You can lie but not deny: SWMR registers with signature properties in systems with Byzantine processes

Abstract

We define and show how to implement SWMR registers that provide properties of unforgeable digital signatures - without actually using such signatures - in systems with Byzantine processes. Intuitively, processes can use these registers to write values as if they are ``signed'', such that these ``signed values'' can be ``verified'' by any process and ``relayed'' to any process. All our register implementations are from SWMR registers, and they work in systems with $n > 3f$ processes, $f$ of which can be Byzantine. We show that these implementations are optimal in the number of Byzantine processes they can tolerate: more precisely, we prove that if $3 \le n \le 3f$, the registers that we propose cannot be implemented from SWMR registers without using signatures. The registers that we introduce in this paper can also be implemented without signatures in message-passing systems with $n > 3f$ processes, $f$ of which can be Byzantine: this is because SWMR registers can be implemented in such systems (Most\'efaoui, Petrolia, Raynal, and Jard 2017).