Function-private Conditional Disclosure of Secrets and Multi-evaluation Threshold Distributed Point Functions
This work enhances privacy in cryptographic protocols for secure multi-party computation, though it appears incremental by building on existing CDS and distributed point function frameworks.
The paper tackles privacy in conditional disclosure of secrets by introducing function-private CDS to hide the condition from third parties, and addresses multi-evaluation threshold distributed point functions to prevent information leakage, with a provably optimal procedure for threshold function secret sharing of polynomials.
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.