Cryptographic Primitives with Hinting Property

Abstract

A hinting pseudorandom generator (PRG) is a potentially stronger variant of PRG with a “deterministic” form of circular security with respect to the seed of the PRG (Koppula and Waters, in: Boldyreva and Micciancio (eds) CRYPTO 2019, Part II, volume 11693 of LNCS, pp 671-700, Springer, Heidelberg, 2019). Hinting PRGs enable many cryptographic applications, most notably CCA-secure public-key encryption and trapdoor functions. In this paper, we study cryptographic primitives with the hinting property, yielding the following results: We present a novel and conceptually simpler approach for designing hinting PRGs from certain decisional assumptions over cyclic groups or isogeny-based group actions, which enables simpler security proofs as compared to the existing approaches for designing such primitives. We also show that the same design approach yields a generic construction of hinting PRGs from a simple cryptographic primitive with algebraic structure, namely a key-homomorphic weak PRF. We introduce hinting pseudorandom functions (PRFs) and hinting weak PRFs, which are natural extensions of the hinting property to PRFs and weak PRFs. We show how to realize circular/KDM-secure symmetric-key encryption from any hinting weak PRF. We demonstrate that our simple approach for building hinting PRGs can be extended to realize hinting weak PRFs from the same set of decisional assumptions. We also show a generic construction of hinting (weak) PRF from any hinting PRG with certain structural properties, thus yielding the first constructions of symmetric-key encryption with full-fledged circular/KDM-security from such hinting PRGs. We propose a stronger version of the hinting property, which we call the functional hinting property, that guarantees security even in the presence of hints about functions of the secret seed/key. We show how to instantiate functional hinting PRGs/weak PRFs for certain (families of) functions by building upon our simple techniques for realizing plain hinting PRGs/weak PRFs. We also demonstrate the applicability of a functional hinting weak PRF with certain algebraic properties in realizing KDM-secure public-key encryption in a black-box manner. We show the first black-box separation between hinting PRFs (and hence, hinting PRGs) from public-key encryption using simple realizations of these primitives given only a random oracle.