Indifferentiability of the Sponge Construction with a Restricted Number of Message Blocks

Abstract

The sponge construction is a popular method for hashing. Quickly after its introduction, the sponge was proven to be tightly indifferentiable from a random oracle up to ≈ 2^c/2 queries, where c is the capacity. However, this bound is not tight when the number of message blocks absorbed is restricted to ℓ < ⌈ c / 2(b−c) ⌉ + 1 (but still an arbitrary number of blocks can be squeezed). In this work, we show that this restriction leads to indifferentiability from a random oracle up to ≈ min { 2^b/2, max { 2^c/2, 2^{b−ℓ×(b−c)} }} queries, where b > c is the permutation size. Depending on the parameters chosen, this result allows to have enhanced security or to absorb at a larger rate for applications that require a fixed-length input hash function.