Finite Fields and Their Applications, ISSN 1071-5797, 01/2014, Volume 25, pp. 222 - 233

We present some new constructions of families of pseudorandom sequences of symbols, which generalize several previous constructions for the binary case.

Pseudorandom sequences | Lehmer problem | Correlation | Exponential sums | Characters | BINARY SEQUENCES | EXPONENTIAL-SUMS | MATHEMATICS, APPLIED | MODULUS | NUMBERS | LIOUVILLE FUNCTION | D-H-LEHMER | MULTIPLICATIVE INVERSE | MATHEMATICS | COMPLEXITY | LARGE FAMILIES

Pseudorandom sequences | Lehmer problem | Correlation | Exponential sums | Characters | BINARY SEQUENCES | EXPONENTIAL-SUMS | MATHEMATICS, APPLIED | MODULUS | NUMBERS | LIOUVILLE FUNCTION | D-H-LEHMER | MULTIPLICATIVE INVERSE | MATHEMATICS | COMPLEXITY | LARGE FAMILIES

Journal Article

Acta Arithmetica, ISSN 0065-1036, 2016, Volume 174, Issue 3, pp. 199 - 215

Journal Article

Designs, Codes and Cryptography, ISSN 0925-1022, 11/2014, Volume 73, Issue 2, pp. 319 - 328

We estimate discrete Fourier transform, ambiguity, and Hamming-auto-correlation of $$m$$ m -ary sequences in terms of their (periodic) correlation measure of...

Information and Communication, Circuits | Correlation | 11T71 | Discrete Fourier transform | Data Encryption | Mathematics | Pseudorandom sequences | Data Structures, Cryptology and Information Theory | Discrete Mathematics in Computer Science | Coding and Information Theory | 94A60 | Combinatorics | Autocorrelation | Ambiguity | BINARY SEQUENCES | MATHEMATICS, APPLIED | COMPUTER SCIENCE, THEORY & METHODS

Information and Communication, Circuits | Correlation | 11T71 | Discrete Fourier transform | Data Encryption | Mathematics | Pseudorandom sequences | Data Structures, Cryptology and Information Theory | Discrete Mathematics in Computer Science | Coding and Information Theory | 94A60 | Combinatorics | Autocorrelation | Ambiguity | BINARY SEQUENCES | MATHEMATICS, APPLIED | COMPUTER SCIENCE, THEORY & METHODS

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 01/2017, Volume 216, p. 589

Pseudorandom binary sequences play a crucial role in cryptography. The classical approach to pseudorandomness of binary sequences is based on computational...

Pseudorandom sequences | Applied mathematics | Lattices | Cryptography | Combinatorics | Pseudorandom binary sequences

Pseudorandom sequences | Applied mathematics | Lattices | Cryptography | Combinatorics | Pseudorandom binary sequences

Journal Article

IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, ISSN 0916-8508, 2014, Volume E97-A, Issue 4, pp. 970 - 974

We determine the linear complexity of binary sequences derived from the polynomial quotient modulo p defined by F(u) equivalent to f(u) - f(p)(u)/p (mod p), 0...

Finite fields | Linear complexity | Cryptography | Polynomial quotients | Pseudorandom binary sequences | finite fields | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | linear complexity | FERMAT QUOTIENTS | CHARACTER SUMS | VALUE SET | COMPUTER SCIENCE, INFORMATION SYSTEMS | cryptography | polynomial quotients | pseudorandom binary sequences | ENGINEERING, ELECTRICAL & ELECTRONIC

Finite fields | Linear complexity | Cryptography | Polynomial quotients | Pseudorandom binary sequences | finite fields | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | linear complexity | FERMAT QUOTIENTS | CHARACTER SUMS | VALUE SET | COMPUTER SCIENCE, INFORMATION SYSTEMS | cryptography | polynomial quotients | pseudorandom binary sequences | ENGINEERING, ELECTRICAL & ELECTRONIC

Journal Article

Chaos, ISSN 1054-1500, 10/2018, Volume 28, Issue 10

We develop a pseudorandom bit generator using chaotic true orbits of the Bernoulli map on real cubic algebraic integers having complex conjugates. Although...

Integers | Pseudorandom sequences | Seeds | Algebra | Computer simulation | Upper bounds | Binary system | Pseudorandom binary sequences

Integers | Pseudorandom sequences | Seeds | Algebra | Computer simulation | Upper bounds | Binary system | Pseudorandom binary sequences

Journal Article

Acta Arithmetica, ISSN 0065-1036, 2008, Volume 133, Issue 2, pp. 109 - 125

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 05/2007, Volume 135, Issue 5, pp. 1309 - 1318

Let p be an odd prime. Define e_n=\left\{\begin{array}{ll}\displaystyle (-1)^{n+\overline{n}}, & \hbox{if n is a quadratic residue mod p},...

Pseudorandom sequences | Integers | Numbers | Mathematical sequences | Mathematical functions | Number theory | Inverse. this work was supported by the nsf | Binary sequence | 60472068) of p. r. china | Pseudorandom | pseudorandom | KLOOSTERMAN SUMS | MATHEMATICS | inverse | BINARY SEQUENCES | MATHEMATICS, APPLIED | LIOUVILLE FUNCTION | D-H-LEHMER | FORMULA | binary sequence

Pseudorandom sequences | Integers | Numbers | Mathematical sequences | Mathematical functions | Number theory | Inverse. this work was supported by the nsf | Binary sequence | 60472068) of p. r. china | Pseudorandom | pseudorandom | KLOOSTERMAN SUMS | MATHEMATICS | inverse | BINARY SEQUENCES | MATHEMATICS, APPLIED | LIOUVILLE FUNCTION | D-H-LEHMER | FORMULA | binary sequence

Journal Article

IEEE Transactions on Information Theory, ISSN 0018-9448, 1998, Volume 44, Issue 2, pp. 814 - 817

Journal Article

Applicable Algebra in Engineering, Communication and Computing, ISSN 0938-1279, 12/2015, Volume 26, Issue 6, pp. 555 - 570

We give the trace representation of a family of binary sequences derived from Euler quotients by determining the corresponding defining polynomials. The result...

Trace function | Theory of Computation | 11B68 | Euler quotients | Fermat quotients | 65C10 | Computer Hardware | Computer Science | Artificial Intelligence (incl. Robotics) | 94A60 | Symbolic and Algebraic Manipulation | Cryptography | 94A55 | Pseudorandom binary sequences | MATHEMATICS, APPLIED | NUMBERS | CHARACTER SUMS | LINEAR COMPLEXITY | DIVISIBILITY | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | VALUE SET | COMPUTER SCIENCE, THEORY & METHODS | Analysis

Trace function | Theory of Computation | 11B68 | Euler quotients | Fermat quotients | 65C10 | Computer Hardware | Computer Science | Artificial Intelligence (incl. Robotics) | 94A60 | Symbolic and Algebraic Manipulation | Cryptography | 94A55 | Pseudorandom binary sequences | MATHEMATICS, APPLIED | NUMBERS | CHARACTER SUMS | LINEAR COMPLEXITY | DIVISIBILITY | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | VALUE SET | COMPUTER SCIENCE, THEORY & METHODS | Analysis

Journal Article

Journal of Information Security, ISSN 2153-1234, 10/2014, Volume 5, Issue 4, pp. 218 - 218

This paper proposes an efficient, high-tech method of construction of pseudorandom binary sequences generators with a repetition period 2 super( n) for n-bit...

Nonlinear feedback | Construction | Feedback | Shift registers | Nonlinearity | Generators | Computer information security | Pseudorandom binary sequences

Nonlinear feedback | Construction | Feedback | Shift registers | Nonlinearity | Generators | Computer information security | Pseudorandom binary sequences

Journal Article

IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, ISSN 0916-8508, 01/2019, Volume E102A, Issue 11, p. 1566

Pseudo-random sequences with good statistical property, such as low autocorrelation, high linear complexity and 2-adic complexity, have been widely applied to...

Pseudorandom sequences | Algorithms | Binary system | Shift registers | Encryption | Magma | Complexity

Pseudorandom sequences | Algorithms | Binary system | Shift registers | Encryption | Magma | Complexity

Journal Article

Optical Engineering, ISSN 0091-3286, 5/2017, Volume 56, Issue 5, pp. 057104 - 057104

The application of electro-optic effect in lithium-niobate-based Mach-Zehnder interferometer to design a 3-bit optical pseudorandom binary sequence (PRBS)...

Mach-Zehnder interferometer | D-FLIP-FLOP | LOGIC XOR | SOA | optical networks | PERFORMANCE | IMPLEMENTATION | Electro-optic effect | GATE | DIFFERENTIAL SCHEME | ALL-OPTICAL XOR | pseudorandom binary sequence | OPTICS

Mach-Zehnder interferometer | D-FLIP-FLOP | LOGIC XOR | SOA | optical networks | PERFORMANCE | IMPLEMENTATION | Electro-optic effect | GATE | DIFFERENTIAL SCHEME | ALL-OPTICAL XOR | pseudorandom binary sequence | OPTICS

Journal Article

14.
Full Text
ON k-ERROR LINEAR COMPLEXITY OF PSEUDORANDOM BINARY SEQUENCES DERIVED FROM EULER QUOTIENTS

ADVANCES IN MATHEMATICS OF COMMUNICATIONS, ISSN 1930-5346, 11/2018, Volume 12, Issue 4, pp. 805 - 816

We investigate the k-error linear complexity of pseudorandom binary sequences of period p(r) derived from the Euler quotients modulo p(r-1) , a power of an odd...

MATHEMATICS, APPLIED | linear complexity | FERMAT QUOTIENTS | CHARACTER SUMS | VALUE SET | k-error linear complexity | pseudorandom binary sequences | COMPUTER SCIENCE, THEORY & METHODS | Cryptography | Euler quotients

MATHEMATICS, APPLIED | linear complexity | FERMAT QUOTIENTS | CHARACTER SUMS | VALUE SET | k-error linear complexity | pseudorandom binary sequences | COMPUTER SCIENCE, THEORY & METHODS | Cryptography | Euler quotients

Journal Article

Designs, Codes and Cryptography, ISSN 0925-1022, 10/2014, Volume 73, Issue 1, pp. 251 - 265

In this paper we give a new family of elliptic curve pseudorandom binary sequences, and study the well-distribution, correlation, linear complexity, collision...

Information and Communication, Circuits | Correlation | Data Encryption | Collision | 11K36 | Mathematics | Binary sequence | Data Structures, Cryptology and Information Theory | 11B50 | Discrete Mathematics in Computer Science | Avalanche effect | Linear complexity | Coding and Information Theory | Well-distribution | 94A60 | Combinatorics | 94A55 | MATHEMATICS, APPLIED | GENERATORS | CONSTRUCTION | COMPUTER SCIENCE, THEORY & METHODS | Disaster victims

Information and Communication, Circuits | Correlation | Data Encryption | Collision | 11K36 | Mathematics | Binary sequence | Data Structures, Cryptology and Information Theory | 11B50 | Discrete Mathematics in Computer Science | Avalanche effect | Linear complexity | Coding and Information Theory | Well-distribution | 94A60 | Combinatorics | 94A55 | MATHEMATICS, APPLIED | GENERATORS | CONSTRUCTION | COMPUTER SCIENCE, THEORY & METHODS | Disaster victims

Journal Article

Optics Communications, ISSN 0030-4018, 2011, Volume 284, Issue 19, pp. 4297 - 4306

An all-optical pseudo random binary sequence (PRBS) generator is designed using serially interconnected discrete Terahertz Optical Asymmetric Demultiplexer...

D flip-flop | Terahertz optical asymmetric demultiplexer (TOAD) | All-optical pseudorandom binary sequence | AMPLIFIERS | LOGIC GATES | ASYMMETRIC DEMULTIPLEXER | REGENERATIVE MEMORY | CIRCULATING SHIFT REGISTER | SAGNAC INTERFEROMETER | NETWORKS | INVERTER | SWITCHES | DEVICES | OPTICS | Circuits | Electronics | Feasibility | Generators | Mathematical models | Optical asymmetric demultiplexers | Standards | Flip-flops

D flip-flop | Terahertz optical asymmetric demultiplexer (TOAD) | All-optical pseudorandom binary sequence | AMPLIFIERS | LOGIC GATES | ASYMMETRIC DEMULTIPLEXER | REGENERATIVE MEMORY | CIRCULATING SHIFT REGISTER | SAGNAC INTERFEROMETER | NETWORKS | INVERTER | SWITCHES | DEVICES | OPTICS | Circuits | Electronics | Feasibility | Generators | Mathematical models | Optical asymmetric demultiplexers | Standards | Flip-flops

Journal Article

IEEE Transactions on Applied Superconductivity, ISSN 1051-8223, 06/2017, Volume 27, Issue 4, pp. 1 - 6

As the digital data links for superconducting circuits advance and higher data throughput per channel becomes possible, timing margins shrink and data...

ADC | digital radio | Receivers | Generators | RSFQ | data link | Engines | pseudorandom binary sequence | Hafnium | digital receiver | channel bonding | direct digitization | Bonding | Field programmable gate arrays | Clocks | field programmable gate arrays | PHYSICS, APPLIED | ENGINEERING, ELECTRICAL & ELECTRONIC | TRANSCEIVER | CONVERTER

ADC | digital radio | Receivers | Generators | RSFQ | data link | Engines | pseudorandom binary sequence | Hafnium | digital receiver | channel bonding | direct digitization | Bonding | Field programmable gate arrays | Clocks | field programmable gate arrays | PHYSICS, APPLIED | ENGINEERING, ELECTRICAL & ELECTRONIC | TRANSCEIVER | CONVERTER

Journal Article

Acta Arithmetica, ISSN 0065-1036, 2006, Volume 125, Issue 1, pp. 11 - 19

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 01/2017, Volume 216, p. 670

In cryptography one needs large families of binary sequences with strong pseudorandom properties. In the last decades many families of this type have been...

Studies | Pseudorandom sequences | Correlation analysis | Binary system | Avalanches | Cryptography | Complexity

Studies | Pseudorandom sequences | Correlation analysis | Binary system | Avalanches | Cryptography | Complexity

Journal Article

Jisuanji Gongcheng / Computer Engineering, ISSN 1000-3428, 09/2012, Volume 38, Issue 18, pp. 100 - 102

One family of pseudorandom binary sequences are constructed from elliptic curves on finite field F(p) by using the multiplicative inverse. The properties of...

Pseudorandom sequences | Construction | Upper bounds | Computation | Correlation analysis | Mathematical analysis | Inverse | Pseudorandom binary sequences

Pseudorandom sequences | Construction | Upper bounds | Computation | Correlation analysis | Mathematical analysis | Inverse | Pseudorandom binary sequences

Journal Article

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