BLISK: Boolean circuit Logic Integrated into the Single Key

The correspondence raises critical questions and suggestions regarding the use of Elliptic Curve Diffie-Hellman (ECDH) and Zero-Knowledge Proofs (ZKPs) in constructing secure communication protocols. The writer expresses confusion over the necessity of ECDH and attached ZKPs for ensuring security within disjunction subtrees of a Conjunctive Normal Form (CNF) policy framework. They propose an alternative method where a designated party from each subtree generates a random secret to share with other members, thus questioning the advantage of ECDH-based key agreement over private broadcast methods.

The writer elaborates on the potential redundancy of storing aggregate secrets for disjunction subtrees, as required in ECDH-based setups, suggesting that a randomly generated secret could serve the same purpose without necessitating stateful storage. This observation leads to a broader inquiry about the intrinsic benefits of employing ECDH for key agreement when the primary goal is to prevent adversaries from disrupting or impersonating honest qualified sets during the signing process. The assertion made implies that as long as all parties agree on the keys during setup, the system's security should be directly reducible to that of MuSig, irrespective of the key agreement mechanism employed.

Furthermore, the email introduces Replicated Secret Sharing (RSS) as a conceptual framework for understanding the proposed alternative. In RSS, each disjunction subtree in a CNF policy corresponds to a group holding replicated secrets, simplifying the Distributed Key Generation (DKG) process to sharing and verifying secrets among participants. The discussion points out that RSS inherently avoids the need for ZKPs, especially in the context of key rotation, thereby simplifying the cryptographic protocol while maintaining security assurances against adversaries lacking access to at least one honest secret.

In essence, the writer questions the complexity and statefulness introduced by ECDH and ZKPs in cryptographic protocols designed for secure group communication and suggests a more straightforward approach based on RSS and shared secrets, highlighting the potential for simplification without compromising security objectives. This perspective invites further examination of the trade-offs between different cryptographic techniques in achieving secure and efficient communication within specified policy frameworks.