Towards cryptanalysis of prime numbers

Natural numbers that defy decomposition into factors lower than themselves provide the basis for entrenching security in the public key encryption world. A variant algorithm of trial division of sieve of Eratosthenes, with its digits split into two unequal components and whose growth centered on dis...

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Main Authors: Yusuf, B.K., Mahmood, A.K., Sulaiman, S.
Format: Conference or Workshop Item
Institution: Universiti Teknologi Petronas
Record Id / ISBN-0: utp-eprints.30500 /
Published: Institute of Electrical and Electronics Engineers Inc. 2016
Online Access: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85010402964&doi=10.1109%2fICCOINS.2016.7783294&partnerID=40&md5=9a5816f163eb089ae455d994441f37a6
http://eprints.utp.edu.my/30500/
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recordtype eprints
spelling utp-eprints.305002022-03-25T07:09:14Z Towards cryptanalysis of prime numbers Yusuf, B.K. Mahmood, A.K. Sulaiman, S. Natural numbers that defy decomposition into factors lower than themselves provide the basis for entrenching security in the public key encryption world. A variant algorithm of trial division of sieve of Eratosthenes, with its digits split into two unequal components and whose growth centered on displacement from its immediate neighbors (i.e., Polignac and Goldbach theorems) was fashioned out. As challenged by Euler's verdict on non-existence of a function that completely generates only primes, our formulation was based both upon multiple linear regression analysis hoping to find a multi-variate function, of degree at most 3, which can predict primes and comparison to Akaike Information Criterion (AIC) for model selection. About 20 billion lower primes of digits less than or equal 12 were subjected to various validation techniques (e.g., Sloane's A006988) and other heuristics for benchmarking purposes. Our results reveal certain desirable features illuminating prime patterns regardless of their chaotic camouflage. © 2016 IEEE. Institute of Electrical and Electronics Engineers Inc. 2016 Conference or Workshop Item NonPeerReviewed https://www.scopus.com/inward/record.uri?eid=2-s2.0-85010402964&doi=10.1109%2fICCOINS.2016.7783294&partnerID=40&md5=9a5816f163eb089ae455d994441f37a6 Yusuf, B.K. and Mahmood, A.K. and Sulaiman, S. (2016) Towards cryptanalysis of prime numbers. In: UNSPECIFIED. http://eprints.utp.edu.my/30500/
institution Universiti Teknologi Petronas
collection UTP Institutional Repository
description Natural numbers that defy decomposition into factors lower than themselves provide the basis for entrenching security in the public key encryption world. A variant algorithm of trial division of sieve of Eratosthenes, with its digits split into two unequal components and whose growth centered on displacement from its immediate neighbors (i.e., Polignac and Goldbach theorems) was fashioned out. As challenged by Euler's verdict on non-existence of a function that completely generates only primes, our formulation was based both upon multiple linear regression analysis hoping to find a multi-variate function, of degree at most 3, which can predict primes and comparison to Akaike Information Criterion (AIC) for model selection. About 20 billion lower primes of digits less than or equal 12 were subjected to various validation techniques (e.g., Sloane's A006988) and other heuristics for benchmarking purposes. Our results reveal certain desirable features illuminating prime patterns regardless of their chaotic camouflage. © 2016 IEEE.
format Conference or Workshop Item
author Yusuf, B.K.
Mahmood, A.K.
Sulaiman, S.
spellingShingle Yusuf, B.K.
Mahmood, A.K.
Sulaiman, S.
Towards cryptanalysis of prime numbers
author_sort Yusuf, B.K.
title Towards cryptanalysis of prime numbers
title_short Towards cryptanalysis of prime numbers
title_full Towards cryptanalysis of prime numbers
title_fullStr Towards cryptanalysis of prime numbers
title_full_unstemmed Towards cryptanalysis of prime numbers
title_sort towards cryptanalysis of prime numbers
publisher Institute of Electrical and Electronics Engineers Inc.
publishDate 2016
url https://www.scopus.com/inward/record.uri?eid=2-s2.0-85010402964&doi=10.1109%2fICCOINS.2016.7783294&partnerID=40&md5=9a5816f163eb089ae455d994441f37a6
http://eprints.utp.edu.my/30500/
_version_ 1741197417325264896
score 11.62408

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