Efficient Completely Context-Hiding Quotable and Linearly Homomorphic Signatures

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Homomorphic signatures are primitives that allow for public computations for a class of specified predicates over authenticated data. An enhanced privacy notion, called complete context-hiding security, was recently motivated by Attrapadung et al. (Asiacrypt’12). This notion ensures that a signature derived from any valid signatures is perfectly indistinguishable from a newly generated signatures (on the same message), and seems desirable in many applications requiring to compute on authenticated data. In this paper, we focus on two useful predicates – namely, substring quotation predicates and linear dependency predicates – and present the first completely context-hiding schemes for these in the standard model. Moreover, our new quotable signature scheme is the first such construction with signatures of linear size. In comparison with the initial scheme of Ahn et al. (TCC 2012), we thus reduce the signature size from O(n logn) to O(n), where n is the message size. Our scheme also allows signing messages of arbitrary length using constant-size public keys.