Secret Sharing and Non-Shannon Information Inequalities

The known secret-sharing schemes for most access structures are not efficient; even for a one-bit secret the length of the shares in the schemes is 2O(n) , where n is the number of participants in the access structure. It is a long standing open problem to improve these schemes or prove that they cannot be improved. The best known lower bound is by Csirmaz (J. Cryptology 97), who proved that there exist access structures with n participants such that the size of the share of at least one party is n/ log n times the secret size. Csirmaz's proof uses Shannon information inequalities, which were the only information inequalities known when Csirmaz published his result. On the negative side, Csirmaz proved that by only using Shannon information inequalities one cannot prove a lower bound of (n) on the share size. In the last decade, a sequence of nonShannon information inequalities were discovered. This raises the hope that these inequalities can help in improving the lower bounds bey...

• Type: Conference
• Year: 2009
• Where: TCC
• Authors: Amos Beimel, Ilan Orlov
• Keywords: Cryptography, Lower Bound, NonShannon Information Inequalities, Shannon Information Inequalities, TCC 2009