Hash Function Constructions from Lightweight Block Ciphers for Fully Homomorphic Encryption

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This paper investigates hash-function constructions derived from lightweight block ciphers, that are suitable for evaluation in fully homomorphic encryption (FHE) settings. We focus on PRINCEv2, a 64-bit lightweight block cipher with 128-bit keys and low algebraic complexity, which is particularly amenable to FHE evaluation. However, the small block size of such ciphers limits the applicability of standard hash-function transforms. Indeed, achieving 128-bit collision resistance in the $(n, 2n)$