Open AccessAnalytical cryptanalysis upon N = p2q utilizing Jochemsz-May strategy
Author(s) -
Nurul Nur Hanisah Adenan,
Muhammad Rezal Kamel Ariffin,
Faridah Yunos,
Siti Hasana Sapar,
Muhammad Asyraf Asbullah
Publication year - 2021
Publication title -
plos one
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.99
H-Index - 332
ISSN - 1932-6203
DOI - 10.1371/journal.pone.0248888
Subject(s) - cryptanalysis , multiplicative function , integer (computer science) , combinatorics , mathematics , factorization , multiplicative inverse , prime factor , inverse , prime (order theory) , polynomial , discrete mathematics , upper and lower bounds , cryptography , coprime integers , computer science , algorithm , mathematical analysis , geometry , programming language
This paper presents a cryptanalytic approach on the variants of the RSA which utilizes the modulus N = p 2 q where p and q are balanced large primes. Supposee ∈ Z +satisfying gcd( e , ϕ ( N )) = 1 where ϕ ( N ) = p ( p − 1)( q − 1) and d < N δ be its multiplicative inverse. From ed − kϕ ( N ) = 1, by utilizing the extended strategy of Jochemsz and May, our attack works when the primes share a known amount of Least Significant Bits(LSBs). This is achievable since we obtain the small roots of our specially constructed integer polynomial which leads to the factorization of N . More specifically we show that N can be factored when the boundδ < 11 9 − 2 94 + 18 γ. Our attack enhances the bound of some former attacks upon N = p 2 q .