An improved key expansion algorithm based on a 2D discrete hyper chaotic map with memristor

Key expansion plays an important role in symmetric block cipher. To generate desired number of round keys that satisfy irreversibility, parallelism and independence, we first constructed a 2D memristor-based discrete hyper chaotic map (2D-MDHCM), through adding a memristor to the 2D discrete hyper chaotic map (2D-DHCM), whose state point has ergodicity in phase space and good randomness in a sufficiently large parameter range. Took advantage of the irreversibility of the chaotic iteration, we designed an irreversible key expansion algorithm, which can generate the round keys in parallel with specified round and flexible length, what's more, each round key can be generated by the initial key independently. Experimental and analysis results demonstrated that the improved key expansion algorithm satisfied irreversibility, parallelism and independence, which enhanced the security of initial key greatly.