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We introduce a formal model for order queries on lists in zero knowledge inthe traditional authenticated data structure model. We call this modelPrivacy-Preserving Authenticated List (PPAL). In this model, the queries areperformed on the list stored in the (untrusted) cloud where data integrity andprivacy have to be maintained. To realize an efficient authenticated datastructure, we first adapt consistent data query model. To this end we introducea formal model called Zero-Knowledge List (ZKL) scheme which generalizesconsistent membership queries in zero-knowledge to consistent membership andorder queries on a totally ordered set in zero knowledge. We present aconstruction of ZKL based on zero-knowledge set and homomorphic integercommitment scheme. Then we discuss why this construction is not as efficient asdesired in cloud applications and present an efficient construction of PPALbased on bilinear accumulators and bilinear maps which is provably secure andzero-knowledge.

Verifiable Member and Order Queries on a List in Zero-Knowledge