We introduce DM-RSA (Dual Modulus RSA), a variant of the RSA cryptosystem that employs two distinct moduli symmetrically to enhance security. By leveraging the Chinese Remainder Theorem (CRT) for decryption, DM-RSA provides increased robustness against side-channel attacks while preserving the efficiency of classical RSA. This approach improves resistance to partial compromise of a modulus and integrates easily into existing infrastructures.