Non-Malleable Secret Sharing against Affine Tampering

Non-malleable secret sharing was recently studied by Goyal and Kumar in independent tampering and joint tampering models for threshold scheme (STOC18) and secret sharing with general access structure (CRYPTO18). We study non-malleable secret sharing in a natural adaptive tampering model, where the share vector is tampered using a function, in a given tampering family, chosen adaptively according to any unauthorised set of shares. Intuitively, the passive privacy adversary of secret sharing and the active adversary characterized by the given tampering family collude. We then focus on the tampering family of affine functions and construct non-malleable secret sharing in the adaptive tampering model. The constructions are modular with an erasure code and an extractor that provides both privacy and non-malleability. We make use of randomness extractors of various flavours, including the seeded/seedless non-malleable extractors. We discuss our results and open problems.

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