TY - GEN

T1 - A Linear Algebraic Approach to Strongly Secure Ramp Secret Sharing for General Access Structures

AU - Eriguchi, Reo

AU - Kunihiro, Noboru

AU - Nuida, Koji

N1 - Funding Information:
ACKNOWLEDGEMENTS This research was partially supported by JST CREST Grant Number JPMJCR14D6, Japan, JSPS KAKENHI Grant Number JP19K22838, and the Ministry of Internal Affairs and Communications SCOPE Grant Number 182103105.
Publisher Copyright:
© 2020 IEICE.

PY - 2020/10/24

Y1 - 2020/10/24

N2 - Secret sharing is a cryptographic technique to share a secret among participants in such a waythat only authorized subsets are able to recover the secret. Ramp secret sharing schemes can achieve better information ratio than perfect schemes while some partial information on a secret which iscomposed of several sub-secrets leaks out. The notion of strong security has been introduced to control the amount of information on every subset of the sub-secrets unauthorized sets can obtain. In this paper, we reduce the construction of strongly secure ramp secret sharing for general access structures to a linear algebraic problem. As a result, we show that previous results on strongly secure network coding imply two constructions of a linear transformation which makes a given linear ramp scheme strongly secure. They are explicit or provide a deterministic algorithm while the previousmethod which works for any linear ramp scheme is probabilistic.

AB - Secret sharing is a cryptographic technique to share a secret among participants in such a waythat only authorized subsets are able to recover the secret. Ramp secret sharing schemes can achieve better information ratio than perfect schemes while some partial information on a secret which iscomposed of several sub-secrets leaks out. The notion of strong security has been introduced to control the amount of information on every subset of the sub-secrets unauthorized sets can obtain. In this paper, we reduce the construction of strongly secure ramp secret sharing for general access structures to a linear algebraic problem. As a result, we show that previous results on strongly secure network coding imply two constructions of a linear transformation which makes a given linear ramp scheme strongly secure. They are explicit or provide a deterministic algorithm while the previousmethod which works for any linear ramp scheme is probabilistic.

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M3 - Conference contribution

AN - SCOPUS:85102652574

T3 - Proceedings of 2020 International Symposium on Information Theory and its Applications, ISITA 2020

SP - 427

EP - 431

BT - Proceedings of 2020 International Symposium on Information Theory and its Applications, ISITA 2020

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 16th International Symposium on Information Theory and its Applications, ISITA 2020

Y2 - 24 October 2020 through 27 October 2020

ER -