Update README.md

README.md

@@ -26,10 +26,17 @@ Other tests: `forge test --no-match-test testRef`
 
 ## Implemented BDE protocols
 
+Below follows a short introduction to the implementation of the protocols in the paper.
+**IMPORTANT** this is an unaudited, proof-of-concept implementation used mainly for benchmarking and exploring practical feasibility and limitations. Do not use this code in a production environment.
+
 ### ElGamal encryption-based
 
+This [version](https://github.com/PopcornPaws/fde/tree/main/src/veck/kzg/elgamal) of the protocol uses exponential ElGamal encryption for generating the ciphertexts. Plaintext data is represented by scalar field elements of the BLS12-381 curve. Since exponential ElGamal relies on a brute-force approach to decrypt the ciphertexts, we needed to ensure that the encrypted scalar field elements are split up into multiple `u32` shards that are easier to decrypt than a single 256 bit scalar. Thus we needed an additional [encryption proof](https://github.com/PopcornPaws/fde/blob/main/src/veck/kzg/elgamal/encryption.rs) whose goal is to prove that the plaintext shards are indeed in the range of `0..u32::MAX` and we also needed to ensure that the plaintext shards can be used to reconstruct the original 256 bit scalar. For this we used simple [`DLEQ` proofs](https://github.com/PopcornPaws/fde/blob/main/src/dleq.rs). For the [range proofs](https://github.com/PopcornPaws/fde/tree/main/src/range_proof), we used a slightly modified version of [this](https://github.com/roynalnaruto/range_proof) implementation, that is based on the work of [Boneh-Fisch-Gabizon-Williamson](https://hackmd.io/@dabo/B1U4kx8XI) with further details discussed in [this blogpost](https://decentralizedthoughts.github.io/2020-03-03-range-proofs-from-polynomial-commitments-reexplained/).
+
 ### Paillier encryption-based
 
+This [version](https://github.com/PopcornPaws/fde/blob/main/src/veck/kzg/paillier/mod.rs) of the protocol uses the Paillier encryption scheme to encrypt the plaintext data. It utilizes the [num-bigint](https://crates.io/crates/num-bigint) crate for proof generation due to working in an RSA group instead of a elliptic curve. Computations are therefore slightly less performant than working with [arkworks](https://github.com/arkworks-rs) libraries, but we gain a lot in the decryption phase where there is no need to split up the original plaintext, generate range proofs and use a brute-force approach for decryption.
+
 ## On-chain components of our protocols
 
 ## Benchmarks