A New Asymmetric Fully Homomorphic Encryption Scheme for Cloud Banking Data by Zana Thalage Omar, Fadhil Salman Abed, Shaimaa Khamees Ahmed

“…The security of the new system depends on the issue of analyzing huge integers, which reach 2048 bits, to their prime factors, which are considered almost impossible or unsolvable. …”
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Private-preserving scientific computation of the rational numbers by Xuhong LIU, Chen SUN

“…As a fundamental part of cryptography, secure multiparty computation (SMC) is a building block of various cryptographic protocols, and it is also a hot topic in the international cryptographic community.In recent years, many SMC problems, such as secret information comparison, secret set problems and secure multiparty computational geometry, have been widely studied.As many practical problems need to be described by rational numbers, it is both theoretically and practically important to study the SMC problems in the rational number field.However, most of the existing researches focus on integers and the studied data are mainly one-dimensional data.There are few researches on secure multiparty computation of multi-dimensional data in the rational number field, but they can’t be generalized.Based on the fractional representation of rational numbers, the new encoding schemes about rational numbers and rational number vectors were proposed, which could encode multi-dimensional data in the rational number field and provided new solutions for other SMC problems in the rational number field.Based on the encoding scheme and one-way hash function, some protocols were designed for equality problems and set problems in the rational number field.These protocols used basic arithmetic operation and hash operation to guarantee efficiency than existing related protocols.And these protocols didn’t limit the range of research data and they were more widely applicable.It proves that these protocols are secure in the semi-honest model using simulation paradigm, and demonstrates the efficiency and the applicability of these protocols by theoretical analysis and experiment.A practical example was also given to illustrate that approaches are more versatile, and they could also be directly used to solve some secure multiparty computational geometry problems in the rational number field.…”
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Understanding Indigenous knowledge of conservation and stewardship before implementing co-production with Western methodologies in resource management by Stafford Maracle, Jennifer Maracle, Stephen Lougheed

“…Long-standing Indigenous knowledge and philosophies offer alternate world­views that can complement Western con­servation and resource management and may strengthen efforts to restore environmental integ­rity and conserve species and ecosystems. Researchers often tout the co-production of knowledge with Indigenous collaborators using frameworks like the Kaswentha (Two Row Wampum—Haudenosau­nee) and the Etuaptmumk (Two Eyed Seeing—Mi’kmaw) without first seek­ing to understand the foundations of Indigenous knowledge itself, and its deep roots in environmen­tal sustainability. …”
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Infinitely Many Trees with Maximum Number of Holes Zero, One, and Two by Srinivasa Rao Kola, Balakrishna Gudla, P. K. Niranjan

“…An L(2,1)-coloring of a simple connected graph G is an assignment f of nonnegative integers to the vertices of G such that fu-fv⩾2 if d(u,v)=1 and fu-fv⩾1 if d(u,v)=2 for all u,v∈V(G), where d(u,v) denotes the distance between u and v in G. …”
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Numerical and graphical description of all axis crossing regions for moduli 4 and 8 which occur befor 1012 by Carter Bays, Richard H. Hudson

“…Let πb,c(x) denote the number of primes ≤x and ≡c(modb), and for positive integers x let Δb(x,c,l)=πb,c(x)−πb,l(x). Negative values of Δ4(x,3,1) less than 1012 occur in six widely spaced regions. …”
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The Analysis of the Indebtedness of Slovak Agricultural Enterprises in Years 2003 and 2009 and Multi-criteria Analysis of Slovak Agricultural Enterprises in Years 2003 and 2009 by Jana Prevužňáková, Katarína Zemková

“…By comparison between the year 2003, the year in which Slovakia joined the EU and the year 2009, we observe an overall increase in the economic result from the negative to the positive integers. The year 2009 from the point of view of the farmers we can apperceive as a positive year in terms of the world prices, which were on the historical highest level. …”
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An improved Fully Homomorphic Encryption model based on N-Primes by Mohammed Anwar Mohammed, Fadhil Salman Abed

“…The proposed model’s security depends on the problem of Factorization the integers to their primary numbers. In this paper, instead of dealing with two prime numbers it is expanded to deal with n prime numbers. …”
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A modeling of budget optimization for the strategic plan of universities by different faculties: a case study in Allameh Tabataba'i University by Hassan Rashidi, Morteza Khorsandi, Fatemeh Shams

“…In addition, sudden economic shocks add to the instability and make it necessary to use the university's financial resources effectively.Methodology: A mathematical optimization model of the type of integers is presented for the management and optimal allocation of financial resources according to the performance and effectiveness of universities' scientific activities.Findings: This model has been implemented to realize nine different activities in the strategic plan of Allameh Tabatabai University, separated by faculties. …”
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A Novel Construction of Substitution Box Based on Polynomial Mapped and Finite Field With Image Encryption Application by Abid Mahboob, Muhammad Asif, Imran Siddique, Aysha Saleem, Muhammad Nadeem, Dariusz Grzelczyk, Jan Awrejcewicz

“…This scheme based on polynomial mapped and finite field which work only for even integers without multiple of 4 in the range (2-254). …”
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Representing and Quantifying Conformational Changes of Kinases and Phosphatases Using the TSR-Based Algorithm by Tarikul I. Milon, Krishna Rauniyar, Sara Furman, Khairum H. Orthi, Yingchun Wang, Vijay Raghavan, Wu Xu

“…We have developed a triangular spatial relationship (TSR)-based algorithm that enables a unique representation of a protein’s 3D structure using a vector of integers (keys). The main objective of this study is to provide structural insight into conformational changes. …”
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Development of a TSR-based method for understanding structural relationships of cofactors and local environments in photosystem I by Lujun Luo, Tarikul I. Milon, Elijah K. Tandoh, Walter J. Galdamez, Andrei Y. Chistoserdov, Jianping Yu, Jan Kern, Yingchun Wang, Wu Xu

“…The Triangular Spatial Relationship (TSR)-based algorithm converts 3D structures into integers (TSR keys). A comprehensive study was conducted, by taking advantage of the PS I 3D structures and the TSR-based algorithm, to answer three questions: (i) Are electron cofactors including P700, A-1 and A0, which are chemically identical chlorophylls, structurally different? …”
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Some New Constructions of <i>q</i>-ary Codes for Correcting a Burst of at Most <i>t</i> Deletions by Wentu Song, Kui Cai, Tony Q. S. Quek

“…In this paper, we construct <i>q</i>-ary codes for correcting a burst of at most <i>t</i> deletions, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>t</mi><mo>,</mo><mi>q</mi><mo>≥</mo><mn>2</mn></mrow></semantics></math></inline-formula> are arbitrarily fixed positive integers. We consider two scenarios of error correction: the classical error correcting codes, which recover each codeword from one read (channel output), and the reconstruction codes, which allow to recover each codeword from multiple channel reads. …”
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On the Normalized Laplacian Spectrum of the Zero-Divisor Graph of the Commutative Ring <inline-formula><math display="inline"><semantics><msub><mstyle mathvariant="bold"><mi mathva... by Ali Al Khabyah, Nazim, Nadeem Ur Rehman

“…Motivated by their work, this article investigates the normalized Laplacian spectrum of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Γ</mo><mo>(</mo><msub><mi mathvariant="double-struck">Z</mi><mi mathvariant="fraktur">n</mi></msub><mo>)</mo></mrow></semantics></math></inline-formula> for a more general class of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="fraktur">n</mi></semantics></math></inline-formula>, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="fraktur">n</mi></semantics></math></inline-formula> is represented as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>p</mi><mn>1</mn><msub><mi>T</mi><mn>1</mn></msub></msubsup><msubsup><mi>p</mi><mn>2</mn><msub><mi>T</mi><mn>2</mn></msub></msubsup></mrow></semantics></math></inline-formula>, with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>p</mi><mn>1</mn></msub></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>p</mi><mn>2</mn></msub></semantics></math></inline-formula> being distinct primes <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><msub><mi>p</mi><mn>1</mn></msub><mo><</mo><msub><mi>p</mi><mn>2</mn></msub><mo>)</mo></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>T</mi><mn>1</mn></msub><mo>,</mo><msub><mi>T</mi><mn>2</mn></msub></mrow></semantics></math></inline-formula> are positive integers.…”
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The Singularity of the <i>K</i>₄ Homeomorphic Graph by Haicheng Ma

“…The singularity of graphs is of certain interest in graph theory and algebraic combinatorics. For positive integers <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>a</mi><mi>i</mi></msub><mo>≥</mo><mn>2</mn></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>i</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mo>…</mo><mo>,</mo><mn>6</mn></mrow></semantics></math></inline-formula>. …”
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