New results in SAT – cryptanalysis of the AES

Abstract

Many significant computational problems can be converted to SAT problems. Although these problems are often encoded by formulas with hundreds of thousands of clauses and propositional variables such formulas can sometimes be effectively solved by contemporary SAT solvers. Such solvers can be successfully used for cryptanalysis of symmetric ciphers. In this case, operations of the cipher are written in the form of Boolean formulas. Then, together with randomly selected bits of the plaintext and the key, it is transformed into a set of clauses corresponding to the encryption of the given algorithm. The ciphertext obtained using SAT solvers is used to create a set of decryption clauses. Using the SAT solver again, we go to the cryptanalysis of the cipher with the selected open text, looking for the bits of the encryption key. In this article, we examine how SAT techniques behave to the AES cipher, the current standard for symmetric encryption. We also compare the results obtained in this case by several SAT solvers.