A C++ Class for Analyzing Vector Boolean Functions from a Cryptographic Perspective

Alvarez Cubero, Jose Antonio and Zufiria Zatarain, Pedro Jose (2010). A C++ Class for Analyzing Vector Boolean Functions from a Cryptographic Perspective. In: "International Conference on Security and Cryptography, SECRYPT 2010", 26/08/2010 - 28/08/2010, Atenas, Grecia.

Description

Title: A C++ Class for Analyzing Vector Boolean Functions from a Cryptographic Perspective
Author/s:
  • Alvarez Cubero, Jose Antonio
  • Zufiria Zatarain, Pedro Jose
Item Type: Presentation at Congress or Conference (Article)
Event Title: International Conference on Security and Cryptography, SECRYPT 2010
Event Dates: 26/08/2010 - 28/08/2010
Event Location: Atenas, Grecia
Title of Book: Proceedings of the International Conference on Security and Cryptography, SECRYPT 2010
Date: 2010
Subjects:
Freetext Keywords: C++ library, Walsh transform, Differential profile, Autocorrelation spectrum, Vector boolean function, Nonlinearity, Linearity distance, Balancedness, Resiliency, Propagation criterion.
Faculty: E.T.S.I. Telecomunicación (UPM)
Department: Matemática Aplicada a las Tecnologías de la Información [hasta 2014]
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

In this paper, a C++ class for analising Vector Boolean Functions from a cryptographic perspective is presented. This implementation uses the NTL library from Victor Shoup, replacing some of the general purpose modules of this library by some more specialized and better suited to cryptography, and adding new modules that complement the existing ones. With this class, we can obtain the classical representation of Vector Boolean Function such as its Truth Table and Algebraic Normal Form (ANF). It is possible to calculate mathematical structures such as the Walsh Spectrum, Linear Profile, Differential Profile and Autocorrelation Spectrum. Cryptographic criteria such as nonlinearity, linearity distance, order of correlation immunity, bal-ancedness, algebraic degree and propagation criterion can be obtained with this class. It permits to find out some interesting cryptologic parameters such as linear structures, linear potential, differential potential and the maximum possible nonlinearity or linearity distance of a Vector Boolean Function with the same dimensions. Finally, operations such as to identify if two Vector Boolean Functions are equal, their sum, direct sum, composition, bricklayering, adding coordinate functions and obtaining the polynomial representation over GF(2n) of a Vector Boolean Function given the irreducible polynomial and its Truth Table are presented.

More information

Item ID: 8149
DC Identifier: http://oa.upm.es/8149/
OAI Identifier: oai:oa.upm.es:8149
Official URL: http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5741669&tag=1
Deposited by: Memoria Investigacion
Deposited on: 10 Aug 2011 08:47
Last Modified: 20 Apr 2016 17:02
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