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Page 3703 of Mathematical Reviews Vol. , Issue 94g [page]

1994 Mathematical Reviews  
(D-BONN-C; Bonn) Efficient randomized generation of optimal algorithms for multiplication in certain finite fields. (English summary) Comput. Complexity 2 (1992), no. 1, 67-96.  ...  Then the main algorithm (for multiplication in a finite field) is described in terms of the preliminary elliptic curve algorithms. Theresa P.  ... 

Efficient Software Implementation for Finite Field Multiplication in Normal Basis [chapter]

Peng Ning, Yiqun Lisa Yin
2001 Lecture Notes in Computer Science  
In this paper, we present new techniques for efficient software implementation of binary field multiplication in normal basis.  ...  Among various arithmetic operations, finite field multiplication is of particular interest since it is a major building block for elliptic curve cryptosystems.  ...  Finite Field GF (2 m ) and Normal Basis Representation The finite field GF (2 m ) is the set of all 2 m possible 0-1 strings of length m, with certain rules for field addition and multiplication.  ... 
doi:10.1007/3-540-45600-7_21 fatcat:lblnb2vatfh67mxvisatad4awq

A Low-Power Design for an Elliptic Curve Digital Signature Chip [chapter]

Richard Schroeppel, Cheryl Beaver, Rita Gonzales, Russell Miller, Timothy Draelos
2003 Lecture Notes in Computer Science  
Our optimizations include using the point-halving algorithm for elliptic curves, field towers to speed up the finite field arithmetic in general, and further enhancements of basic finite field arithmetic  ...  In the case of squaring, square root, and solving the equation a = z 2 + z for z (which we call "QSolve"), we note that the algorithmic descriptions can be reduced to simple XORs of the input bits.  ...  The authors would like to thank Mark Torgerson for many useful discussions and comments.  ... 
doi:10.1007/3-540-36400-5_27 fatcat:zojqd2cwvbfslip63obhllsjeu

Efficient software implementations of large finite fieldsGF(2n) for secure storage applications

Jianqiang Luo, Kevin D. Bowers, Alina Oprea, Lihao Xu
2012 ACM Transactions on Storage  
We show that by exploiting known techniques, as well as new optimizations, we are able to efficiently support operations over finite fields of interest.  ...  Finite fields are widely used in constructing error-correcting codes and cryptographic algorithms.  ...  We aim to optimize the performance of a general software implementation for finite fields. There are several open source implementations for finite fields.  ... 
doi:10.1145/2093139.2093141 fatcat:fmtftcckbbh3vny3ii5wv5xzny

Page 7944 of Mathematical Reviews Vol. , Issue 97M [page]

1997 Mathematical Reviews  
finite fields.  ...  Asymptotic efficiency of the new algorithms is estimated and numerical results are given.”  ... 

Page 5419 of Mathematical Reviews Vol. , Issue 82m [page]

1982 Mathematical Reviews  
Ideas of linear systems theory are used to deal with the statistical properties of fields and waves in random moving media.  ...  The systems in question vary randomly in space and time, and the inputs and outputs are random fields.  ... 

Network coding over the 232−5 prime field

Morten Videbaek Pedersen, Janus Heide, Peter Vingelmann, Frank H. P. Fitzek
2013 2013 IEEE International Conference on Communications (ICC)  
Creating efficient finite field implementations has been an active research topic for several decades.  ...  In this paper we investigate the use of prime fields with a field size of 2 32 − 5, as this allows implementations which combines high field sizes and low complexity.  ...  For this reason we will refer to this type of finite field as an Optimal Prime Field (OPF).  ... 
doi:10.1109/icc.2013.6654986 dblp:conf/icc/PedersenHVF13 fatcat:isf2g6pfircmdcawbumhzu4w7y

Special issue computational algebraic complexity editorial

Erich Kaltofen, Bruno Buchberger
1990 Journal of symbolic computation  
Shoup (1990) has been able to show that primitive elements in large finite fields can be selected using few random bits.  ...  The article by R6nyal studies, from an algorithmic point of view, the Wedderburn-Artin structure theory of finite dimensional associative algebras over a finite field.  ... 
doi:10.1016/s0747-7171(08)80010-7 fatcat:wrri7sabmjb4tpqtqyfbwuoa6e

Optimal Path Analysis for Solving Nonlinear Equations with Finite Local Error

Xiaoxiao Ma, Xiaojuan Chen
2022 North atlantic university union: International Journal of Circuits, Systems and Signal Processing  
Firstly, according to the finite condition of local error, the optimization objective function of nonlinear equations is established.  ...  Because the traditional method of solving nonlinear equations takes a long time, an optimal path analysis method for solving nonlinear equations with limited local error is designed.  ...  The particle swarm optimization algorithm is initialized as a random solution of a bunch of random particles, and then the optimal solution is found through iteration.  ... 
doi:10.46300/9106.2022.16.13 fatcat:uufdqmtfcnefnmygty5i734g6u

Page 1555 of Mathematical Reviews Vol. , Issue 92c [page]

1992 Mathematical Reviews  
The algorithm has a random number of recursive levels and it reduces the generation of the Poisson random variable with parameter A to generating gamma, binomial and other Poisson random variables (with  ...  1555 65D cost) of a known recursive method for generating Poisson random variables with parameter A.  ... 

Page 1661 of Mathematical Reviews Vol. , Issue 91C [page]

1991 Mathematical Reviews  
Summary: “An efficient parallel algorithm (RNC?) for the two- processor scheduling problem is presented.  ...  Three types of tasks are considered that are based on different accuracy criteria for the roots. A general type of implementable algorithm is defined.  ... 

Structural Damage Recognition Based on the Finite Element Method and Quantum Particle Swarm Optimization Algorithm

Xin Zhang, Junjie Zhang, Yutao Hu, Tao Tang, Jianhai Yang, Yuxiang Zhang
2020 IEEE Access  
Therefore, the combination of finite element method and quantum particle swarm optimization algorithm is quite effective for guaranteeing high accuracy and efficiency for damage parameters' recognition  ...  And after multiple iteration optimization of the artificial intelligence algorithm -quantum particle swarm optimization algorithm QPSO, the identification error of damage parameters including location  ...  In other words, when the generated random number is greater than 0.5, "-" is taken, otherwise "+" is taken.  ... 
doi:10.1109/access.2020.3026068 fatcat:lzrg64vxtjcfdniwagrfwvlq4e

Efficient Random Network Coding for Distributed Storage Systems [chapter]

Ádám Visegrádi, Péter Kacsuk
2014 Lecture Notes in Computer Science  
This paper presents our experiences about the realization of random network coding based on the discrete logarithm of the finite field.  ...  We discuss possible performance optimizations for such a system, and provide performance measurement results focusing on data storage scenarios.  ...  In our implementation, we used discrete logarithm tables to perform finite field multiplications.  ... 
doi:10.1007/978-3-642-54420-0_38 fatcat:mh23acy7zffnjeinfgpffu3j24

Page 1449 of Mathematical Reviews Vol. , Issue 99b [page]

1991 Mathematical Reviews  
Among other things, this construction allows for the development of wavelet transforms over finite fields. Potential applications of this construct in algebraic coding are discussed.”  ...  Monagan, Efficient multivariate factorization over finite fields (15-28); Peter Boyvalenkov and Danyo Danev, On maximal codes in polynomial metric spaces (29-38); Massimo Caboara, Pasqualina Conti and  ... 

Simulation Analysis of Multiple BP Decoding Algorithm and FFT-BP Decoding Algorithm

Xin Wei, Zhigang Li, Zheng Dou
2017 International Journal of Communications, Network and System Sciences  
In order to solve the problem that the original decoding algorithm of multi-band LDPC codes is high and is not conducive to hardware implementation, two simplified decoding algorithms for multi-band LDPC  ...  The simulation results show that the FFT-BP decoding algorithm is more convenient and efficient.  ...  Multivariate LDPC Coding Algorithm Definition and Operation of Finite Field GF (q) Domain Field F is a set of elements that define two operations, plus "+" and multiplication " "and both of which satisfy  ... 
doi:10.4236/ijcns.2017.108b027 fatcat:jo5q5xmupjavnefffzpcsmrfg4
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