Symbolic and algebraic computation
, 1990
"... The problem of interpolating multivariate polynomials whose coefficient domain is the rational numbers is considered. The effect of intermediate number growth on a speeded BenOr and Tiwari algorithm is studied. Then the newly developed modular algorithm is presented. The computing times for the spe ..."
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The problem of interpolating multivariate polynomials whose coefficient domain is the rational numbers is considered. The effect of intermediate number growth on a speeded BenOr and Tiwari algorithm is studied. Then the newly developed modular algorithm is presented. The computing times for the speeded BenOr and Tiwari and the modular algorithm are compared, and it is shown that the modular algorithm is markedly superior. 1 Introduction Symbolic expressions, that is multivariate polynomials with rational coefficients, are often difficult to manipulate explicitly due to exponential growth in their size. An example is the computation of the determinant of a matrix with polynomial entries. When using straightforward Gaussian elimination over the polynomial entry domain, it can happen that intermediate subdeterminants are very large polynomials while the final answer is an expression of modest size. In this case, however, we can obtain the value of the determinant for a specialization ...
Algorithmbased lowpower and highperformance multimedia signal processing
 Proceedings of the IEEE
, 1998
"... Low power and high performance are the two most important criteria for many signalprocessing system designs, particularly in realtime multimedia applications. There have been many approaches to achieve these two design goals at many different implementation levels ranging from verylargescaleint ..."
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Low power and high performance are the two most important criteria for many signalprocessing system designs, particularly in realtime multimedia applications. There have been many approaches to achieve these two design goals at many different implementation levels ranging from verylargescaleintegration fabrication technology to system design. However, the major drawback is that present approaches are either too costly or not efficient enough. In this paper, we review the works that have been done at various levels and focus on the algorithmbased approaches for lowpower and highperformance design of signalprocessing systems. We present the concept of multirate computing that originates from filterbank design, then show how to employ it along with the other algorithmic methods to develop lowpower and highperformance signalprocessing systems. The proposed multirate design methodology is systematic and applicable to many problems. We demonstrate in this paper that multirate computing is a powerful tool at the algorithmic level that enables designers to achieve either significant power reduction or high throughput depending on their choice. Design examples on basic multimedia processing blocks such as filtering, source coding, and channel coding are given. A digitalsignalprocessing engine that is an adaptive reconfigurable architecture is also derived from the common features of our approach. Such an architecture forms a new generation of highperformance embedded signal processor based on the adaptive computing model. The goal of this paper is to demonstrate the flexibility and effectiveness of algorithmbased approaches and to show that the multirate approach is an effective and systematic design methodology to achieve lowpower and highthroughput signal processing at the algorithmic and architectural level.
High Performance Algorithms To Solve Toeplitz And Block Toeplitz Matrices
, 1996
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AlgorithmBased LowPower/HighSpeed ReedSolomon Decoder Design
 IEEE Trans. on Circuits and SystemsII: Analog and Digital Signal Processing
, 2000
"... Abstract—With the spread of Reed–Solomon (RS) codes to portable wireless applications, lowpower RS decoder design has become important. This paper discusses how the Berlekamp Massey Decoding algorithm can be modified and mapped to obtain a lowpower architecture. In addition, architecture level mod ..."
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Abstract—With the spread of Reed–Solomon (RS) codes to portable wireless applications, lowpower RS decoder design has become important. This paper discusses how the Berlekamp Massey Decoding algorithm can be modified and mapped to obtain a lowpower architecture. In addition, architecture level modifications that speedup the syndrome and error computations are proposed. Then the VLSI architecture and design of the proposed lowpower/highspeed decoder is presented. The proposed design is compared with a normal design that does not use these algorithm/architecture modifications. The power reduction when compared to the normal design is estimated. The results indicate a power reduction of about 40 % or a speedup of 1.34. Index Terms—Berlekamp Massey algorithm, Channel coding,