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

TL;DR

This paper enhances privacy in conditional secret disclosure by making the pre-decided condition itself private and introduces threshold distributed point functions with secure multi-evaluation, along with optimal secret sharing methods.

Contribution

It introduces function-private CDS that keeps the condition secret, derives a new function secret sharing scheme, and presents an optimal threshold secret sharing procedure for polynomials.

Findings

Function-private CDS prevents revealing the condition to third parties.

New function secret sharing scheme derived from function-private CDS.

Optimal threshold secret sharing method for polynomials in finite fields.

Abstract

Conditional disclosure of secrets (CDS) allows multiple parties to reveal a secret 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 introducing function-private CDS wherein the pre-decided condition is never revealed to the third party. We also derive a function secret sharing scheme from our function-private CDS solution. The second problem that we consider concerns threshold distributed point functions, which allow one to split a point function such that at least a threshold number of shares are required to evaluate it at any given input. We consider a setting wherein a point function is split among a set of parties such that multiple evaluations do not leak non-negligible information about it. Finally, we present a provably optimal procedure to perform threshold function secret sharing of any polynomial in a finite field.