Zerocoin looks to combat the public nature of the blockchain. If you use Bitcoin then, if you don’t follow very strict rules, you may have your privacy compromised.

Once users started having their privacy taken away in their cryptocurrency transactions, third-party coin mixing services sprung up to obscure the trail of cryptocurrency transactions. 

In May 2013, Matthew D. Green, Ian Miers, and Christina Garman proposed the Zerocoin protocol. This helped users step away from mixing services and step into a cryptocurrency where transactions can be anonymized. The theory behind Zerocoin was taking a coin and destroying it, then minting an equal amount, which would erase its history.

At first, the Zerocoin protocol was to be integrated into the Bitcoin network.

Unfortunately, Zerocoin was not accepted by the Bitcoin community. 

The original developers of the Zerocoin protocol, undaunted, launched the protocol into an independent cryptocurrency in September 2016, which they then called Zcoin (XZC).

Zcoin used the Zerocoin protocol and Proof-of-work with memory intensive Merkle tree proof algorithm. The mining system helped ordinary users mine and use the coin. 

Unfortunately, in April 2018, a cryptographic flaw was found in the Zerocoin protocol which led to Zcoin plummeting in value.

The flaw allowed attackers to destroy the coins owned by other users. Then, the attackers would create coins while stealing users' coins.

Since then the flaw has been more or less patched up and now transactions which use the Zerocoin feature are drawn from an escrow pool. Then, after going through the zerocoin protocol, each coin's transaction history is erased and the users in the escrow pool get new coins returned to them without any history. These transactions are verified by zero-knowledge proofs -- which are used to prove a statement is true without revealing any details about the previous questions.

So if you’re looking to find a coin that gives you full control over your financial data, then consider if Zcoin or other privacy coins using the zerocoin protocol are something you should consider. And take into account that all privacy coins are new and may have undiscovered flaws.