Threshold Signatures from Inner Product Argument: Succinct, Weighted, and Multi-threshold

Das, Sourav; Camacho, Philippe; Xiang, Zhuolun; Nieto, Javier; Bünz, Benedikt; Ren, Ling

doi:10.1145/3576915.3623096

We witness an increase in applications like cryptocurrency wallets, which involve users issuing signatures using private keys. To protect these keys from loss or compromise, users commonly outsource them to a custodial server. This creates a new point of failure, because compromise of such a server leaks the user’s key, and if user authentication is implemented with a password then this password becomes open to an offline dictionary attack (ODA). A better solution is to secret-share the key among a set of servers, possibly including user’s own device(s), and implement password authentication and signature computation using threshold cryptography. We propose a notion of augmented password-protected threshold signature (aptSIG) scheme which captures the best possible security level for this setting. Using standard threshold cryptography techniques, i.e. threshold password authentication and threshold signatures, one can guarantee that compromising up to t out of n servers reveals no information on either the key or the password. However, we extend this with a novel property, that compromising even all n servers also does not leak any information, except via an unavoidable ODA attack, which reveals the key only if the attacker guesses the password. We define aptSIG in the Universally Composable (UC) framework and show that it can be constructed very efficiently, using a black-box composition of any UC threshold signature [13] and a UC augmented Password-Protected Secret Sharing (aPPSS), which we define as an extension of prior notion of PPSS [30]. As concrete instantiations we obtain secure aptSIG schemes for ECDSA (in the case of t=n-1) and BLS signatures with very small overhead over the respective threshold signature. Finally, we note that both the notion and our generic solution for augmented password-protected threshold signatures can be generalized to password-protecting MPC for any keyed functions.

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