A comparison of Carlet's second-order nonlinearity bounds

被引：1

作者：

Mesnager, Sihem ^{[1
]}

McGrew, Gavin ^{[2
]}

Davis, James ^{[2
]}

Steele, Dayton ^{[2
]}

Marsten, Katherine ^{[2
]}

机构：

[1] Univ Paris VIII, CNRS, Dept Math, UMR 7539 LAGA & Telecom ParisTech, Paris, France

[2] Univ Richmond, Dept Math & Comp Sci, Richmond, VA 23173 USA

来源：

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS | 2017年 / 94卷 / 03期

关键词：

Nonlinearity; Boolean; functions; derivative; concatenation; LOW-ORDER APPROXIMATION; BOOLEAN FUNCTIONS; CRYPTANALYSIS;

D O I：

10.1080/00207160.2015.1112002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Carlet provides two bounds on the second-order nonlinearity of Boolean functions. We construct a family of Boolean functions where the first bound (the presumed weaker bound) is tight and the second bound is strictly worse than the first bound. We show that the difference between the two bounds can be made arbitrarily large.

引用

页码：427 / 436

页数：10

共 50 条

[21] Bounds for contractive semigroups and second-order systems
Veselic, Kresimir
OPERATOR THEORY IN KREIN SPACES AND NONLINEAR EIGENVALUE PROBLEMS, 2006, 162 : 293 - 308
[22] Threshold Conditions for Bulk Second-Order Nonlinearity and Near-Surf ace Second-Order Nonlinearity in Thermally Poled Infrasil Silica
Mingxin Qiu
Toru Mizunaml
Terao Shimomura
Michitaka Ohtaki
Optical Review, 2001, 8 : 159 - 162
[23] First-order and second-order conditions for error bounds
Wu, ZL
Ye, JJ
SIAM JOURNAL ON OPTIMIZATION, 2004, 14 (03) : 621 - 645
[24] Dynamics and stability of a laser system with second-order nonlinearity
Falter, S
Du, KM
Liao, Y
Quade, M
Zhang, J
Loosen, P
Poprawe, R
OPTICS LETTERS, 1997, 22 (09) : 609 - 611
[25] Surface and bulk contributions to the second-order nonlinearity of gold
Wang, Fu Xiang
Rodriguez, Francisco J.
Kauranen, Martti
Albers, Willem M.
Ahorinta, Risto
Sipe, John E.
2009 CONFERENCE ON LASERS AND ELECTRO-OPTICS AND QUANTUM ELECTRONICS AND LASER SCIENCE CONFERENCE (CLEO/QELS 2009), VOLS 1-5, 2009, : 2393 - +
[26] Second-order Nonlinearity Induced Unconventional Photon Blockade
Y. H. Zhou
Qi-Cheng Wu
Biaoliang Ye
Liyuan Xue
H. Z. Shen
International Journal of Theoretical Physics, 2019, 58 : 472 - 479
[27] Optical recording of second-order nonlinearity in a chacohalide glass
Lopez-Lago, E
Couderc, V
Griscom, L
Smektala, F
Barthélémy, A
JOURNAL DE PHYSIQUE IV, 2002, 12 (PR5): : 213 - 214
[28] The lower bound of second-order nonlinearity of cubic functions
Gong, Luozhong
Fang, Guobing
ARS COMBINATORIA, 2018, 136 : 255 - 261
[29] Second-order Nonlinearity Induced Unconventional Photon Blockade
Zhou, Y. H.
Wu, Qi-Cheng
Ye, Biaoliang
Xue, Liyuan
Shen, H. Z.
INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS, 2019, 58 (02) : 472 - 479
[30] Second-order nonlinearity in poled-polymer systems
Burland, Donald M.
Miller, Robert D.
Walsh, Cecilia A.
Chemical Reviews, 1994, 94 (01)

← 1 2 3 4 5 →