Collision Spectrum, Entropy Loss, T-Sponges, and Cryptanalysis of GLUON-64

In this paper, we investigate the properties of iterative non-injective functions and the security of primitives where they are used. First, we introduce the Collision Probability Spectrum (cps) parameter to quantify how far from a permutation a function is. In particular, we show that the output size decreases linearly with the number of iterations whereas the collision trees grow quadratically. Secondly, we investigate the t-sponge construction and show how certain cps and rate values lead to an improved preimage attack on long messages. As an example, we nd collisions for the gluon64 internal function, approximate its cps, and show an attack that violates the security claims. For instance, if a message ends with a sequence of 1 Mb (respectively 1 Gb) of zeros, then our preimage search takes time 2 (respectively 2) instead of 2.