A Formal Analysis for RSA Attacks by Term Rewriting Systems

The high security for RSA cryptosystem depends on the less power of attacks broken it. This subject can be reduced to find the prim numbers and integer factors. Any attack besides the brute force attack, may succeed and obtain plaintext or private key. So, it is necessary to keep the RSA cryptosystem security against attacks. In this paper, we proposed a formal cryptanalysis for RSA cryptosystem, by term rewriting systems (TRS) and termination proving. We have embedded one RSA attack in a TRS model, such that attack has been successes on the RSA cryptosystem if and only if its TRS model has been terminated. Since the automated termination proving of TRSs has been grown in the last years, our work will promise.