Accountability for Misbehavior in Threshold Decryption via Threshold Traitor Tracing

A t-out-of-n threshold decryption system assigns key shares to n parties so that any t of them can decrypt a well-formed ciphertext. Existing threshold decryption systems are not secure when these parties are rational actors: an adversary can offer to pay the parties for their key shares. The problem is that a quorum of t parties, working together, can sell the adversary a decryption key that reveals nothing about the identity of the traitor parties. This provides a risk-free profit for the parties since there is no accountability for their misbehavior—the information they sell to the adversary reveals nothing about their identity. This behavior can result in a complete break in many applications of threshold decryption, such as encrypted mempools, private voting, and sealed-bid auctions. In this work we propose a solution to this problem. Suppose a quorum of t or more parties construct a decoder algorithm  \(D(\cdot )\) that takes as input a ciphertext and outputs the corresponding plaintext or \(\bot \) . They sell D to the adversary. Our threshold decryption systems are equipped with a tracing algorithm that can trace D to members of the quorum that created it. The tracing algorithm is only given blackbox access to D and will identify some members of the misbehaving quorum. The parties can then be held accountable, which may discourage them from selling the decoder D in the first place. Our starting point is standard (non-threshold) traitor tracing, where n parties each holds a secret key. Every party can decrypt a well-formed ciphertext on its own. However, if a subset of parties \(\mathcal{J} \subseteq [n]\) collude to create a pirate decoder \(D(\cdot )\) that can decrypt well-formed ciphertexts, then it is possible to trace D to at least one member of \(\mathcal{J}\) using only blackbox access to the decoder D. In this work we develop the theory of traitor tracing for threshold decryption, where now only a subset \(\mathcal{J} \subseteq [n]\) of t or more parties can collude to create a pirate decoder \(D(\cdot )\) . This problem has recently become quite important due to the real-world deployment of threshold decryption in encrypted mempools, as we explain in the paper. While there are several non-threshold traitor tracing schemes that we can leverage, adapting these constructions to the threshold decryption settings requires new cryptographic techniques. We present a number of constructions for traitor tracing for threshold decryption, and note that much work remains to explore the large design space.