On Boolean Functions to Resist Algebraic Attacks - Some Necessary Conditions

von Dalai, Deepak Kumar
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Dalai, Deepak Kumar On Boolean Functions to Resist Algebraic Attacks - Some Necessary Conditions
Dalai, Deepak Kumar - On Boolean Functions to Resist Algebraic Attacks - Some Necessary Conditions

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Beschreibung

Certain properties of Boolean functions that are necessary to resist algebraic attacks are discussed. A necessary condition to resist algebraic attacks is that the function f should not have relations like fg=0 or (1+f)h=0, where g, h are nonzero functions of low degrees. The function g (resp. h) is called the annihilator of f (resp 1+f). "Algebraic Immunity(AI) of f" or, "AI(f)" is used to denote the minimum degree of the annihilators of f or 1+f. However, AI is not a sufficient condition to resist all kinds of algebraic attacks, but it is one of the most important necessary conditions. Some fundamental results like relationship between the AI and nonlinearity, the number of LI annihilators at certain degree, AI of some existing cryptographically significant functions are discussed. The first construction method to generate Boolean functions on n variables with highest possible AI is presented. Then a basic theory to generate a function with high AI is presented and is applied to construct. Other properties of these functions are studied. How the number of homogeneous linear equations, which by solving, the existence of d-degree annihilator is decided, can be reduced is analyzed.

Mitwirkende

Autor:
Dalai, Deepak Kumar

Weitere Informationen

Biografie:
Deepak Kumar Dalai received the MSc(Math) degree in 2001 from Utkal University, India, and the MTech(Comp Sc) degree in 2003 from Indian Statistical Institute. He received Ph.D. from Indian Statistical Institute in 2006. Currently, he is an Assistant Professor at NISER, Bhubaneswar, India. His research interests are cryptology and combinatorics.
Sprache:
Englisch
Seitenanzahl:
152
Medientyp:
Taschenbuch
Verlag:
VDM Verlag Dr. Müller

Stammdaten

Produkttyp:
Taschenbuch
Verpackungsabmessungen:
0.22 x 0.15 x 0.009 m; 0.272 kg
GTIN:
09783639266856
DUIN:
6NC4H8EPASH
CHF 55.55
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