Cryptology ePrint Archive: Report 2015/1089

Linear Secret Sharing Schemes from Error Correcting Codes and Universal Hash Functions

Ronald Cramer and Ivan Bjerre Damgård and Nico Döttling and Serge Fehr and Gabriele Spini

Abstract: We present a novel method for constructing linear secret sharing schemes (LSSS) from linear error correcting codes and linear universal hash functions in a blackbox way. The main advantage of this new construction is that the privacy property of the resulting secret sharing scheme essentially becomes independent of the code we use, only depending on its rate. This allows us to fully harness the algorithmic properties of recent code constructions such as efficient encoding and decoding or efficient list-decoding. Choosing the error correcting codes and universal hash functions involved carefully, we obtain solutions to the following open problems:

- A linear near-threshold secret sharing scheme with both linear time sharing and reconstruction algorithms and large secrets (i.e. secrets of size Omega(n)). Thus, the computational overhead per shared bit in this scheme is constant.

- An efficiently reconstructible robust secret sharing scheme for n/3 <= t < (1 - epsilon) n/2 corrupted players (for any constant epsilon > 0) with shares of optimal size O(1 + sec / n) and secrets of size Omega(n + sec), where sec is the security parameter.

Category / Keywords: foundations / Linear Secret Sharing Schemes, Linear Time Sharing, Robust Secret Sharing

Original Publication (in the same form): IACR-EUROCRYPT-2015

Date: received 9 Nov 2015, last revised 9 Nov 2015

Contact author: nico doettling at cs au dk

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Version: 20151109:093514 (All versions of this report)

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