An extension of Massey scheme for secret sharing

2014 IEEE International Symposium on Information Theory

2014

It was recently shown that RGHW (relative generalized Hamming weight) exactly expresses the security of linear ramp secret sharing scheme. In this paper we determine the true value of the asymptotic metric for RGHW previously proposed by Zhuang et al. in 2013. Then we propose new asymptotic metrics useful for investigating the optimal performance of linear ramp secret sharing scheme constructed from a pair of linear codes. We also determine the true values of the proposed metrics in many cases.

Section: Introductionmentioning

confidence: 90%

New asymptotic metrics for relative generalized Hamming weight

2014 IEEE International Symposium on Information Theory

2014

“…Both secret and shares are traditionally classical information. There exists a close connection between secret sharing and classical error-correcting codes [4,12,15,16,29,34,44].…”

Section: Introductionmentioning

confidence: 99%

Message randomization and strong security in quantum stabilizer-based secret sharing for classical secrets

2020

Des. Codes Cryptogr.

We improve the flexibility in designing access structures of quantum stabilizer-based secret sharing schemes for classical secrets, by introducing message randomization in their encoding procedures. We generalize the Gilbert-Varshamov bound for deterministic encoding to randomized encoding of classical secrets. We also provide an explicit example of a ramp secret sharing scheme with which multiple symbols in its classical secret are revealed to an intermediate set, and justify the necessity of incorporating strong security criterion of conventional secret sharing. Finally, we propose an explicit construction of strongly secure ramp secret sharing scheme by quantum stabilizers, which can support twice as large classical secrets as the McEliece-Sarwate strongly secure ramp secret sharing scheme of the same share size and the access structure. Keywords Secret sharing • Quantum error-correcting code • Gilbert-Varshamove bound • Strong security Mathematics Subject Classification 94A62 • 81P70 • 94B65 This is one of several papers published in Designs, Codes and Cryptography comprising the "Special Issue on Coding and Cryptography 2019".

“…Both secret and shares are traditionally classical information. There exists a close connection between secret sharing and classical error-correcting codes [3,7,10,11,19,23,31].…”

Section: Introductionmentioning

confidence: 99%

Classical access structures of ramp secret sharing based on quantum stabilizer codes

2019

Quantum Inf Process

In this paper, we consider to use the quantum stabilizer codes as secret sharing schemes for classical secrets. We give necessary and sufficient conditions for qualified and forbidden sets in terms of quantum stabilizers. Then, we give a Gilbert-Varshamovtype sufficient condition for existence of secret sharing schemes with given parameters, and by using that sufficient condition, we show that roughly 19% of participants can be made forbidden independently of the size of classical secret, in particular when an n-bit classical secret is shared among n participants having 1-qubit share each. We also consider how much information is obtained by an intermediate set and express that amount of information in terms of quantum stabilizers. All the results are stated in terms of linear spaces over finite fields associated with the quantum stabilizers.