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Perfect Algebraic Immune Functions
[chapter]

2012
*
Lecture Notes in Computer Science
*

A

doi:10.1007/978-3-642-34961-4_12
fatcat:f25zqpqnczbfvbyh6azklosdt4
*perfect**algebraic**immune**function*is a Boolean*function*with*perfect**immunity*against*algebraic*and fast*algebraic*attacks. ... The main results are that for a*perfect**algebraic**immune*balanced*function*the number of input variables is one more than a power of two; for a*perfect**algebraic**immune*unbalanced*function*the number of ... The first author would like to thank Dingyi Pei for his enlightening conversations on the resistance of Boolean*functions*against*algebraic*attacks. ...##
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Almost perfect algebraic immune functions with good nonlinearity

2014
*
2014 IEEE International Symposium on Information Theory
*

More exactly, they achieve optimal

doi:10.1109/isit.2014.6875151
dblp:conf/isit/LiuL14a
fatcat:rv2apospand4dda7hqe3cwikti
*algebraic**immunity*and almost*perfect**immunity*to fast*algebraic*attacks. The*functions*of such family are balanced and have optimal*algebraic*degree. ... [IEEE TIT 59(1): 653-664, 2013], are almost*perfect**algebraic**immune*for any integer k ≥ 3. ... Acknowledgment The authors would like to thank Yin Zhang for his helpful discussions on the*immunity*to fast*algebraic*attacks, thank Shaoyu Du for her helpful discussions on the nonlinearity, and thank ...##
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1-Resilient Boolean Functions on Even Variables with Almost Perfect Algebraic Immunity

2017
*
Security and Communication Networks
*

A Boolean

doi:10.1155/2017/6268230
fatcat:xrqvbci5uffkfexma5ohzkw34q
*function*is*perfect**algebraic**immune*if it is with*perfect**immunity*against*algebraic*and fast*algebraic*attacks. ... Implementation results also show that they are almost*perfect**algebraic**immune**functions*. ... [20] initiated*perfect**algebraic**immune*(PAI)*functions*, Boolean*functions*with*perfect**immunity*against*algebraic*and fast*algebraic*attacks. ...##
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Fast algebraic immunity of Boolean functions and LCD codes
[article]

2020
*
arXiv
*
pre-print

Further, we evaluate our parameter for two secondary constructions of Boolean

arXiv:2006.08372v1
fatcat:5vgxykilvjbelc63eidathbwmq
*functions*. Moreover, A coding-theory approach to the characterization of*perfect**algebraic**immune**functions*is presented. ... Via this characterization, infinite families of binary linear complementary dual codes (or LCD codes for short) are obtained from*perfect**algebraic**immune**functions*. ... Let f be a*perfect**algebraic**immune**function*. The*perfect**algebraic**immune**function*f has degree at least n − 1 (see [36] ). By Theorem 2 and F AI(f ) = n, RM(e, n) D is LCD for any 1 ≤ e ≤ n. ...##
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Cardinality spectra of components of correlation immune functions, bent functions, perfect colorings, and codes

2012
*
Problems of Information Transmission
*

We study cardinalities of components of

doi:10.1134/s003294601201005x
fatcat:smqtsua4drhnnbcppcna2tj3xq
*perfect*codes and colorings, correlation*immune**functions*, and bent*function*(sets of ones of these*functions*). ... For*perfect*colorings with certain parameters and for correlation*immune**functions*, we find components of some of the above-given cardinalities. ...*ALGEBRAIC*DEGREE OF*PERFECT*COLORINGS AND CORRELATION*IMMUNE**FUNCTIONS*Each Boolean*function*f : E n → E can be represented as a Zhegalkin polynomial (in*algebraic*normal form) f (x 1 , . . . , x n ) = ...##
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Strengthening Crypto-1 Cipher Against Algebraic Attacks

2015
*
Journal of ICT Research and Applications
*

In addition, another modified Crypto-1, using the modified feedback

doi:10.5614/itbj.ict.res.appl.2015.9.1.5
fatcat:cxu5k3oaufdvtbo2yh7en5jube
*function*and a modified filter*function*, had the lowest percentage of revealed variables. ... Experimental testing showed that the amount of memory and CPU time needed were highest when attacking the modified Crypto-1 using the modified feedback*function*and the original filter*function*. ... with*perfect**algebraic**immunity*is a power of two (2 s ) [6] . ...##
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Constructions of vectorial Boolean functions with good cryptographic properties

2016
*
Science China Information Sciences
*

Unfortunately,

doi:10.1007/s11432-015-0863-3
fatcat:uylw4di2vfeejmrowpso2kryoq
*perfect*nonlinear*functions*cannot be used directly because they are not balanced or correlation*immune*. ... In addition, to resist Berlekamp-Massay attack, the*functions*we used should have high*algebraic*degree. ... Unfortunately,*perfect*nonlinear*functions*cannot be used directly because they are not balanced or correlation*immune*. ...##
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A longtime season of friendship and scientific collaboration

2022
*
Journal of Algebraic Hyperstructures and Logical Algebras
*

In many ways the

doi:10.52547/hatef.jahla.3.1.5
fatcat:gtraqnyjtvcenj3mwg7fvgp55q
*immune*system is a black box; although many of its inputs and outputs are known, exactly how the system achieves its*function*is the subject of many investigations. ...*Perfect*M V -*algebras*form a full subcategory of the category of all M V -*algebras*. We denote the category of*perfect*M V -*algebras*by*Perfect*. ... It is introduced an*immune*dynamic n-valued Lukasiewicz logic ID L n on the base of n-valued Lukasiewicz logic L n and corresponding to it*immune*dynamic M V n -*algebra*(IDL n -*algebra*), 1 < n < ω, which ...##
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A remark on algebraic immunity of Boolean functions
[article]

2013
*
arXiv
*
pre-print

In this correspondence, an equivalent definition of

arXiv:1305.5919v1
fatcat:ilnkzeternegdj24k5d5nknlhi
*algebraic**immunity*of Boolean*functions*is posed, which can clear up the confusion caused by the proof of optimal*algebraic**immunity*of the Carlet-Feng ...*function*and some other*functions*constructed by virtue of Carlet and Feng's idea. ... For an n-variable Boolean*function*, the*algebraic**immunity*of it is upper bounded by ⌈ n 2 ⌉ [3] , and when this upper bound is attained, it is often known as an*algebraic**immunity*optimal*function*, or ...##
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High Security Frequency/Time Hopping Sequence Generators

2007
*
2007 3rd International Workshop on Signal Design and Its Applications in Communications
*

*functions*are correlation-

*immune*by the Fourier transform • X. ... N • g: p-ary bent

*function*, i.e.

*perfect*nonlinear

*function*, with N arguments Theorem 4 Let a p-ary

*function*f with N + 2 arguments be given by f (X 1 , X 2 , . . . , X N +2 ) = a 1 X 1 + a 2 X 2 + a ... Other attacks • Attacker may try an

*algebraic*attack by multiplying the combinatorial

*function*f by a well-chosen multivariate polynomial ⇒ By increasing the order of F p , the monomials of linear equations ...

##
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Page 23 of Mathematical Reviews Vol. , Issue 83a
[page]

1983
*
Mathematical Reviews
*

A sample result (Theorem 2.3) is that every recursive Boolean

*algebra*with infinitely many atoms is isomorphic to a recursive Boolean*algebra*in which the set of atoms is*immune*. ... Section four uses Sacks forcing with*perfect*trees to produce a minimal E,-degree. ...##
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Construction of correlation immune Boolean functions

2000
*
The Australasian Journal of Combinatorics
*

Constructions of higher order correlation

dblp:journals/ajc/WuD00
fatcat:jow7v6lmprfhfknychvx65irse
*immune**functions*as well as*algebraic*non-degenerate correlation*immune**functions*are discussed in particular. ... It is shown in this paper that every correlation*immune*Boolean*function*of n variables can be written as f(x) = g(xG T ), where 9 is an*algebraic*non-degenerate Boolean*function*of k (k :::; n) variables ... In this paper we investigate the inherent structure of correlation*immune**functions*in terms of*algebraic*degeneration and subsequently the constructions of*functions*with concrete correlation*immunity*...##
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An Algebraic Solution for the Kermack-McKendrick Model
[article]

2016
*
arXiv
*
pre-print

We present an

arXiv:1609.09313v2
fatcat:7ir54bbs6bayrk6atsf7whh264
*algebraic*solution for the Susceptible-Infective-Removed (SIR) model originally presented by Kermack-McKendrick in 1927. ... Then, using*algebraic*techniques and some well justified numerical assumptions we obtain an analytic solution for the integral. ... The basic reproductive number R 0 = βτ , the infection curve (that is the asymptotic number of removed as*function*of R 0 ) are concepts that found in the SIR model the basement that provide the*perfect*...##
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On Exact Algebraic [Non-]Immunity of S-Boxes Based on Power Functions
[chapter]

2006
*
Lecture Notes in Computer Science
*

In this paper we are interested in

doi:10.1007/11780656_7
fatcat:aiqmjpgmcrawdkjjie4n745scq
*algebraic**immunity*of several well known highly-nonlinear vectorial Boolean*functions*(or Sboxes), designed for block and stream ciphers. ... Instead of complex and "explicit" Boolean*functions*we have then simple and "implicit"*algebraic*relations that can be combined to fully describe the secret key of the system. ... . 10 Which S-box has the Lowest*Algebraic**Immunity*? ...##
###
Page 625 of Mathematical Reviews Vol. , Issue 96b
[page]

1996
*
Mathematical Reviews
*

@ with a Noetherian congruence lattice such that the word problem on @ is undecidable. (3) Fi- nally, they construct a finitely generated r.e.

*perfect**algebra*with*immune*as well as nonimmune transversals ... A (total) recursive*function*f admits 9 if 7 is a congruence on the*algebra*(w, f). Let F be a finite set of recursive*functions*such that f admits 7 for each f € F. Define an*algebra*¥% = (w/y,F). ...
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