Asymptotic Bound for RSA Variant with Three Decryption Exponents

Authors : Saıdu ISAH ABUBAKAR, Ibrahim ZAİD, Amınu ALHAJI IBRAHIM

Pages : 1-6

Doi:10.33187/jmsm.1135988

View : 20 | Download : 11

Publication Date : 2023-04-30

Article Type : Research Paper

Abstract :This paper presents a cryptanalysis attack on the RSA variant with modulus $N=p^rq$ for $r\\geq 2$ with three public and private exponents $insert ignore into journalissuearticles values(e_1,d_1);,$ $insert ignore into journalissuearticles values(e_2,d_2);,$ $insert ignore into journalissuearticles values(e_3,d_3);$ sharing the same modulus $N$ where $p$ and $q$ are consider to prime having the same bit size. Our attack shows that we get the private exponent $\\sigma_1\\sigma_2\\sigma_3<\\leftinsert ignore into journalissuearticles values(\\frac{r-1}{r+1}\\right);^4$, which makes the modulus vulnerable to Coppersmith\`s attacks and can lead to the factorization of $N$ efficiently where $d_1 The asymptotic bound of our attack is greater than the bounds for May \\cite{May}, Zheng and Hu \\cite{Z}, and Lu et al. \\cite{Y} for $2\\leq r \\leq 10$ and greater than Sarkar\`s \\cite{Sarkar1} and \\cite{Sarkar} bounds for $5 \\leq r \\leq10$.
Keywords : Asymptotic, Bound, Cryptanalysis, Decryption, Exponents, RSA variants