TY - GEN
T1 - Near-optimal secret sharing and error correcting codes in AC0
AU - Cheng, Kuan
AU - Ishai, Yuval
AU - Li, Xin
N1 - Publisher Copyright:
© 2017, International Association for Cryptologic Research.
PY - 2017
Y1 - 2017
N2 - We study the question of minimizing the computational complexity of (robust) secret sharing schemes and error correcting codes. In standard instances of these objects, both encoding and decoding involve linear algebra, and thus cannot be implemented in the class AC0. The feasibility of non-trivial secret sharing schemes in AC0 was recently shown by Bogdanov et al. (Crypto 2016) and that of (locally) decoding errors in AC0 by Goldwasser et al. (STOC 2007). In this paper, we show that by allowing some slight relaxation such as a small error probability, we can construct much better secret sharing schemes and error correcting codes in the class AC0. In some cases, our parameters are close to optimal and would be impossible to achieve without the relaxation. Our results significantly improve previous constructions in various parameters. Our constructions combine several ingredients in pseudorandomness and combinatorics in an innovative way. Specifically, we develop a general technique to simultaneously amplify security threshold and reduce alphabet size, using a two-level concatenation of protocols together with a random permutation. We demonstrate the broader usefulness of this technique by applying it in the context of a variant of secure broadcast.
AB - We study the question of minimizing the computational complexity of (robust) secret sharing schemes and error correcting codes. In standard instances of these objects, both encoding and decoding involve linear algebra, and thus cannot be implemented in the class AC0. The feasibility of non-trivial secret sharing schemes in AC0 was recently shown by Bogdanov et al. (Crypto 2016) and that of (locally) decoding errors in AC0 by Goldwasser et al. (STOC 2007). In this paper, we show that by allowing some slight relaxation such as a small error probability, we can construct much better secret sharing schemes and error correcting codes in the class AC0. In some cases, our parameters are close to optimal and would be impossible to achieve without the relaxation. Our results significantly improve previous constructions in various parameters. Our constructions combine several ingredients in pseudorandomness and combinatorics in an innovative way. Specifically, we develop a general technique to simultaneously amplify security threshold and reduce alphabet size, using a two-level concatenation of protocols together with a random permutation. We demonstrate the broader usefulness of this technique by applying it in the context of a variant of secure broadcast.
UR - http://www.scopus.com/inward/record.url?scp=85033804412&partnerID=8YFLogxK
U2 - 10.1007/978-3-319-70503-3_14
DO - 10.1007/978-3-319-70503-3_14
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AN - SCOPUS:85033804412
SN - 9783319705026
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 424
EP - 458
BT - Theory of Cryptography - 15th International Conference, TCC 2017, Proceedings
A2 - Kalai, Yael
A2 - Reyzin, Leonid
T2 - 15th International Conference on Theory of Cryptography, TCC 2017
Y2 - 12 November 2017 through 15 November 2017
ER -