eth Root Attack on Dual Modulus RSA

<span lang="EN-US">The Rivest–Shamir–Adleman (RSA) algorithm relies on the presumed difficulty of integer factorization, making it vulnerable to certain attacks, particularly in the quantum era. One proposed variant, dual modulus RSA, is claimed to enhance resilience against specific cryptanalytic techniques. This study evaluates its security by applying an e^th-root attack using an advanced fraction method. The results demonstrate that the plaintext can be recovered without the private key, confirming that dual modulus RSA, like standard RSA, remains susceptible under particular conditions. Although dual modulus RSA incurs higher computational cost, the attack remains effective. These findings suggest that structural changes alone do not guarantee improved security and emphasize the need for rigorous cryptanalysis of RSA variants against established mathematical attacks.</span>