Successful cryptanalytic attacks upon RSA moduli N = pq

• Main Authors: Abubakar, Saidu Isah, Kamel Ariffin, Muhammad Rezal, Asbullah, Muhammad Asyraf
• Format: Article
• Language: English
• Published: Institute for Mathematical Research, Universiti Putra Malaysia 2019
• Online Access: http://psasir.upm.edu.my/id/eprint/76378/1/10.pdf; http://psasir.upm.edu.my/id/eprint/76378/; http://einspem.upm.edu.my/journal/fullpaper/vol13saugust/10.pdf
• Institution: Universiti Putra Malaysia

This paper reports four new cryptanalytic attacks which show that t instances of RSA moduli Ns = psqs for s = 1, . . . , t where t ≥ 2 can be simultaneously factored in polynomial time using simultaneous Diophantine approximations and lattice basis reduction techniques. We construct four system of equations of the form esd − ksφ(Ns) = 1, esds − kφ(Ns) = 1, esd − kφ(Ns) = zs and esds − kφ(Ns) = zs using N – [(a i+1/i + b i+1/i / 2(ab) i+1/2i + a 1/j + b 1/j / 2(ab) 1/2j) √N] + 1 as a good approximations of φ(Ns) for unknown positive integers d, ds, ks, k, and zs . In our attacks, we found an improved short decryption exponent bound of some reported attacks.