One of the main shortcomings of classical distributed cryptography is its reliance on a certain fraction of participants remaining honest. Typically, honest parties are assumed to follow the protocol and not leak any information, even if acting dishonestly would benefit them economically. More realistic models used in blockchain consensus rely on weaker assumptions, namely that no large coalition of corrupt parties exists, although every party can act selfishly. This is feasible since, in a consensus protocol, active misbehavior can be detected and „punished” by other parties. However, „information leakage”—where an adversary reveals sensitive information via, for example, a subliminal channel—is often impossible to detect and, therefore, much more challenging to address.
A recent approach to address this problem was proposed by Dziembowski, Faust, Lizurej, and Mielniczuk (ACM CCS 2024), who introduced a new concept called secret sharing with snitching. This primitive guarantees that, as long as no large coalition of mutually trusting parties exists, every leakage of the shared secret produces a „snitching proof” indicating that some party participated in the illegal reconstruction of the secret. This holds in a very strong model, where mutually distrusting parties use an MPC protocol to reconstruct any information about the shared secret. Such a „snitching proof” can be sent to a smart contract (modeled as a „judge”) deployed on the blockchain, which punishes the offending party financially.
In this paper, we extend the results from the work presented at CCS’24 by addressing its two main shortcomings. First, we significantly strengthen the attack model by considering the case where mutually distrusting parties can also rely on a trusted third party (e.g., a smart contract). We call this new primitive “strong secret sharing with snitching” (SSSS).
We present an SSSS protocol that is secure in this model. Secondly, unlike the construction from CCS’24, our protocol does not require the honest parties to perform any MPC computations on hash functions. In addition to its theoretical interest, this improvement is of practical importance, as it allows the construction of SSSS from any (even very „MPC-unfriendly”) hash function.
Authors: Jan Bormet, Stefan Dziembowski, Sebastian Faust, Tomasz Lizurej, Marcin Mielniczuk