One of the biggest challenges facing the entire crypto ecosystem is privacy, where the use of applications does not imply making an important part of our data public on the network, so that anyone can see and analyze it.

Zero-knowledge proofs (ZKP) have emerged as a valuable tool in cryptography due to their ability to prove knowledge of information without revealing it, as well as to improve scalability in the context of zk-rollups.

Although ZKPs offer significant benefits in terms of privacy and scalability, they face significant limitations that restrict their applicability in certain scenarios.

First, ZKPs often rely on trusted third parties to store and compute hidden information, which limits their permissionless composability as other applications may need to access that data off-chain. This approach is reminiscent of web2 cloud computing, where it is necessary to introduce an element of trust into an otherwise decentralized environment.

Second, state transition in ZKPs is done via plaintext, meaning users must trust third parties to handle their unencrypted data. This raises concerns about the security and privacy of the data being handled, as the disclosure of sensitive information could almost certainly be exploited by malicious parties.

Finally, ZKPs may not be suitable for applications that require knowledge of a shared private state, to generate evidence about the local private state.

This requirement is common in groups, such as AMM groups or private lending groups, where shared status information is essential to effectively validate transactions.

Faced with these limitations, fully homomorphic cryptography (FHE) emerges as a promising alternative. FHE is a cryptography scheme that allows calculations to be performed on encrypted data without the need to first decrypt it.

This means that users can encrypt their data and send it to third parties for processing, without compromising the privacy of the information.

In the context of blockchain applications, FHE offers the possibility of maintaining a shared private state, which can be critical in scenarios where privacy is a concern.

For example, in a decentralized AMM, FHE could be used to hide information about exchange operations, maintaining user privacy while validating on-chain transactions.

However, FHE also presents its own challenges, the most notable being being too computationally intensive, which can lead to significant latency in the execution of operations.

Additionally, it requires careful management to avoid corruption of encrypted data, which can be difficult in certain contexts.

Despite these limitations, the development of FHE is underway, and its adoption is expected to increase, as the combination of FHE with other technologies (such as multi-party computing (MPC) and ZKPs) can offer more complete solutions. to guarantee privacy in blockchain applications.

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