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Generalized hyper-bent functions over GF(p)
2007
Discrete Applied Mathematics
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In this paper, we extend the concept of binary 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. ...
doi:10.1016/j.dam.2006.11.007
fatcat:u6xnmvopgbfndijaxxm6zeesa4
Generalization of Boolean Functions Properties to Functions Defined over GF(p)
2012
Journal of Computer Science
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Approach: We 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) . ...
doi:10.3844/jcssp.2012.809.814
fatcat:3bduurfp2bgtpjyghyrl5xyy4m
Hyper-bent Functions
[chapter]
2001
Lecture Notes in Computer Science
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In this paper we introduce a new class of 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] . ...
doi:10.1007/3-540-44987-6_25
fatcat:h57djycjm5dvxdvcw7bipowhdm
New designs for signal sets with low cross correlation, balance property, and large linear span: GF(p) case
2002
IEEE Transactions on Information Theory
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New designs for families of sequences 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. ...
doi:10.1109/tit.2002.804044
fatcat:ozves4s3irhz5avtgfxedfefji
Boolean Functions with Large Distance to All Bijective Monomials: N Odd Case
[chapter]
2001
Lecture Notes in Computer Science
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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. ...
doi:10.1007/3-540-45537-x_4
fatcat:ts7x4rvgazhxjlnokn5cqyqyx4
Page 5528 of Mathematical Reviews Vol. , Issue 2002H
[page]
2002
Mathematical Reviews
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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
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We introduce the notion of k-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. ...
doi:10.1134/s1990478908040133
fatcat:wfszouacajbizk4r4h2eh27hii
On Relationships among Avalanche, Nonlinearity, and Correlation Immunity
[chapter]
2000
Lecture Notes in Computer Science
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2 n−1− 1 2 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. ...
doi:10.1007/3-540-44448-3_36
fatcat:tuclmwzbqrapbjmm4e4vtiauxq
Connections among nonlinearity, avalanche and correlation immunity
2003
Theoretical Computer Science
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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. ...
doi:10.1016/s0304-3975(02)00319-5
fatcat:4goegm2qojcyrj7xke4oopdsyy
On Pivot Orbits of Boolean Functions
[article]
2006
arXiv
pre-print
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We establish lower bounds on the number of flat spectra of a Boolean 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 . ...
arXiv:math/0604396v1
fatcat:lxztvjpc4feydftzfwgwzu24d4
On Cryptographic Propagation Criteria for Boolean Functions
1999
Information and Computation
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We finally give a 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. ...
doi:10.1006/inco.1998.2763
fatcat:yjehp6r6prc5znycgb56trc5a4
On O(a^2) effects in gradient flow observables
[article]
2015
arXiv
pre-print
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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 ∞ −∞ ...
arXiv:1411.6706v2
fatcat:igbz4syzu5bibpwgc2rmfoeg7e
On the propagation criterion of degree l and order k
[chapter]
1998
Lecture Notes in Computer Science
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We determine those Boolean 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). ...
doi:10.1007/bfb0054146
fatcat:iqg5k6ababd5fhvl6xv6z7ox3i
On Exact Algebraic [Non-]Immunity of S-Boxes Based on Power Functions
[chapter]
2006
Lecture Notes in Computer Science
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These attacks are not always feasible in practice but are in 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. ...
doi:10.1007/11780656_7
fatcat:aiqmjpgmcrawdkjjie4n745scq
Effect of renal function on renal responsiveness to parathyroid hormone in primary hyperparathyroidism and chronic renal failure
1985
European Journal of Clinical Investigation
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Urinary cyclic AMP analysed as a 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. ...
doi:10.1111/j.1365-2362.1985.tb00141.x
pmid:2985400
fatcat:qtykerkyynfxnovbqfsi2xezuy
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