Research ArticleOpen accessEvery word in the titleON SELF-INVERSE BINARY MATRICES OVER THE BINARY GALOIS FIELDAli Muhammad Ali Rushdi, Fares Ahmad Muhammad GhalebAn important class of square binary matrices over the simplest finite or Galois Field GF(2) is the class of involutory or Self-Inverse (SI) matrices. These matrices are of significant utility in prominent engineering applications such as the study of the Preparata Transformation or the analysis of synchronous Boolean Networks. Therefore, it is essential to devise appropriate methods, not only for … …Journal of Mathematics and Statistics, Vol. 9, Issue 3 · 4 Sep 2013 · 7,248 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleGroup Re-keying Protocol Based on Modular Polynomial Arithmetic Over Galois Field GF(2n)Sundaram Sudha, Azman Samsudin, Mohammad Ahmad AliaProblem statement: In this study we propose a group re-keying protocol based on modular polynomial arithmetic over Galois Field GF(2n). Common secure group communications requires encryption/decryption for group re-keying process, especially when a group member is leaving the group. Approach: This study proposes secret keys multiplication protocol based on modular polynomial arithmetic (SKMP), which eliminates the need for the encryption/decryption … …American Journal of Applied Sciences, Vol. 6, Issue 9 · 30 Sep 2009 · 7,165 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleReconfigurable Elliptic Curve Crypto-Hardware Over the Galois Field GF(2163)Mohamed Abdelkader Bencherif, Hamid Bessalah, Abderrezak GuessoumProblem statement: In the last decade, many hardware designs of elliptic curves cryptography have been developed, aiming to accelerate the scalar multiplication process, mainly those based on the Field Programmable Gate Arrays (FPGA), the major issue concerned the ability of embedding this strategic and strong algorithm in a very few hardware. That is, finding an optimal solution to the one … …American Journal of Applied Sciences, Vol. 6, Issue 8 · 31 Aug 2009 · 7,346 accessesView PDFCite
Research ArticleOpen accessIn the keywordsEfficient Realization of S-Box based reduced Residue of Prime Numbers using Virtex-5 and Virtex-6 FPGAsMohammed H. Al MijalliProblem statement: The S-Box transformation is a computationally intensive and important operation of the Advanced Encryption Standard (AES). Approach: This study presents the comparative study between reduced Residue of Prime Numbers and Galois Filed GF (28) based SBoxes using Virtex-5 and Virtex-6 FPGA devices. The implementation of S-Boxes is done using Very High speed integrated circuit Hardware Description Language (VHDL). … …American Journal of Applied Sciences, Vol. 8, Issue 8 · 18 Jul 2011 · 6,975 accessesView PDFCite
Research ArticleOpen accessIn the keywordsA Bit-Serial Multiplier Architecture for Finite Fields Over Galois FieldsHero Modares, Yasser Salem, Rosli Salleh, Majid Talebi ShahgoliProblem statement: A fundamental building block for digital communication is the Public-key cryptography systems. Public-Key Cryptography (PKC) systems can be used to provide secure communications over insecure channels without exchanging a secret key. Implementing Public-Key cryptography systems is a challenge for most application platforms when several factors have to be considered in selecting the implementation platform. Approach: The most popular … …Journal of Computer Science, Vol. 6, Issue 11 · 23 Oct 2010 · 8,431 accessesView PDFCite
Research ArticleOpen accessIn the keywordsHARDWARE REALIZATION OF HIGH SPEED ELLIPTIC CURVE POINT MULTIPLICATION USING PRECOMPUTATION OVER GF(P)N. Shylashree, V. SridharTwo new theoretical approaches for the hardware realization of high speed elliptic curve point multiplication over a prime field (GF(p)) are presented. These hardware implementations use multiple units of elliptic curve point doublers, point adders and multiplexers. The modular hardware approach used here provides high speed and scalability. …Journal of Computer Science, Vol. 10, Issue 7 · 4 Feb 2014 · 6,611 accessesView PDFCite
Research ArticleOpen accessIn the abstractFundamental Properties of the Galois CorrespondenceAyinde S. Olukayode, Oyekan E. AbiodunProblem Statement: Let K is the splitting field of a polynomial f(x) over a field F and αn be the roots of f in K. Let G be embedded as a subgroup of the symmetric group ς. We determined the Galois group G, and the subgroup. Approach: computed some auxiliary polynomials that had roots in K, where the permutation of … …Journal of Mathematics and Statistics, Vol. 4, Issue 4 · 31 Dec 2008 · 7,292 accessesView PDFCite