Pattern Matching in Encrypted Stream from Inner Product Encryption

Abstract

Functional encryption features secret keys, each associated with a key function f, which allow to directly recover f(x) from an encryption of x, without learning anything more about x. This property is particularly useful when delegating data processing to a third party as it allows the latter to perform its task while ensuring minimum data leakage. However, this generic term conceals a great diversity in the cryptographic constructions that strongly differ according to the functions f they support. A recent series of works has focused on the ability to search a pattern within a data stream, which can be expressed as a function f. One of the conclusions of these works was that this function f was not supported by the current state-of-the-art, which incited their authors to propose a new primitive called Stream Encryption supporting Pattern Matching (SEPM). Some concrete constructions were proposed but with some limitations such as selective security or reliance on non-standard assumptions. In this paper, we revisit the relations between this primitive and two major subclasses of functional encryption, namely Hidden Vector Encryption (HVE) and Inner Product Encryption (IPE). We indeed first exhibit a generic transformation from HVE to SEPM, which immediately yields new efficient SEPM constructions with better features than existing ones. We then revisit the relations between HVE and IPE and show that we can actually do better than the transformation proposed by Katz, Sahai and Waters in their seminal paper on predicate encryption. This allows to fully leverage the vast state-of-the-art on IPE which contains adaptively secure constructions proven under standard assumptions. This results in countless new SEPM constructions, with all the features one can wish for. Beyond that, we believe that our work sheds a new light on the relations between IPE schemes and HVE schemes and in particular shows that some of the former are more suitable to construct the latter.