Making Large Hash Functions From Small Compression Functions

We explore the idea of creating a hash function that produces an s-bit digest from a compression function with an n-bit output, where s > n. This is accomplished by truncating a hash function with a digest size of ln-bits. Our work answers the question of how large l can be while creating a digest of sn-bits securely. We prove that our construction is secure with respect to preimage resistance and collision resistance for s ≤ 2n.