2024-03-28T11:13:20Z
https://eprints.maths.manchester.ac.uk/cgi/oai2
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:173
2017-11-08T18:18:29Z
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https://eprints.maths.manchester.ac.uk/173/
How to Check for Short Cycles in Large Nonlinear Feedback Shift Registers
Petrides, George
Mykkeltveit, Johannes
40 Sequences, series, summability
68 Computer science
In \cite{Ly} it is claimed that for a given large nonlinear feedback shift register it is hard to check whether short cycles have been embedded by the given method. The purpose of the present note is to show how to check for short cycles in general using our proposed algorithm. To implement the algorithm we introduce the notion of nonlinear complexity and try to classify sequences into nonlinear complexity classes.
2006-03-08
MIMS Preprint
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/173/1/nonlin3.pdf
Petrides, George and Mykkeltveit, Johannes (2006) How to Check for Short Cycles in Large Nonlinear Feedback Shift Registers. [MIMS Preprint]
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:571
2017-10-20T14:12:18Z
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https://eprints.maths.manchester.ac.uk/571/
On the onset of oscillatory convection in molten gallium
Hof, B.
Juel, Anne
Zhao, L.
Ben Hadid, H.
Henry, D.
Mullin, T.
40 Sequences, series, summability
47 Operator theory
The results of experimental and numerical investigations of the onset of oscillatory convection in a sidewall heated rectangular cavity of molten gallium are reported. Detailed comparisons are made between experimental observations and calculations from numerical simulations of a three-dimensional Boussinesq model. The onset of time-dependence takes place through supercritical Hopf bifurcations and the loci of critical points in the ($\hbox{\it Gr}, \hbox{\it Pr}$)-plane are qualitatively similar with excellent agreement between the frequencies of the oscillatory motion. This provides a severe test of the control of the experiment since the mode of oscillation is extremely sensitive to imperfections.
Detailed numerical investigations reveal that there are a pair of Hopf bifurcations which exist on two asymmetric states which themselves arise at a subcritical pitchfork from the symmetric state. There is no evidence for this in the experiment and this qualitative difference is attributed to non-Boussinesq perturbations which increase with $\hbox{\it Gr}$.
However, the antisymmetric spatial structure of the oscillatory state is robust and is present in both the experiment and the numerical model. Moreover, the detailed analysis of the numerical results reveals the origins of the oscillatory instability.
2004
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/571/1/S0022112004000527a.pdf
Hof, B. and Juel, Anne and Zhao, L. and Ben Hadid, H. and Henry, D. and Mullin, T. (2004) On the onset of oscillatory convection in molten gallium. Journal of Fluid Mechanics, 515. pp. 391-413. ISSN 0022-1120
http://journals.cambridge.org/action/displayIssue?iid=247280
10.1017/S0022112004000527
10.1017/S0022112004000527
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:847
2017-10-20T14:12:28Z
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https://eprints.maths.manchester.ac.uk/847/
Cryptographic Applications of Non-Commutative
Algebraic Structures and Investigations of
Nonlinear Recursions
Petrides, George
20 Group theory and generalizations
40 Sequences, series, summability
68 Computer science
In this thesis we investigate the application of non-commutative algebraic structures and nonlinear recursions in cryptography. To begin with, we demonstrate that the public key cryptosystem based on the word problem on the Grigorchuk groups, as proposed by M. Garzon and Y. Zalcstein [8], is insecure. We do this by exploiting information contained in the public key in order to construct a key which behaves like the private key and allows successful decryption of ciphertexts.
Further on, we present a new block cipher with key-dependent S-boxes, based on the Grigorchuk groups. To the best of our knowledge, it is the first time groups are used in a block cipher, whereas they have been extensively used in public key cryptosystems. The study of the cipher’s properties is, at this stage, purely theoretical.
Finally, we investigate the notion of nonlinear complexity, or maximal order complexity as it was first defined in 1989 [15], for sequences. Our main purpose is to begin classification of periodic binary sequences into nonlinear complexity classes. Previous work on the subject also includes approximation of the size of each class, found in [7]. Once the classification is completed, we can use it to show how to perform checks for short cycles in large nonlinear feedback shift registers using our proposed algorithm.
2006
Thesis
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/847/1/GeorgePetridesThesis.pdf
Petrides, George (2006) Cryptographic Applications of Non-Commutative Algebraic Structures and Investigations of Nonlinear Recursions. Doctoral thesis, Manchester Institute for Mathematical Sciences, The University of Manchester.
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2128
2017-10-20T14:13:13Z
7374617475733D707562
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7375626A656374733D4D5343:4D53435F3430
7375626A656374733D4D5343:4D53435F3635
74797065733D61727469636C65
https://eprints.maths.manchester.ac.uk/2128/
Fast solvers for discretized Navier-Stokes problems using vector extrapolation
Duminil, Sebastien
Sadok, Hassane
Silvester, David
15 Linear and multilinear algebra; matrix theory
40 Sequences, series, summability
65 Numerical analysis
We discuss the design and implementation of a vector extrapolation method for computing numerical solutions of the steady-state Navier-Stokes equation system. We describe a “proof of concept” implementation of vector extrapolation, and we illustrate its effectiveness when integrated into the Incompressible Flow Iterative Solution Software (IFISS) package.
2014-06-13
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/2128/1/fast_Navier.pdf
Duminil, Sebastien and Sadok, Hassane and Silvester, David (2014) Fast solvers for discretized Navier-Stokes problems using vector extrapolation. Numerical Algorithms, 66 (1). pp. 89-104. ISSN 1017-1398
10.1007/s11075-013-9726-7
10.1007/s11075-013-9726-7