Abstract
Newly developed techniques have been recently documented, which capitalize on the security provided by prime power modulus denoted as N = prqs where2 ≤ s < r. Previousresearchprimarilyconcentrated on the factorization of the modulus of type at minimum N = p3q2. In contrast, within the context of 2 ≤ s < r, we address scenarios in the modulus N = p2q (i.e. r = 2 and s = 1) still need to be covered, showing a significant result to the field of study. This work presents two factorization approaches for the multiple moduli Ni = p2 iqi, relying on a good approximation of the Euler’s totient function ϕ(Ni). The initial method for factorization deals with the multiple moduli Ni = p2 iqi derived from m public keys (Ni,ei) and is interconnected through the equation eid − kiϕ(Ni) = 1. In contrast, the second factorization method is associated with the eidi − kϕ(Ni) = 1. By reorganizing the equations as a simultaneous Diophantine approximation problem and implementing the LLL algorithm, it becomes possible to factorize the list of moduli Ni = p2 iqi concurrently, given that the unknowns d, di, k, and ki are suff iciently small. The key difference between our results and the referenced work is that we cover a real-world cryptosystem that uses the modulus N =p2q. In contrast, the previous work covers a hypothetical situation of modulus in the form of N = prqs.
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.