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 applica-
tions, and relatively few works have considered it. Notable exceptions are the work on
zero-knowledge sets introduced in [MRK03], and recent work on size-hiding private set
intersection [ADCT11]. 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 only 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, non-black-box extraction assumptions, hardness
assumptions against super-polynomial time adversaries, or other controversial/strong
assumptions).
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.