Asymptotic Bound for RSA Variant with Three Decryption Exponents

Abstract

This paper presents cryptanalysis attack on RSA variant with modulus $N=p^rq$ for $r\geq 2$ with three public and private exponents $(e_1,d_1),$ $(e_2,d_2),$ $(e_3,d_3)$ sharing the same modulus $N$ where $p$ and $q$ are consider to be primes having the same bit size. Our attack shows that we get the private exponent $\sigma