The RSA (Rivest, Shamir and Adleman) is one of the most preferred algorithms for asymmetric cryptography. Modular exponentiation is the time consuming part of RSA algorithm. It’s a common way to use parallel processing to achieve faster results in terms of speed. In this study, a new method exploiting parallel processing is proposed for RSA cryptography. This parallel method employs the hypercube interconnection network that has been attempted for the first time in this paper. The theoretical foundations show that the encrypted data resulting from the proposed method and the original RSA are the same and the method can be employed to make the RSA parallel which leads to speedup.