Displaying similar documents to “Nonlinearity of the round function”

WWW-based Boolean function minimization

Sebastian Tomaszewski, Ilgaz Celik, George Antoniou (2003)

International Journal of Applied Mathematics and Computer Science

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In this paper a Boolean minimization algorithm is considered and implemented as an applet in Java. The application is based on the Quine-McCluskey simplification technique with some modifications. The given application can be accessed on line since it is posted on the World Wide Web (WWW), with up to four variables, at the URL http://www.csam.montclair.edu/~antoniou/bs. After extensive testing, the performance of the algorithm has been found to be excellent. The proposed application...

Algorithms for Computing the Linearity and Degree of Vectorial Boolean Functions

Bouyuklieva, Stefka, Bouyukliev, Iliya (2016)

Serdica Journal of Computing

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In this article, we study two representations of a Boolean function which are very important in the context of cryptography. We describe Möbius and Walsh Transforms for Boolean functions in details and present effective algorithms for their implementation. We combine these algorithms with the Gray code to compute the linearity, nonlinearity and algebraic degree of a vectorial Boolean function. Such a detailed consideration will be very helpful for students studying the design of block...

Efficient calculation of the Reed-Muller form by means of the Walsh transform

Piotr Porwik (2002)

International Journal of Applied Mathematics and Computer Science

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The paper describes a spectral method for combinational logic synthesis using the Walsh transform and the Reed-Muller form. A new algorithm is presented that allows us to obtain the mixed polarity Reed-Muller expansion of Boolean functions. The most popular minimisation (sub-minimisation) criterion of the Reed-Muller form is obtained by the exhaustive search of all the polarity vectors. This paper presents a non-exhaustive method for Reed-Muller expansions. The new method allows us to...

Dedicated spectral method of Boolean function decomposition

Piotr Porwik, Radomir Stankovic (2006)

International Journal of Applied Mathematics and Computer Science

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Spectral methods constitute a useful tool in the analysis and synthesis of Boolean functions, especially in cases when other methods reduce to brute-force search procedures. There is renewed interest in the application of spectral methods in this area, which extends also to the closely connected concept of the autocorrelation function, for which spectral methods provide fast calculation algorithms. This paper discusses the problem of spectral decomposition of Boolean functions using...

Scalable PP-1 block cipher

Krzysztof Bucholc, Krzysztof Chmiel, Anna Grocholewska-Czuryło, Ewa Idzikowska, Izabela Janicka-Lipska, Janusz Stokłosa (2010)

International Journal of Applied Mathematics and Computer Science

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A totally involutional, highly scalable PP-1 cipher is proposed, evaluated and discussed. Having very low memory requirements and using only simple and fast arithmetic operations, the cipher is aimed at platforms with limited resources, e.g., smartcards. At the core of the cipher's processing is a carefully designed S-box. The paper discusses in detail all aspects of PP-1 cipher design including S-box construction, permutation and round key scheduling. The quality of the PP-1 cipher...

Modus ponens on Boolean algebras revisited.

Enric Trillas, Susana Cubillo (1996)

Mathware and Soft Computing

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In a Boolean Algebra B, an inequality f(x,x --> y)) ≤ y satisfying the condition f(1,1)=1, is considered for defining operations a --> b among the elements of B. These operations are called Conditionals'' for f. In this paper, we obtain all the boolean Conditionals and Internal Conditionals, and some of their properties as, for example, monotonicity are briefly discussed.

On Boolean modus ponens.

Sergiu Rudeanu (1998)

Mathware and Soft Computing

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An abstract form of modus ponens in a Boolean algebra was suggested in [1]. In this paper we use the general theory of Boolean equations (see e.g. [2]) to obtain a further generalization. For a similar research on Boolean deduction theorems see [3].