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Analytical cryptanalysis upon N = p2q utilizing Jochemsz-May strategy.

Nurul Nur Hanisah Adenan¹, Muhammad Rezal Kamel Ariffin^1,2, Faridah Yunos²

¹Institute for Mathematical Research, Universiti Putra Malaysia, Serdang, Selangor, Malaysia.

|March 24, 2021

Summary

This summary is machine-generated.

This study introduces a new cryptanalytic attack on RSA variants with modulus N=p^2q. The attack successfully factors N when primes share a known number of least significant bits (LSBs), improving upon previous methods.

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Area of Science:

Cryptography
Number Theory
Computer Science

Background:

The RSA cryptosystem is a widely used public-key encryption method.
Security of RSA relies on the difficulty of factoring large integers.
Variants like N=p^2q present unique cryptanalytic challenges.

Purpose of the Study:

To develop a novel cryptanalytic approach for RSA variants with modulus N=p^2q.
To improve the factorization bounds for such RSA variants.

Main Methods:

The study employs an extended strategy based on Jochemsz and May.
It involves constructing a specialized integer polynomial to find small roots.
The attack leverages the property of shared Least Significant Bits (LSBs) between primes p and q.

Main Results:

The paper demonstrates a successful factorization of N=p^2q when primes share a known amount of LSBs.
The proposed attack enhances the factorization bound compared to previous methods.
The factorization is achieved when the bound [Formula: see text] is met.

Conclusions:

The developed cryptanalytic method offers improved efficiency for factoring specific RSA variants.
This research contributes to understanding the security vulnerabilities of RSA with modulus N=p^2q.
The findings highlight the importance of prime number generation in cryptographic security.