Trustworthy Approaches to RSA: Efficient Exploitation Strategies Based on Common Modulus

With the increasing integration of crowd computing, new vulnerabilities emerge in widely used cryptographic systems like the RSA cryptosystem, whose security is based on the factoring problem. It is strongly advised to avoid using the same modulus to produce two pairs of public-private keys, as the cryptosystem would be rendered vulnerable to common modulus attacks. Such attacks can take two forms: one that aims to factorize the common modulus based on one key pair and the other that aims to decrypt certain ciphertexts generated by two public keys if the keys are co-prime. This paper introduces a new type of common modulus attack on the RSA cryptosystem. In our proposed attack, given one public-private key pair, an attacker can obtain the private key corresponding to a given public key in RSA decryption. This allows the adversary to decrypt any ciphertext generated using this public key. It is worth noting that the proposed attack can be used in the CRT model of RSA. In addition, we propose a parallelizable factoring algorithm with an order equivalent to a cyclic attack in the worst-case scenario.