  An auditable register extends the classical register with an audit operation
that returns information on the read operations performed on the register. In
this paper, we study Byzantine resilient auditable register implementations in
an asynchronous message-passing system. Existing solutions implement the
auditable register on top of at least 4f+1 servers, where at most $f$ can be
Byzantine. We show that 4f+1 servers are necessary to implement auditability
without communication between servers, or implement does not implement strong
auditability when relaxing the constraint on the servers' communication,
letting them interact with each other. In this setting, it exists a solution
using 3f+1 servers to implement a simple auditable atomic register. In this
work, we implement strong auditable register using 3f+1 servers with server to
server communication, this result reinforced that with communication between
servers, auditability (event strong auditability) does not come with an
additional cost in terms of the number of servers.
