Title :
Multiplicative secret sharing schemes from Reed-Muller type codes
Author :
Duursma, Iwan ; Shen, Jiashun
Author_Institution :
Dept. of Math., Univ. of Illinois, Urbana, IL, USA
Abstract :
Multiplicative linear secret sharing schemes are the building blocks for multiparty computation protocols. Such schemes can be defined in terms of linear codes with an additional algebraic structure. We show that Reed-Muller codes have the required additional structure and we introduce a more general class of Reed-Muller type codes suitable for linear secret sharing and multiparty computation. The codes have highly structured generator and parity check matrices that can be used for very efficient implementations over the binary field.
Keywords :
Reed-Muller codes; cryptographic protocols; linear codes; matrix algebra; parity check codes; Reed-Muller type codes; algebraic structure; binary field; building blocks; highly structured generator; linear codes; linear secret sharing; multiparty computation protocols; multiplicative secret sharing schemes; parity check matrices; Cryptography; Generators; Geometry; Linear code; Vectors; Linear secret sharing scheme; Reed-Muller code;
Conference_Titel :
Information Theory Proceedings (ISIT), 2012 IEEE International Symposium on
Conference_Location :
Cambridge, MA
Print_ISBN :
978-1-4673-2580-6
Electronic_ISBN :
2157-8095
DOI :
10.1109/ISIT.2012.6283999
