Homomorphic Quorum System Brief Mathematical Overview Post-Quantum 1 Introduction Post-Quantum(PQ)hasdevelopedaquorumorconsensussystemthatreinforcessegregationofdutyin digitaldomain. Thisusesawell-studiedtechniqueintheareaofsecurity,knownasthresholdsignature. Inessence,itisbasedonanasymmetriccryptosysteminwhichtheprivate-keyissplitintoanumberof fragments1. Inordertoproduceadigitalsignature,asu?cientnumberofparticipantsarerequiredto producesignaturefragmentswhicharelaterhomomorphicallycombinedtoproduceadigitalsignature. These fragmentscan be shared between multiple stakeholdersand in a corporate environment, these couldbetherelevantdivisionalmanagersorsupervisors. Splittingtheprivate-keyinthiswayremovesthesinglepointoffailurebyeliminatingtheriskthat the private-key can be lost, stolen or abused, and introduces true separation of duties in the digital realm. This piece of technology has uses in every serious business, with applications ranging from protectingarchivestoensuringauthorisedaccesstoasystemholdingsensitiveinformation. While threshold signature may be implemented in a hardware module, the system that PQ has developed removes the need to procure and maintain such an expensive hardware module. PQ’s system can be deployed on any cloud infrastructure, and it leverages the secure-enclave on mobile devicestoperformdistributedcryptographicoperations. Beingonmobile,thesystemo?ersadistinct advantage over a hardware alternative, where a fragment holder can participate in a quorum even if he/sheisnotphysicallypresent. This document describes the mathematical operations be