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Conditional disclosure of secrets (CDS) allows multiple parties to reveal asecret to a third party if and only if some pre-decided condition is satisfied.In this work, we bolster the privacy guarantees of CDS by introducingfunction-private CDS wherein the pre-decided condition is never revealed to thethird party. We also derive a function secret sharing scheme from ourfunction-private CDS solution. The second problem that we consider concernsthreshold distributed point functions, which allow one to split a pointfunction such that at least a threshold number of shares are required toevaluate it at any given input. We consider a setting wherein a point functionis split among a set of parties such that multiple evaluations do not leaknon-negligible information about it. Finally, we present a provably optimalprocedure to perform threshold function secret sharing of any polynomial in afinite field.

Function-private Conditional Disclosure of Secrets and Multi-evaluation Threshold Distributed Point Functions