TY - GEN

T1 - Multi-linear secret-sharing schemes

AU - Beimel, Amos

AU - Ben-Efraim, Aner

AU - Padró, Carles

AU - Tyomkin, Ilya

PY - 2014/1/1

Y1 - 2014/1/1

N2 - Multi-linear secret-sharing schemes are the most common secret-sharing schemes. In these schemes the secret is composed of some field elements and the sharing is done by applying some fixed linear mapping on the field elements of the secret and some randomly chosen field elements. If the secret contains one field element, then the scheme is called linear. The importance of multi-linear schemes is that they provide a simple non-interactive mechanism for computing shares of linear combinations of previously shared secrets. Thus, they can be easily used in cryptographic protocols. In this work we study the power of multi-linear secret-sharing schemes. On one hand, we prove that ideal multi-linear secret-sharing schemes in which the secret is composed of p field elements are more powerful than schemes in which the secret is composed of less than p field elements (for every prime p). On the other hand, we prove super-polynomial lower bounds on the share size in multi-linear secret-sharing schemes. Previously, such lower bounds were known only for linear schemes.

AB - Multi-linear secret-sharing schemes are the most common secret-sharing schemes. In these schemes the secret is composed of some field elements and the sharing is done by applying some fixed linear mapping on the field elements of the secret and some randomly chosen field elements. If the secret contains one field element, then the scheme is called linear. The importance of multi-linear schemes is that they provide a simple non-interactive mechanism for computing shares of linear combinations of previously shared secrets. Thus, they can be easily used in cryptographic protocols. In this work we study the power of multi-linear secret-sharing schemes. On one hand, we prove that ideal multi-linear secret-sharing schemes in which the secret is composed of p field elements are more powerful than schemes in which the secret is composed of less than p field elements (for every prime p). On the other hand, we prove super-polynomial lower bounds on the share size in multi-linear secret-sharing schemes. Previously, such lower bounds were known only for linear schemes.

KW - Dowling geometries

KW - Ideal secret-sharing schemes

KW - multi-linear matroids

UR - http://www.scopus.com/inward/record.url?scp=84958549041&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-54242-8_17

DO - 10.1007/978-3-642-54242-8_17

M3 - Conference contribution

AN - SCOPUS:84958549041

SN - 9783642542411

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

SP - 394

EP - 418

BT - Theory of Cryptography - 11th Theory of Cryptography Conference, TCC 2014, Proceedings

PB - Springer Verlag

T2 - 11th Theory of Cryptography Conference on Theory of Cryptography, TCC 2014

Y2 - 24 February 2014 through 26 February 2014

ER -