Research ArticleOpen accessEvery word in the titleThe Importance of Numbers and the Need to Study Primes: The Prime QuestionsMatthew Curtis, Gurudeo A. TularamProblem statement: The study of prime numbers is important today as it was in ancient times. The level of interest in any form of mathematics of students in Australian high schools is decreasing and furthermore the level of interest in number theory is also less that it was before; prime numbers is not being considered as an area of interest … …Journal of Mathematics and Statistics, Vol. 7, Issue 4 · 14 Sep 2011 · 9,656 accessesView PDFCite
Research ArticleOpen accessIn the keywordsProof of Frankl's Conjecture: A Non-Constructive ApproachYonghong LiuLet U be a finite set and X a family of nonempty subsets of U,which is closed under unions. We establish a connection between Frankl'sconjecture and equipollence sets, in which a complementary set is anEquipollence set on the Frobenius group. We complete the proof of theunion-closed sets using a non-constructive approach. The proof relies upon thatwe need to prove, that … …Journal of Mathematics and Statistics, Vol. 18, Issue 1 · 21 Sep 2022 · 6,171 accessesView PDFCite
Research ArticleOpen accessIn the keywordsThe Linear and Quadratic Nature of Sequences for Determining Prime Numbers by Elimination of CompositesJonathan M. Dugas, Brian M. O’ConnorA previously derived set of sequences for generating prime numbers is modified by various algebraic and trigonometric manipulations. The modified sequences are then used to more efficiently generate prime numbers. The modified sequences are simplified from their original form and are much easier to implement into a computer program. It is shown by computation that the modified sequences more efficiently … …Journal of Mathematics and Statistics, Vol. 14, Issue 1 · 16 May 2018 · 7,405 accessesView PDFCite
Research ArticleOpen accessIn the abstractH-RABIN CRYPTOSYSTEMHayder Raheem HashimCryptography is the science of using mathematics that's used to hide information or data that is being sent between participants in a way that prevents other people from reading it. The need of exchanging messages secretly promoted the creation of cryptosystems to enable receivers to interpret the exchanged information. In this study, a particular public key cryptosystem called Rabin Cryptosystem … …Journal of Mathematics and Statistics, Vol. 10, Issue 3 · 10 May 2014 · 7,640 accessesView PDFCite
Research ArticleOpen accessIn the abstractOn the Derived Subgroups of Some Finite GroupsS. Rashid, N. H. Sarmin, A. Erfanian, N. M. Mohd AliProblem statement: In this study we focus on the derived subgroup of nonabelian 3-generator groups of order p3q, where p and q are distinct primes and p < q. Our main objective is to compute the derived subgroup for these groups up to isomorphism. Approach: In a group G, the derived subgroup G' = [G, G] is generated by the … …Journal of Mathematics and Statistics, Vol. 8, Issue 1 · 8 Feb 2012 · 7,514 accessesView PDFCite
Research ArticleOpen accessIn the abstractReduce Computation Steps Can Increase the Efficiency of Computation AlgorithmZulkarnain Md. AliProblem statement: Lucas function is a special form of second-order linear recurrence relation. It is used in LUC cryptosystems. The performance of LUC cryptosystem depends on the size of public key, messages and two relatively primes. The increasing of size of these parameters will increase the computation time need to perform the LUC Cryptosystem computation. The efficiency means the quality … …Journal of Computer Science, Vol. 6, Issue 10 · 24 Aug 2010 · 7,015 accessesView PDFCite
Research ArticleOpen accessIn the abstractInteger Factorization: Solution via Algorithm for Constrained Discrete Logarithm ProblemBoris S. VerkhovskyProblem statement: During the last thirty years many public-key cryptographic protocols based on either the complexity of integer factorization of large semiprimes or the Discrete Logarithm Problem (DLP) have been developed. Approach: Although several factorization algorithms with sub-exponential complexity have been discovered, the recent RSA Factoring Challenge demonstrated that it was still necessary to use several thousand computers working in … …Journal of Computer Science, Vol. 5, Issue 9 · 30 Dec 2009 · 7,156 accessesView PDFCite
Research ArticleOpen accessIn the abstractAccelerated Search for Gaussian Generator Based on Triple Prime IntegersBoris S. Verkhovsky, Md Shiblee SadikProblem statement: Modern cryptographic algorithms are based on complexity of two problems: Integer factorization of real integers and a Discrete Logarithm Problem (DLP). Approach: The latter problem is even more complicated in the domain of complex integers, where Public Key Cryptosystems (PKC) had an advantage over analogous encryption-decryption protocols in arithmetic of real integers modulo p: The former PKC have … …Journal of Computer Science, Vol. 5, Issue 9 · 30 Sep 2009 · 6,517 accessesView PDFCite
Research ArticleOpen accessIn the abstractA Numerical Test on the Riemann Hypothesis with ApplicationsN. K. Oladejo, I. A. AdetundeProblem statement: The Riemann hypothesis involves two products of the zeta function ζ(s) which are: Prime numbers and the zeros of the zeta function ζ(s). It states that the zeros of a certain complex-valued function ζ (s) of a complex number s ≠ 1 all have a special form, which may be trivial or non trivial. Zeros at the negative … …Journal of Mathematics and Statistics, Vol. 5, Issue 1 · 31 Mar 2009 · 7,859 accessesView PDFCite