The problem BitMix solves

While various privacy-preserving solutions leveraging zero-knowledge proofs and homomorphic encryption exist for conventional transactions within Ethereum Virtual Machine (EVM) compatible chains, there remains a critical vulnerability in cross-chain message passing protocols - specifically in blockchain bridges. Empirical evidence from multiple authoritative sources demonstrates this systemic weakness:
The REKT database's vulnerability tracking, Chainalysis's longitudinal analysis of bridge exploits, and Elliptic's comprehensive study of cross-chain vulnerabilities collectively indicate that bridge protocols represent the highest-value attack vectors in the DeFi ecosystem. This is further corroborated by DeFiLlama's Total Value Locked (TVL) metrics and SlowMist's security incident reports.
We propose BitMix, a novel protocol that extends privacy guarantees to cross-chain bridge operations through the application of multiplicative homomorphic properties inherent in Elliptic Curve Cryptography (ECC). Similar to how Tornado Cash implements zero-knowledge circuits to break transaction graph linkability through deposit-withdrawal unlinkability, BitMix leverages the homomorphic relationship between private keys and their corresponding public keys on the secp256k1 curve.
Specifically, given the curve point multiplication property where:

P = k * G (where P is the public key, k is the private key, and G is the generator point)
(k1 * G) + (k2 * G) = (k1 + k2) * G

This homomorphic property enables the construction of a privacy-preserving bridge protocol where:
Cross-chain message verification remains cryptographically sound
The linkability between source and destination addresses is obfuscated
The underlying bridge operation maintains verifiable integrity
This approach presents advantages over traditional mixers by extending privacy guarantees across heterogeneous consensus domains while maintaining the fundamental security properties required for trustless bridge operations

Challenges we ran into

1. In a hypersensitive market with more filler's avaibale to accept user's orders there might be cases where a single user gets matched to multiple fillers. For this we came up with a regulatory service which provides SACP's on bitcoin or by using HTLC's on etheruem that ensure only one is to one matching happens while getting incentized to stay available for enabling more trades.

2. We needed fast implementions of SPV and ECIES encyption both in dev time and performance to show appealing demo's which wouldn't have been possible without Succinct's SP1 and their prover network.

Additional Features

1.Lighting network compatability. Example transaction : https://mempool.space/testnet4/address/tb1qltptfs70ehd463ysl4znrez430kurl0gfzmg2w
2.One feature that we planned as cherry on the top was a small game where eople can bet on bitcoin block timestamps that we thought would offer a more fun persecptive to what possible with Bitcoin state relaying systems like Citrea.