Cheater Identifiable Secret Sharing Schemes via Multi-Receiver Authentication

We introduce two publicly cheater identifiable secret sharing (CISS) schemes with efficient reconstruction, tolerating t < k/2 cheaters. Our constructions are based on (k, n) threshold Shamir scheme, and they feature a novel application of multi-receiver authentication codes to ensure integrity of shares. The first scheme, which tolerates rushing cheaters, has the share size |S|(n−t)/ n+t+2 in the general case, that can be ultimately reduced to |S|(k−t)/ k+t+2 assuming that all the t cheaters are among the k reconstructing players. The second scheme, which tolerates non-rushing cheaters, has the share size |S|(n− t)/ . These two constructions have the smallest share size among the existing CISS schemes of the same category, when the secret is a single field element. In addition, we point out that an improvement in the share size to |S|/ n−b(k−1)/3c+1 can be achieved for a CISS tolerating t < k/3 rushing cheaters presented by Xu et al. at IWSEC 2013.