BLISK: Boolean circuit Logic Integrated into the Single Key

This development addresses the limitations of current methods by allowing for more nuanced control over who can spend bitcoins without compromising privacy or efficiency. Traditional mechanisms offered by Bitcoin, such as threshold/multisignatures and scripts, present certain drawbacks. Threshold signatures, while efficient and private, are only able to express cardinality, meaning they can't accommodate more intricate conditions beyond simple k-of-n scenarios. Scripts offer greater expressiveness but fall short in practice due to visibility issues and practical limitations.

A Proof of Concept (PoC) framework has been developed that compiles a monotone boolean policy—integrating AND/OR logic—over users' long-term keys into a single signature verification key, represented by one Elliptic Curve (EC) point. This approach ensures that the on-chain component remains straightforward, entailing the verification of a singular Schnorr signature against one key, thereby keeping all policy complexity off-chain. The significance of this advancement lies in its ability to articulate policies which threshold signatures cannot accurately represent, such as (A ∨ B) ∧ (C ∨ D), showcasing its capability for structural expression as opposed to mere numerical counting.

The framework utilizes well-established cryptographic primitives to achieve its goals: MuSig2 for AND gates, Elliptic Curve Diffie-Hellman (ECDH) for OR gates, and Non-Interactive Zero-Knowledge proofs (e.g., Bulletproofs) to ensure the verifiability of circuit resolutions and prevent dishonesty in OR-gate execution. Additionally, the system is designed with a setup phase that allows for non-interactive key rotation and permits users to continue utilizing their existing long-term keys, unlike threshold Distributed Key Generation (DKG) systems that necessitate new key material.

This innovative approach opens up new possibilities for Bitcoin's functionality by enabling complex policy enforcement without revealing the policy itself to external parties, thus maintaining privacy and security. It represents a blend of privacy, efficiency, and expressiveness in digital currency transactions. For further reading and a deeper understanding of this framework, references include a detailed academic paper available at https://eprint.iacr.org/2026/088.pdf and an explainer blog post at https://hackmd.io/@olkurbatov/HJm5h0JH-l. Although not ready for production use, the framework's codebase can be found at https://github.com/zero-art-rs/blisk, inviting feedback and further development from the community.