Appendix A: Expression for crosscorrelation between maximal length sequences using their autocorrelation functions

AbstractS-box is the basic component of symmetric cryptographic algorithms, and its cryptographic properties play a key role in security of the algorithms. In this paper we give the distributions of Walsh spectrum and the distributions of autocorrelation functions for (n + 1)-bit S-boxes in [12]. We obtain the nonlinearity of (n + 1)-bit S-boxes, and one necessary and sufficient conditions of (n + 1)-bit S-boxes satisfying m-order resilient. Meanwhile, we also give one characterization of (n + 1)-bit S-boxes satisfying t-order propagation criterion. Finally, we give one relationship of the sum-of-squares indicators between an n-bit S-box S0 and the (n + 1)-bit S-box S (which is constructed by S0).

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Pseudo-random sequences with non-maximal length realized according to the Galois scheme based on the primitive polynomial in degree

Journal of Physics Conference Series ◽

10.1088/1742-6596/1658/1/012036 ◽

2020 ◽

Vol 1658 ◽

pp. 012036

Author(s):

V A Pesoshin ◽

V M Kuznetsov ◽

A S Kuznetsova

Keyword(s):

Maximal Length ◽

Random Sequences ◽

Primitive Polynomial

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Maximal-length pseudorandom number generator

[1989] Proceedings. The Twenty-First Southeastern Symposium on System Theory ◽

10.1109/ssst.1989.72439 ◽

2003 ◽

Cited By ~ 2

Author(s):

J.J. Komo ◽

W.J. Park

Keyword(s):

Maximal Length ◽

Pseudorandom Number ◽

Pseudorandom Number Generator ◽

Number Generator

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Comments on Kinetic Equation for Autocorrelation Functions

Journal of Mathematical Physics ◽

10.1063/1.1664943 ◽

1969 ◽

Vol 10 (6) ◽

pp. 964-974 ◽

Cited By ~ 13

Author(s):

P. Résibois ◽

J. Brocas ◽

G. Decan

Keyword(s):

Kinetic Equation ◽

Autocorrelation Functions

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Load Distribution of Parallel Springs With Random Length and Stiffness

Journal of Vibration and Acoustics ◽

10.1115/1.3269460 ◽

1987 ◽

Vol 109 (4) ◽

pp. 402-406 ◽

Cited By ~ 1

Author(s):

Go¨ran Gerbert ◽

Jacques de Mare´

Keyword(s):

Uniform Distribution ◽

Load Distribution ◽

Simple Formula ◽

Mechanical Design ◽

Numerical Results ◽

Maximal Length ◽

Major Influence ◽

Length Variation ◽

Spring Stiffness ◽

Failure Risk

There are many applications in mechanical design where load distribution is modelled with parallel springs. Here random variation in spring length and spring stiffness is considered. Length variation is assumed to be the major influence and the case with uniform distribution is analyzed in detail. Small variations in spring stiffness are included. Numerical results are given. A simple formula is presented which gives the maximal length deviation as a function of the number of springs. The formula is based on a 10 percent failure risk which is a common number in practical mechanical design.

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