2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/31775We propose a new homomorphic public-key cryptosystem over arbitrary nonidentity finite group based on the difficulty of the membership problem for groups of integer matrices. Besides, a homomorphic cryptosystem is designed for the first time over finite commutative rings.Cryptography and SecurityI.2.1; I.1.2; F.2.1Homomorphic public-key cryptosystems over groups and ringstext