On verification of restricted extended affine equivalence of vectorial boolean functions

Download
2012
Sınak, Ahmet
Vectorial Boolean functions are used as S-boxes in cryptosystems. To design inequivalent vectorial Boolean functions resistant to known attacks is one of the challenges in cryptography. Verifying whether two vectorial Boolean functions are equivalent or not is the final step in this challenge. Hence, finding a fast technique for determining whether two given vectorial Boolean functions are equivalent is an important problem. A special class of the equivalence called restricted extended affine (REA) equivalence is studied in this thesis. We study the verification complexity of REA-equivalence of two vectorial Boolean functions for some types, namely types I to VI. We first review the verification of the REA-equivalence types I to IV given in the recent work of Budaghyan and Kazymyrov (2012). Furthermore, we present the complexities of the verification of REA-equivalence types I and IV in the case basic simultaneous Gaussian elimination method is used. Next, we present two new REA-equivalence types V and VI with their complexities. Finally, we give the algorithms of each type I to VI with their MAGMA codes.

Suggestions

On Verification of Restricted Extended Affine Equivalence of Vectorial Boolean Functions
Özbudak, Ferruh; Yayla, Oğuz (2015-02-01)
Vectorial Boolean functions are used as substitution boxes in cryptosystems. Designing inequivalent functions resistant to known attacks is one of the challenges in cryptography. In doing this, finding a fast technique for determining whether two given functions are equivalent is a significant problem. A special class of the equivalence called restricted extended affine (REA) equivalence is studied in this paper. We update the verification procedures of the REA-equivalence types given in the recent work of ...
On statistical analysis of synchronous stream ciphers
Sönmez Turan, Meltem; Doğanaksoy, Ali; Department of Cryptography (2008)
Synchronous stream ciphers constitute an important class of symmetric ciphers. After the call of the eSTREAM project in 2004, 34 stream ciphers with different design approaches were proposed. In this thesis, we aim to provide a general framework to analyze stream ciphers statistically. Firstly, we consider stream ciphers as pseudo random number generators and study the quality of their output. We propose three randomness tests based on one dimensional random walks. Moreover, we theoretically and experimenta...
Divisibility properties on boolean functions using the numerical normal form
Göloğlu, Faruk; Yücel, Melek D; Department of Cryptography (2004)
A Boolean function can be represented in several different forms. These different representation have advantages and disadvantages of their own. The Algebraic Normal Form, truth table, and Walsh spectrum representations are widely studied in literature. In 1999, Claude Carlet and Phillippe Guillot introduced the Numerical Normal Form. NumericalNormal Form(NNF) of a Boolean function is similar to Algebraic Normal Form, with integer coefficients instead of coefficients from the two element field. Using NNF re...
Integrable KdV systems: Recursion operators of degree four
Gurses, M; Karasu, Atalay (1999-01-25)
The recursion operator and bi-Hamiltonian formulation of the Drinfeld-Sokolov system are given. (C) 1999 Elsevier Science B.V.
Statistical analysis of block ciphers and hash functions
Sulak, Fatih; Doğanaksoy, Ali; Department of Cryptography (2011)
One of the most basic properties expected from block ciphers and hash functions is passing statistical randomness testing, as they are supposed to behave like random mappings. Previously, testing of AES candidate block ciphers was done by using the statistical tests defined in the NIST Test Suite. As some of the tests in this suite require long sequences, data sets are formed by concatenating the outputs of the algorithms obtained from various input types. However, the nature of block cipher and hash functi...
Citation Formats
A. Sınak, “On verification of restricted extended affine equivalence of vectorial boolean functions,” M.S. - Master of Science, Middle East Technical University, 2012.