Small Prime Divisors Attack and Countermeasure against the RSA-OTP Algorithm

Abstract

One-time password algorithms are widely used in digital services to improve security. However, many such solutions use a constant secret key to encrypt (process) one-time plaintexts. A paradigm shift from constant to one-time keys could introduce tangible benefits to the application security field. This paper analyzes a one-time password concept for the Rivest–Shamir–Adleman algorithm, in which each key element is hidden, and the value of the modulus is changed after each encryption attempt. The difference between successive moduli is exchanged between communication sides via an unsecure channel. Analysis shows that such an approach is not secure. Moreover, determining the one-time password element (Rivest–Shamir–Adleman modulus) can be straightforward. A countermeasure for the analyzed algorithm is proposed.