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New Jochemsz–May Cryptanalytic bound for RSA system utilizing common Modulus N = p2q

This paper describes an attack on the Rivest, Shamir and Adleman (RSA) cryptosystem utilizing the modulus N = p 2 q where p and q are two large balanced primes. Let e1 ,e2 < Nγ be the integers such that d1 , d2 < Nδ be their multiplicative inverses. Based on the two key equations e1d1 −...

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Main Authors: Adenan, Nurul Nur Hanisah, Ariffin, Muhammad Rezal Kamel, Sapar, Siti Hasana, Abd Ghafar, Amir Hamzah, Asbullah, Muhammad Asyraf
Format: Article
Published: MDPI 2021
Online Access:http://psasir.upm.edu.my/id/eprint/94352/
https://www.mdpi.com/2227-7390/9/4/340
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spelling my.upm.eprints.943522023-04-07T03:51:55Z http://psasir.upm.edu.my/id/eprint/94352/ New Jochemsz–May Cryptanalytic bound for RSA system utilizing common Modulus N = p2q Adenan, Nurul Nur Hanisah Ariffin, Muhammad Rezal Kamel Sapar, Siti Hasana Abd Ghafar, Amir Hamzah Asbullah, Muhammad Asyraf This paper describes an attack on the Rivest, Shamir and Adleman (RSA) cryptosystem utilizing the modulus N = p 2 q where p and q are two large balanced primes. Let e1 ,e2 < Nγ be the integers such that d1 , d2 < Nδ be their multiplicative inverses. Based on the two key equations e1d1 − k1φ(N) = 1 and e2d2 − k2φ(N) = 1 where φ(N) = p(p − 1)(q − 1), our attack works when the primes share a known amount of least significant bits (LSBs) and the private exponents share an amount of most significant bits (MSBs). We apply the extended strategy of Jochemsz–May to find the small roots of an integer polynomial and show that N can be factored if δ < 11 10 + 9 4 α − 1 2 β − 1 2 γ − 1 30 p 180γ + 990α − 180β + 64. Our attack improves the bounds of some previously proposed attacks that makes the RSA variant vulnerable. MDPI 2021-02-08 Article PeerReviewed Adenan, Nurul Nur Hanisah and Ariffin, Muhammad Rezal Kamel and Sapar, Siti Hasana and Abd Ghafar, Amir Hamzah and Asbullah, Muhammad Asyraf (2021) New Jochemsz–May Cryptanalytic bound for RSA system utilizing common Modulus N = p2q. Mathematics, 9 (4). art. no. 340. pp. 1-13. ISSN 2227-7390 https://www.mdpi.com/2227-7390/9/4/340 10.3390/math9040340
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
description This paper describes an attack on the Rivest, Shamir and Adleman (RSA) cryptosystem utilizing the modulus N = p 2 q where p and q are two large balanced primes. Let e1 ,e2 < Nγ be the integers such that d1 , d2 < Nδ be their multiplicative inverses. Based on the two key equations e1d1 − k1φ(N) = 1 and e2d2 − k2φ(N) = 1 where φ(N) = p(p − 1)(q − 1), our attack works when the primes share a known amount of least significant bits (LSBs) and the private exponents share an amount of most significant bits (MSBs). We apply the extended strategy of Jochemsz–May to find the small roots of an integer polynomial and show that N can be factored if δ < 11 10 + 9 4 α − 1 2 β − 1 2 γ − 1 30 p 180γ + 990α − 180β + 64. Our attack improves the bounds of some previously proposed attacks that makes the RSA variant vulnerable.
format Article
author Adenan, Nurul Nur Hanisah
Ariffin, Muhammad Rezal Kamel
Sapar, Siti Hasana
Abd Ghafar, Amir Hamzah
Asbullah, Muhammad Asyraf
spellingShingle Adenan, Nurul Nur Hanisah
Ariffin, Muhammad Rezal Kamel
Sapar, Siti Hasana
Abd Ghafar, Amir Hamzah
Asbullah, Muhammad Asyraf
New Jochemsz–May Cryptanalytic bound for RSA system utilizing common Modulus N = p2q
author_facet Adenan, Nurul Nur Hanisah
Ariffin, Muhammad Rezal Kamel
Sapar, Siti Hasana
Abd Ghafar, Amir Hamzah
Asbullah, Muhammad Asyraf
author_sort Adenan, Nurul Nur Hanisah
title New Jochemsz–May Cryptanalytic bound for RSA system utilizing common Modulus N = p2q
title_short New Jochemsz–May Cryptanalytic bound for RSA system utilizing common Modulus N = p2q
title_full New Jochemsz–May Cryptanalytic bound for RSA system utilizing common Modulus N = p2q
title_fullStr New Jochemsz–May Cryptanalytic bound for RSA system utilizing common Modulus N = p2q
title_full_unstemmed New Jochemsz–May Cryptanalytic bound for RSA system utilizing common Modulus N = p2q
title_sort new jochemsz–may cryptanalytic bound for rsa system utilizing common modulus n = p2q
publisher MDPI
publishDate 2021
url http://psasir.upm.edu.my/id/eprint/94352/
https://www.mdpi.com/2227-7390/9/4/340
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score 13.211869

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