Randomized Cunningham Numbers in Cryptography

ISBN-13: 9786139858477 / Angielski / Miękka / 2018 / 144 str.

Bhupendra Nath Tiwari; Joshua Muyiwa Adeegbe; Jude Kuipo Kibindé

Opis

In this research, we study primality testing of arbitrary integers via number theory, randomized algorithms and optimization theories. Concerning fundamentals of modern cryptography, we focus on the cryptanalysis, cryptosystems and RSA keys, which are widely used in secure communications, e.g., banking systems and other platforms with an online security. For a given n-bit integer N, our consideration is realized as a decision problem, viz. an optimized algorithm rendering the output YES, if N is a prime, and NO otherwise. In order to design such an algorithm, we begin by examining essential ingredients from the number theory, namely, divisibility, modular arithmetic, integer representations, distributions of primes, primality testing algorithms, greatest common divisor, least common multiplication, pseudoprimes, Np-hard discrete logarithm problem, residues and others. Hereby, we give special attention to the congruence relations, Chinese remainder theorem and Fermat's little theorem towards the optimal primality testing of an integer. Finally, we anticipate optimized characterizations of Cunningham numbers in the light of randomization theory and their applications to cryptography.

O autorze

Tiwari, Bhupendra Nath
Dr. Bhupendra Nath Tiwari an alumnus of JNU New Delhi, IIT Kanpur and INFN-LNF Rome is an Assistant Professor, Er. Joshua Muyiwa Adeegbe is a CSE graduate and Er. Jude Kuipo Kibindé is a CNS postgraduate scholar at UIST, "St. Paul the Apostle" - Ohrid, R. of Macedonia. Our research interests include theoretical and mathematical aspects of S & T.