Indifferentiability of 3-Round Confusion-Diffusion Networks

Substitution-Permutation Networks (SPNs) are a popular and powerful technique for designing block ciphers. Confusion-Diffusion Networks (CDNs), as formalised by Dodis et al. at Eurocrypt’16, treat unkeyed SPNs as a means of extending the domain of public permutations. Dodis et al. showed that 5-round CDNs are indifferentiable from an ideal permutation, and subsequent works by Da et al. at Indocrypt’21 and Nandi et al. at C2SI’23 have established that 2-round CDNs cannot achieve the weaker notion of sequential indifferentiability even with non-linear diffusion layers. In this paper we show for the first time that 3-round CDNs with linear diffusion layers can achieve indifferentiability from an ideal permutation.