International Association
for Cryptologic Research

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 find collisions for the GLUON-64 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 $2^{115.3}$ (respectively $2^{105.3}$) instead of $2^{128}$.