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.
翻译:有条件披露机密(CDS) 允许多个当事人向第三方透露机密,如果而且只有在某些事先决定的条件得到满足的情况下,才能向第三方披露机密。 在这项工作中,我们通过引入功能-私人CDS,加强CDS的隐私保障,其中决定前的条件从未向第三方披露。我们还从功能-私人CDS解决方案中得出了一个功能性秘密共享计划。我们认为,第二个问题涉及阈值分配点功能,它允许一个点函数分割一个点函数,这样至少需要一定数量的股份才能在任何特定投入中评估它。我们考虑一个设定,即点函数在一组缔约方之间分割,这样多个评估不会泄露关于该条件的不可忽略的信息。最后,我们提出了一个可以肯定的最佳程序,以进行临界秘密共享,在一定的字段中,任何组合性共享。