iosr-Jm   Volume-17 ~ Issue-5 ~ Sep. – Oct. 2021

Abstract: In this paper, we present two new decryption exponent cryptanalysis on.....

Keywords: Prime power, Factorization, Cryptanalysis, Encryption, Decryption, Euler Toitient function, attacks and Continued fraction

[1]. Ariffin et. al. (2018). New Cryptanalytic Attack on RSA Modulus N = pq Using Small Prime Difference Method. Malysia Journal of Mathematical Sciences
[2]. Ariffin M. R. K. and Shehu S. (2016). Cryptanalysis on prime power RSA modulus of the form 𝑁 = 𝑝𝑟𝑞. International of Applied Mathematical Research; pp. 167 -175.
[3]. Blömer, J. and May, A., (2004). A generalized Wiener attack on RSA. In International Workshop on Public Key Cryptography; Springer: Berlin/Heidelberg, Germany, pp. 1–13.
[4]. Chen, et al., (2009). A Generalization of de Weger's Method. In Proceedings of the 2009 Fifth International Conference on Information Assurance and Security, Xi'an, China, 18–20 August 2009; Volume 1, pp. 344–347.
[5]. D. Boneh, G. Durfee (1999), Cryptanalysis of RSA with private key d less than 𝑁0.292, Advances in Cryptology - Proceedings of Eurocrypt '99, Lecture Notes in Comp. Sci. 1952

Abstract: In this paper, we present a new attack on RSA in the presence of three encryption and decryption exponents 𝑒𝑖 and 𝑑𝑖 for 𝑖=1,2,3 respectively with the same modulus N. The attack is an extension of Guo's attack on RSA using continued fraction method to find new.....

Keywords: Prime power, Factorization, Cryptography, Encryption, Decryption and Continued fraction

[1]. Ariffin M. R. K. and Shehu S. (2016). Cryptanalysis on prime power RSA modulus of the form 𝑁 = 𝑝𝑟𝑞. International of Applied Mathematical Research; pp. 167 -175.
[2]. Blömer, J. and May, A., (2004). A generalized Wiener attack on RSA. In International Workshop on Public Key Cryptography; Springer: Berlin/Heidelberg, Germany, pp. 1–13.
[3]. Boneh D. and Durfe G. (1999), Cryptanalysis of RSA with private key d less than 𝑁0.292, Advances in Cryptology - Proceedings of Eurocrypt '99, Lecture Notes in Comp. Sci. 1952, 1–11.
[4]. de Weger, B. (2002), Cryptanalysis of RSA with small prime difference, Applicable Algebra in Engineering, Communication and Computing, Vol. 13(1), pp. 17-28.
[5]. Hinek, M.J., (2007). Cryptanalysis of RSA and Its Variants; Chapman and Hall/CRC: Boca Raton, FL, USA.

Abstract: Background: For infinite products of compact spaces, Tychonoff's theorem asserts that their product is compact, in the product topology. Tychonoff's theorem is shown to be equivalent to the axiom of choice. In this paper, we show that any countable product of compact metric spaces iscompact, without using Tychonoff's theorem. The proof needs only basic and standard facts of compact metric spaces and the Bolzano-Weierstrass property. Moreover, the component spaces need not be assumed to be copies of the same compact metric space, and each component space can be an arbitrary nonempty compact metric space independently. Materials and Methods: Total boundedness together with completeness of a metric space implies its compactness. Completeness of a product of complete.....

Keywords: Metric Spaces; Bolzano-Weierstrass Property; Compactness; Completeness; Total Boundedness......

[1]. Fred H. Croom. Principles of Topology. Cengage Learning India Pvt.Ltd. Indian Reprint 2008
[2]. George F. Simmons. Introduction to Topology and Modern Analysis. McGraw-Hill Inc. Printed by Robert E. Krieger Publishing Company Inc. 1963
[3]. Serge Lang. Real Analysis. Addison-Wesley Publishing Company Inc.1983
[4]. Serge Lang. Real and Functional Analysis. Springer-Verlag Inc. New York, 1993
[5]. Walter Rudin. Principles of Mathematical Analysis. McGraw-Hill Inc. 1976.

Abstract: Following the wonderful geometrical construction of Ramanujan we propose a geometrical magnitude that solve the old problem –find a square whose area is equal to that of a given circle.

Key Word: pi, chord, circle, square

[1]. R. D. SarvaJagannadha Reddy. No more a mathematical impossibility – Square root of pi found. International Journal of Engineering Sciences & Research Technology. 19-42-ST 374, STV Nagar, Titupati-51750, INDIA, 2016.
[2]. R. D. SarvaJagannadha Reddy. Durga Method of squaring the circle.IOSR Journal of Mathematics. IOSR-JM. E-ISSN:2278-5728,p-ISSN:2319=765X2319-765X Volume 10, Issue1 ver.IV.(Feb.2014),PP14-15
[3]. R. D. SarvaJagannadha Reddy. Supporting Evidence to the Exact Value from the Works of Hippocrates of Quios. Alfred S. Posamentier and Ingmar Lehman.IOSR Journal of Mathematics. IOSR-JM. E-ISSN:2278-5728,p-ISSN:2319=765X Volume 10, Issue 2 ver II (Mar-Apr 2014),PP09-12.
[4]. S. Ramanujan. Journal of the Indian Mathematical Society 1913, 138..

Abstract:In this work, closed forms of the sum formulas......

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Abstract: For a function to admit Fourier transform it has to be absolutely integrable, that is, in other words this function has to be of class . The present work presents a part of the Fourier transform theory that allows the analysis of the behavior of certain functions in the spaces......

[1]. Bronson, R., Gabriel Costa (SA). Differential Equations. Third edition. Mexico: McGraw Hill Education.
[2]. Churchil, R. And James Ward, B.(1987). Fourier Series and Boundary value problems. 5th ed. United states: McGraw Hill
[3]. Ramos, E.(2008). Mathematical Analysis IV for Science and Engineering student. second edition. Lima-Peru: New editions
[4]. Tchikoko, A. (2020). Lessons from Equations in Partial Derivatives. Sevilla: Punto Rojo Libros, SL

Abstract: In the present paper, we formulate the pulmonary blood flow in veins. Keeping in view the nature of pulmonary circulatory system in human body, the viscosity increases in the arterioles due to formation of roulex along axis by red blood cells, as we know the Lungs are remote from heart and proximate to the Asthma. P.N. Pandey and V. Upadhyay have considered the blood flow of two phased, one of which is that of red blood cells and other is Plasma. They have also applied the Herschel Bulkley non-Newtonian Model in bio-fluid mechanical set-up. We have collected a clinical data in case of Asthma for Hematocrit v/s Blood Pressure. The graphical presentation for particular parametric value is much closed to the clinical observation. The overall presentation is in tonsorial form and solution technique adapted is analytical as well as numerical. The role of Hematocrit is explicit in the determination of blood pressure in case of pulmonary disease-Asthma.

[1]. Upadhyay V.; some phenomena in two phase blood flow; 2000
[2]. Debnath L. On a micro - continuum model of pulsatile blood flow, Act Mechanica 24 : 165 - 177, (1976),
[3]. Jones D.S. and Sleeman B.D. Differential Equation and Mathematical Biology6 G.A. and V., (1976),
[4]. Upadhyay V. and Pandey P.N. Newtonian Model of two phase blood flow in aorta and arteries proximate to the heart, Proc., of third Con. of Int Acad. Phy. Sci., (1999)
[5]. Upadhyay V. and Pandey P.N. A Power Law model of two phase blood flow in arteries remote form the heart, Proc. of thilrd con. of Int. Acad. Phy. Sci. (1999),

Abstract: Background: Cataract is a clouding of the lens of the eye that causes visual disturbances and is the main cause of blindness. The report on the results of the Basic Health Research shows that the prevalence of cataract blindness in the Riau Islands Province is 1.4%, exceeding the WHO blindness prevalence limit of 0.5%. One type of cataract with the largest number of sufferers is senile cataract. Based on the results of inpatient visits in 2017 at the Muhammad Sani Hospital, Riau Islands, senile cataract was the case with the highest visits. Given the high incidence of senile cataract, preventive measures are needed to control the factors that cause senile cataract....

Key Word: Senile Cataract; Muhammad Sani Hospital Riau Island; Moderating; Partial Least Square.

[1] Kementerian Kesehatan Republik Indonesia (Kemenkes RI). (2014). Situasi Gangguan Penglihatan dan Kebutaan. Pusat Data dan Informasi Kementerian Kesehatan RI, (http://www.depkes.go.id/resources/ download/pusdatin/infodatin/infodatin-penglihatan. pdf. Diakses 04 Februari 2021).
[2] Riset Kesehatan Dasar (Riskesdas). (2013). Laporan Hasil Riset Kesehatan Dasar Tahun 2013. Badan Penelitian dan Pengembangan Kesehatan, Kementerian Kesehatan RI, (http://www.depkes.go.id/ resources/download/general/Hasil%20Riskesdas%202013.pdf. Diakses 28 Maret 2020).
[3] Ilyas, Sidarta. (2001). Penuntun Ilmu Penyakit Mata. Jakarta: Fakultas Kedokteran Universitas Indonesia.
[4] James, B., Chew, C., & Bron, A. (2006). Lecture Note: Oftalmologi, Edisi Kesembilan. Jakarta: Penerbit Erlangga.