Differential analysis of the Extended Generalized Feistel Networks

•Point out mistakes in the security evaluation of EGFN against differential attack.•Construct a class of differential conflicting with designers' evaluation for EGFN.•Give a method to search a special type of differential with high probability.•Our results show that EGFN always exist high probability iterative differential.

This paper studies the differential analysis of Extended Generalized Feistel Networks (EGFNs). First we construct a class of differential characteristics which conflict with designers' evaluation of minimal number of active S-boxes for EGFN. Then by analyzing the difference cancellation property of EGFN, we propose a method to search a special type of differential characteristics with high probability. We obtain the best case of this kind of differential characteristic for EGFN with block number 4≤k≤324≤k≤32. Our results show that for EGFN with k≥8k≥8 there always exist high probability iterative differential characteristics and their number of active S-boxes for 20-round all are equal to 26. Therefore, the actual ability of EGFN resisting differential analysis may be a lot weaker than evaluated by designers and larger block size cannot improve the situation.