A Small Initial Investigation into A Key-Dependent Random Permutation with an Example in PRESENT
D. Dhebar, Sabah Jassim · Computer and Information Technology · 2018
In this paper we demonstrate a way to create a random permutation component directly from a symmetric key; we call this the Bipartite Graph Function (BGF). The idea is that the BGF will inherit the entropy of the key and therefore produce unpredictable permutations. We first show, by a few small initial trials, that the BGF retains the expected number of fixed points as for any random permutation. Then, as a secondary idea, we explain how one might use the BGF to replace a permutation in a block cipher and chose PRESENT to demonstrate an example. Several small trials that focussed on different Hamming distances showed BGF-PRESENT compared well with PRESENT. Indeed, both ciphers produced near ideal Hamming distances of n/2 = 32 in all trials. The BGF may therefore be a useful tool to protect ciphers that have weak fixed permutations that can be exploited by attacks such as the statistical saturation attack.