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We call this model Privacy-Preserving Authenticated List (PPAL).
In this model, the queries are performed on the list stored in the (untrusted) cloud where data integrity and privacy have to
be maintained. To realize an efficient authenticated data structure, we first adapt consistent data query model.
To this end we introduce a formal model called Zero-Knowledge List (ZKL) scheme which generalizes consistent membership queries in zero-knowledge
to consistent membership and order queries on a totally ordered set in zero knowledge. We present a construction of ZKL based on zero-knowledge set
and homomorphic integer commitment scheme. Then we discuss why this construction is not as efficient as desired in cloud applications and
present an efficient construction of PPAL based on bilinear accumulators and bilinear maps which is provably secure and zero-knowledge.
We show a protocol that does not have this drawback. Specifically, in our protocol the client obtains a bound on the communication complexity of each session at the start of the session. Additionally the protocol is constant-rounds. Our protocol is fully concurrent, and assumes only collision-resistant hash functions. The proof requires considerably different techniques than those of Persiano and Visconti. Our main technical tool is an adaptation of the \"committed-simulator\" technique of Deng et. al [FOCS 09].