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Generalized hyper-bent functions over GF(p)

2007
*
Discrete Applied Mathematics
*

In this paper, we extend the concept of binary

doi:10.1016/j.dam.2006.11.007
fatcat:u6xnmvopgbfndijaxxm6zeesa4
*hyper*-*bent**functions*introduced by Carlet to*functions*defined*over**GF*(*p*). We show that such*functions*must be quadratic. ... We also provide the necessary and sufficient conditions on the symmetric coefficient matrix corresponding to the quadratic form of f : Z n*p*→ Z*p*that guarantee that f is a*hyper*-*bent**function*. ... Results Here, we*generalize*the concept of*hyper*-*bent**functions*to*functions*defined*over**GF*(*p*). Definition 5. ...##
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Generalization of Boolean Functions Properties to Functions Defined over GF(p)

2012
*
Journal of Computer Science
*

Approach: We

doi:10.3844/jcssp.2012.809.814
fatcat:3bduurfp2bgtpjyghyrl5xyy4m
*generalize*some of the previous results on cryptographic Boolean*functions*to*functions*defined*over**GF*(*p*);*p*> 2. ... We also derive an upper bound for the dimension of the linear space of the*functions*defined*over**GF*(*p*). Finally, we present a method to construct a*bent**function*from semi-*bent**functions*. ... The concept of*hyper*-*bent**function*was extended to*functions**over**GF*(*p*) in (Youssef, 2007) . ...##
###
Hyper-bent Functions
[chapter]

2001
*
Lecture Notes in Computer Science
*

In this paper we introduce a new class of

doi:10.1007/3-540-44987-6_25
fatcat:h57djycjm5dvxdvcw7bipowhdm
*bent**functions*which we call*hyper*-*bent**functions*. ... We also extend our results to vectorial*hyper*-*bent**functions*. ... We would like to thank Claude Carlet for encouraging us to keep the "*hyper*-*bent*" term and for attracting our attention to references [6] and [7] . ...##
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New designs for signal sets with low cross correlation, balance property, and large linear span: GF(p) case

2002
*
IEEE Transactions on Information Theory
*

New designs for families of sequences

doi:10.1109/tit.2002.804044
fatcat:ozves4s3irhz5avtgfxedfefji
*over**GF*( ) with low cross correlation, balance property, and large linear span are presented. ... The key idea of the new designs is to use short -ary sequences of period with the two-level autocorrelation*function*together with the interleaved structure to construct a set of long sequences with the ... ACKNOWLEDGMENT The author wishes to thank*P*. ...##
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Boolean Functions with Large Distance to All Bijective Monomials: N Odd Case
[chapter]

2001
*
Lecture Notes in Computer Science
*

*Hyper*-

*bent*

*functions*achieve the maximal minimum distance to all the coordinate

*functions*of all bijective monomials. ... However, this class of

*functions*exists only for

*functions*with even number of inputs. ... At Eurocrypt' 2001, Youssef and Gong [19] introduced a new class of

*bent*

*functions*which they called

*hyper*-

*bent*

*functions*. ...

##
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Page 5528 of Mathematical Reviews Vol. , Issue 2002H
[page]

2002
*
Mathematical Reviews
*

A 40 (1985), no. 1, 90-107; MR 871:05075},

*bent**functions**over**GF*(*p** ) defined by A. S. Ambrosimov [Diskret. Mat. 6 (1994), no. 3, 50-60; MR 96e:03033] and perfect nonlinear*functions*. ... Summary: “In this paper, the author*generalizes*perfect nonlin- ear*functions*and discusses the relationships among*bent**functions**over*Z,, defined by*P*. V. Kumar, R. A. Scholtz and L. R. Welch [J. ...##
###
Bent functions with stronger nonlinear properties: K-bent functions

2008
*
Journal of Applied and Industrial Mathematics
*

We introduce the notion of k-

doi:10.1134/s1990478908040133
fatcat:wfszouacajbizk4r4h2eh27hii
*bent**function*, i.e., a Boolean*function*with even numberm of variables v 1 , . . . , v m that can be approximated with all*functions*of the form u, v j ⊕ a in the equally bad ... Namely, the vectors of values for the*functions*u, v k ⊕ a are codewords of the code A k m . ... For every even m, they proved the existence of such*hyper*-*bent**functions*. C. Carlet and*P*. Gaborit [9] and independently A. S. Kuzmin, V. T. Markov, A. A. Nechaev, and A. B. ...##
###
On Relationships among Avalanche, Nonlinearity, and Correlation Immunity
[chapter]

2000
*
Lecture Notes in Computer Science
*

2 n−1− 1 2

doi:10.1007/3-540-44448-3_36
fatcat:tuclmwzbqrapbjmm4e4vtiauxq
*p*. ... We establish, for the first time, an explicit and simple lower bound on the nonlinearity N f of a Boolean*function*f of n variables satisfying the avalanche criterion of degree*p*, namely, N f ≥ 2 n−1 − ... Zheng and Zhang [26] proved that Boolean*functions*satisfying the avalanche criterion in a*hyper*-space coincide with certain*bent**functions*. ...##
###
Connections among nonlinearity, avalanche and correlation immunity

2003
*
Theoretical Computer Science
*

*Over*the years researchers have identiÿed a number of indicators that forecast nonlinear properties of these

*functions*. ... 2 n−1−(1=2)

*p*. ... Zheng and Zhang [29] proved that Boolean

*functions*satisfying the avalanche criterion in a

*hyper*-space coincide with certain

*bent*

*functions*. ...

##
###
On Pivot Orbits of Boolean Functions
[article]

2006
*
arXiv
*
pre-print

We establish lower bounds on the number of flat spectra of a Boolean

arXiv:math/0604396v1
fatcat:lxztvjpc4feydftzfwgwzu24d4
*function*, depending on internal structures, with respect to the I,H^n and I,H,N^n sets of transforms. ... We also construct a family of Boolean*functions*of degree higher than two with a large number of flat spectra with respect to I,H^n, and compute a lower bound on this number. ... The example used in the proof of lemma 3 was taken from an interesting catalogue of homogeneous*bent**functions*, as provided by [5] . Theorem 7. Let m :*GF*(2) n →*GF*(2) and*p*:*GF*(2) n → Z 4 . ...##
###
On Cryptographic Propagation Criteria for Boolean Functions

1999
*
Information and Computation
*

We finally give a

doi:10.1006/inco.1998.2763
fatcat:yjehp6r6prc5znycgb56trc5a4
*general*construction of nonquadratic*functions*satisfying EPC(l) of order k. ... We determine the*functions*on*GF*(2) n which satisfy the propagation criterion of degree n&2, PC(n&2). ... For n even, these*functions*were characterized in [8] . They were called*hyper*-*bent*. We give this characterization in Proposition 7 for n even and extend it to n odd. ...##
###
On O(a^2) effects in gradient flow observables
[article]

2015
*
arXiv
*
pre-print

*function*Σ(u, a/L) =ḡ 2

*GF*(2L) at u =ḡ 2

*GF*(L) = 2.6057 for lattice sizes L/a = 8, 12, 16, 24 and with scale factor s = 2. ... We here follow the convention where c 2 multiplies the "

*bent*rectangles" or "chairs", and c 3 the "parallelograms". where corrections are O(a 4 ) and J n,m = t (m+n)/2 ∞ −∞ d 4

*p*e −2t

*p*2

*p*n

*p*m ∞ −∞ ...

##
###
On the propagation criterion of degree l and order k
[chapter]

1998
*
Lecture Notes in Computer Science
*

We determine those Boolean

doi:10.1007/bfb0054146
fatcat:iqg5k6ababd5fhvl6xv6z7ox3i
*functions*on*GF*(2)" which satisfy the propagation criterion of degree l and order k _> n -/ -2. All of theses*functions*are quadratic. ... We design nonquadratic Boolean*functions*satisfying the criterion PC(e) of order k by using the Maiorana-McFarland construction involving nonlinear mappings derived from nonlinear codes. ... Preparata code) being greater than or equal to 2 'r~-I -2"~ (resp. being equal to 3) , the*function*f of corollary 18 can be defined so that it is (2 'n-1 -2~ -1)resilient (resp. 2-resilient). ...##
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On Exact Algebraic [Non-]Immunity of S-Boxes Based on Power Functions
[chapter]

2006
*
Lecture Notes in Computer Science
*

These attacks are not always feasible in practice but are in

doi:10.1007/11780656_7
fatcat:aiqmjpgmcrawdkjjie4n745scq
*general*very powerful. ... In this paper we are interested in algebraic immunity of several well known highly-nonlinear vectorial Boolean*functions*(or Sboxes), designed for block and stream ciphers. ... Gong:*Hyper*-*bent**Functions*, In Eurocrypt 2001, LNCS 2045, pp 406-419, Springer, 2001. ...##
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Effect of renal function on renal responsiveness to parathyroid hormone in primary hyperparathyroidism and chronic renal failure

1985
*
European Journal of Clinical Investigation
*

Urinary cyclic AMP analysed as a

doi:10.1111/j.1365-2362.1985.tb00141.x
pmid:2985400
fatcat:qtykerkyynfxnovbqfsi2xezuy
*function*of the serum calcium and parathyroid hormone in the differential diagnosis of*hyper*- calcaemia. J Clin Invest 1977; 59:14-21. ... Like Schneider & Jutzler [5], we found a close correlation between basal plasma cAMP and plasma creatinine*over*a wide range of impaired renal*function*. High basal plasma cAMP concentra- 42 I. G. ...
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