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

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