  Bitcoin's single leader consensus protocol (Nakamoto consensus) suffers from
significant transaction throughput and network scalability issues due to the
computational requirements of it Proof-of-Work (PoW) based leader selection
strategy. To overcome this, committee-based approaches (e.g., Elastico) that
partition the outstanding transaction set into shards and (randomly) select
multiple committees to process these transactions in parallel have been
proposed and have become very popular. However, by design these committee or
shard-based blockchain solutions are easily vulnerable to the Sybil attacks,
where an adversary can easily compromise/manipulate the consensus protocol if
it has enough computational power to generate multiple Sybil committee members
(by generating multiple valid node identifiers). Despite the straightforward
nature of these attacks, they have not been systematically analyzed. In this
paper, we fill this research gap by modelling and analyzing Sybil attacks in a
representative and popular shard-based protocol called Elastico. We show that
the PoW technique used for identifier or ID generation in the initial phase of
the protocol is vulnerable to Sybil attacks, and a node with high hash-power
can generate enough Sybil IDs to successfully compromise Elastico. We
analytically derive conditions for two different categories of Sybil attacks
and perform numerical simulations to validate our theoretical results under
different network and protocol parameters.
