We study a secret sharing problem with three secrets where the secrets are allowed to be related to each other, i.e., only certain combinations of the three secrets are permitted. The dealer produces three shares such that every pair of shares reveals a unique secret and reveals nothing about the other two secrets, other than what can be inferred from the revealed secret. For the case of binary secrets, we exactly determine the minimum amount of randomness required by the dealer, for each possible set of permitted combinations. Our characterization is based on new lower and upper bounds.

翻译：我们研究了一个涉及三个秘密的秘密共享问题，其中秘密之间允许存在关联，即仅允许特定的三种秘密组合。分发者生成三个份额，使得每一对份额能够揭示一个唯一的秘密，且除从该秘密中可推断的信息外，不泄露其他两个秘密的任何信息。对于二元秘密的情况，我们精确确定了针对每一种可能的允许秘密组合集，分发者所需的最小随机量。我们的刻画基于新的下界和上界。