A new way was be ginning to extend and improve distributed networks, by introducing Bitcoin and Blockchain. S ecurity and scalability are the most important issues for change centralized networks to distributed networks with Blockchain. The Nakamoto's Blockchain is secure, but it is not scalable because it needs too much computational power, so this is not useful in different usage. Finally, scientists propose Sharding as the best solution for scalability of the Blockchain. Elastico was the first S hard -based Blockchain , and some other protocols were proposed to improve its operation. All of these protocols are weak against the Sybil attack . In this attack, the attacker tries to impersonate and make a lot of fake ids to increase his influence and his vote in the network. So he can annul consensus in some shards or he can change the output of some shards and puts his favorite transactions in the Blockchain. In this thesis, we talk about S hard- baseed protocols in details, then we analyzed one of these protocols, Elastico , about security against Sybil attack . we found that the PoW that used to ID generation in the initial phases of this protocol, is vulnerable against Sybil attack and the node with high hash power can generate many fake IDs. He can control the shard when his ID s entered the shard. In the following, we have expressed the attack conditions and the goals that the attacker may be following. Then , we obtained some equations to calculation the attacker's success probability in the Sybil attack . After that, we simulated the initial phases of the Elastico and simulated this attack in that. According to our observations , we can say, the node that has 25\\% hash power of the entire network who can generate 25\\% of the total IDs of the network, can doing the attack with success probability about 0.2. So the PoW is not a suitable way for ID generation in the Shard- based protocols. Key Words : Blockchain, Sharding, Proof of Work, Sybil Attack, Success Probability.
