TY - GEN

T1 - How to share a secret, infinitely

AU - Komargodski, Ilan

AU - Naor, Moni

AU - Yogev, Eylon

N1 - Publisher Copyright:
© International Association for Cryptologic Research 2016.

PY - 2016

Y1 - 2016

N2 - Secret sharing schemes allow a dealer to distribute a secret piece of information among several parties such that only qualified subsets of parties can reconstruct the secret. The collection of qualified subsets is called an access structure. The best known example is the k-threshold access structure, where the qualified subsets are those of size at least k. When k = 2 and there are n parties, there are schemes where the size of the share each party gets is roughly log n bits, and this is tight even for secrets of 1 bit. In these schemes, the number of parties n must be given in advance to the dealer. In this work we consider the case where the set of parties is not known in advance and could potentially be infinite. Our goal is to give the tth party arriving the smallest possible share as a function of t. Our main result is such a scheme for the k-threshold access structure where the share size of party t is (k − 1) ・ log t + poly(k) ・ o(log t). For k = 2 we observe an equivalence to prefix codes and present matching upper and lower bounds of the form log t + log log t + log log log t + O(1). Finally, we show that for any access structure there exists such a secret sharing scheme with shares of size 2t−1.

AB - Secret sharing schemes allow a dealer to distribute a secret piece of information among several parties such that only qualified subsets of parties can reconstruct the secret. The collection of qualified subsets is called an access structure. The best known example is the k-threshold access structure, where the qualified subsets are those of size at least k. When k = 2 and there are n parties, there are schemes where the size of the share each party gets is roughly log n bits, and this is tight even for secrets of 1 bit. In these schemes, the number of parties n must be given in advance to the dealer. In this work we consider the case where the set of parties is not known in advance and could potentially be infinite. Our goal is to give the tth party arriving the smallest possible share as a function of t. Our main result is such a scheme for the k-threshold access structure where the share size of party t is (k − 1) ・ log t + poly(k) ・ o(log t). For k = 2 we observe an equivalence to prefix codes and present matching upper and lower bounds of the form log t + log log t + log log log t + O(1). Finally, we show that for any access structure there exists such a secret sharing scheme with shares of size 2t−1.

UR - http://www.scopus.com/inward/record.url?scp=84994845390&partnerID=8YFLogxK

U2 - 10.1007/978-3-662-53644-5_19

DO - 10.1007/978-3-662-53644-5_19

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AN - SCOPUS:84994845390

SN - 9783662536438

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

SP - 485

EP - 514

BT - Theory of Cryptography - 14th International Conference, TCC 2016-B, Proceedings

A2 - Smith, Adam

A2 - Hirt, Martin

PB - Springer Verlag

T2 - 14th International Conference on Theory of Cryptography, TCC 2016-B

Y2 - 31 October 2016 through 3 November 2016

ER -