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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.