Secure Database Commitments and Universal Arguments of Quasi Knowledge

In this work we focus on a simple database commitment functionality where besides the standard security properties, one would like to hide the size of the input of the sender. Hiding the size of the input of a player is a critical requirement in some applications, and relatively few works have considered it. Notable exceptions are the work on zero-knowledge sets introduced ini¾?[14], and recent work on size-hiding private set intersectioni¾?[1]. However, neither of these achieves a secure computation i.e., a reduction of a real-world attack of a malicious adversary into an ideal-world attack of the proposed functionality. The first result of this submission consists in defining "secure" database commitment and in observing that previous constructions do not satisfy this definition. This leaves open the question of whether there is any way this functionality can be achieved. We then provide an affirmative answer to this question by using new techniques that combined together achieve "secure" database commitment. Our construction is in particular optimized to require only a constant number of rounds, to provide non-interactive proofs on the content of the database, and to rely on the existence of a family of CRHFs. This is the first result where input-size hiding secure computation is achieved for an interesting functionality and moreover we obtain this result with standard security i.e., simulation in expected polynomial time against fully malicious adversaries, without random oracles, without non-black-box extraction assumptions, without hardness assumptions against super-polynomial time adversaries. A key building block in our construction is a universal argument enjoying an improved proof of knowledge property, that we call quasi-knowledge. This property is significantly closer to the standard proof of knowledge property than the weak proof of knowledge property satisfied by previous constructions.