On Compression Functions over Small Groups with Applications to Cryptography. (arXiv:2208.02468v1 [math.GR])

In the area of cryptography, fully homomorphic encryption (FHE) enables any
entity to perform arbitrary computation on encrypted data without decrypting
the ciphertexts. An ongoing group-theoretic approach to construct FHE schemes
uses a certain "compression" function $F(x)$ implemented by group operators on
a given finite group $G$ (i.e., it is given by a sequence of elements of $G$
and variable $x$), which satisfies that $F(1) = 1$ and $F(\sigma) = F(\sigma^2)
= \sigma$ where $\sigma \in G$ is some element …

applications compression cryptography functions math