Report on the First DES Fixed Points for Non-Weak Keys: Case-Study of Hacking an IoT Environment

Fixed points can be defined as $\mathcal {E}_{K}(P)=P$ for a key $K$ and plaintext $P$ where $\mathcal {E}$ is the encryption function. For the Data Encryption Standard (DES) algorithm there are four weak keys, such that $\mathcal {E}_{K}(\mathcal {E}_{K}(P))=P$ for all $P$ . For each weak key there are 2³² fixed points where all the sixteen round keys are the same. While there is a high probability that DES has fixed points for non-weak keys, nobody has reported such $(P,K)$ pairs until now. Performing $1000 \times 2^{56}$ DES encryption operations using 256 Xilinx Spartan-6 parallel cost-effective FPGAs we answer the question of Judy H. Moore and Gustavus J. Simmons: we report the first known DES fixed points where all round keys are different. A case study is presented where an IoT based Sensor Device Authentication Algorithm ( $SDAA$ ) can be exploited using DES fixed points.