1/ Fully Homomorphic Encryption (FHE) allows computation over encrypted data. It is a privacy-preserving primitive in programmable cryptography that allows secure processing. Zero to Start: Applied FHE Part 1: mirror.xyz/privacy-scalin…  & Part 2 mirror.xyz/privacy-scalin….  A thread🧵

2/ FHE shares fundamental components with traditional cryptography like encryption, decryption, and key generation.There are four categories of homomorphic encryption:

Product @PrivacyScaling @Ethereum | @Delphi Digital | Nomad

3/ FHE holds immense significance in blockchain technology because it can perform encrypted data computations within a trustless environment. Some applications include private transactions, MEV protection, scaling, DAO voting, and blind auctions.

4/ In a privacy-preserving dark pool, traders can place private orders that are executed with FHE without "alerting" the open market of their intentions and potentially giving away high-value alpha.

5/ FHE is an extension of public key cryptography, not a replacement for ZKPs or MPC. ZKPs will be vital because they can be used to generate proofs of correctly constructed FHE ciphertexts.

6/ While MPC is network bound, FHE and ZKPs are compute bound. Each acts as an individual building block and serves a distinct cryptographic purpose.

7/ FHE is not practical with Ethereum today due to the size of ciphertexts and the cost of computation on-chain. Several projects are working on FHE at the moment: @zama_fhe  (TFHE)  @SunscreenTech  (BFV Compiler)  @FhenixIO  (FHE Rollups)

8/ The open problems for FHE fall into three categories: usability, composability, and performance. Challenges predominantly revolve around data efficiency due to large ciphertext and bootstrapping key sizes.

9/ Realizing FHE’s full potential demands overcoming these challenges and integration with other cryptographic primitives like ZKPs and MPCs.