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portada Randomized Cunningham Numbers in Cryptography (in English)
Type
Physical Book
Author
Publisher
Language
Inglés
Pages
144
Format
Paperback
Dimensions
22.9 x 15.2 x 0.9 cm
Weight
0.22 kg.
ISBN13
9786139858477
Categories

Randomized Cunningham Numbers in Cryptography (in English)

Bhupendra Nath Tiwari (Author) · Joshua Muyiwa Adeegbe (Author) · Jude Kuipo Kibindé (Author) · LAP Lambert Academic Publishing · Paperback

Randomized Cunningham Numbers in Cryptography (in English) - Tiwari, Bhupendra Nath ; Adeegbe, Joshua Muyiwa ; Kuipo Kibindé, Jude

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Synopsis "Randomized Cunningham Numbers in Cryptography (in English)"

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.

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