TY - GEN

T1 - Secret sharing and non-shannon information inequalities

AU - Beimel, Amos

AU - Orlov, Ilan

N1 - Funding Information:
Partially supported by the Frankel Center for Computer Science at the Ben-Gurion University.

PY - 2009/11/9

Y1 - 2009/11/9

N2 - 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 2 O(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/logn 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 ω(n) on the share size. In the last decade, a sequence of non-Shannon information inequalities were discovered. This raises the hope that these inequalities can help in improving the lower bounds beyond n. However, in this paper we show that all the inequalities known to date cannot prove a lower bound of ω(n) on the share size.

AB - 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 2 O(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/logn 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 ω(n) on the share size. In the last decade, a sequence of non-Shannon information inequalities were discovered. This raises the hope that these inequalities can help in improving the lower bounds beyond n. However, in this paper we show that all the inequalities known to date cannot prove a lower bound of ω(n) on the share size.

UR - http://www.scopus.com/inward/record.url?scp=70350660861&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-00457-5_32

DO - 10.1007/978-3-642-00457-5_32

M3 - Conference contribution

AN - SCOPUS:70350660861

SN - 3642004563

SN - 9783642004568

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 539

EP - 557

BT - Theory of Cryptography - 6th Theory of Cryptography Conference, TCC 2009, Proceedings

T2 - 6th Theory of Cryptography Conference, TCC 2009

Y2 - 15 March 2009 through 17 March 2009

ER -