Non-existence of homomorphic general sharing schemes for some key spaces

Abstract

TIornomorphic t h r e s h d t i schcines ivcre introduced by Be-naloh and have found several applications. In this payer we prove t h a t tlicrc d o not exist, perfect finite homomorphic generai rnonotoric stinrins schemes for which thr key +pace IS .L finite nun-Abeiian group (except for very particiilar ;LCCCSS i t , r n c t n r v s ;. This r r s u l t i s valid For tlie itlost general case, +. g. , if each participant ieceives shares from differelit i e t s and w h e n t h e w setc are not IIP We extend t h e definition of humomnrphic threshold ccherne LD d l o w ihclt t h e homomorphic propert). is $ d i d for two-operations LVhen the set of keys is a finite Roolean Aigebra o r a