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

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. More precisely, we first define SWMR verifiable registers. 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. We give a signature-free implementation of such registers from plain SWMR registers in systems with n > 3f processes, f of which can be Byzantine. We also give a signature-free implementation of SWMR sticky registers from SWMR registers in systems with n > 3f processes. Once the writer p writes a value υ into a SWMR sticky register R, the register never changes its value. Note that the value υ can be considered "signed" by p: once p writes υ in R, p cannot change the value in R or deny that it wrote υ in R, and every reader can verify that p wrote υ just by reading R. This holds even if the writer p of R is Byzantine. We prove that our implementations are optimal in the number of Byzantine processes they can tolerate. Since SWMR registers can be implemented in message-passing systems with Byzantine processes and n > 3f [11], the results in this paper also show that one can implement verifiable registers and sticky registers in such systems.