A Cheating-Detectable (k, L, n) Ramp Secret Sharing Scheme

Wataru NAKAMURA; Hirosuke YAMAMOTO; Terence CHAN

doi:10.1587/transfun.E100.A.2709

A Cheating-Detectable (k, L, n) Ramp Secret Sharing Scheme

Wataru NAKAMURA, Hirosuke YAMAMOTO, Terence CHAN

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In this paper, we treat (k, L, n) ramp secret sharing schemes (SSSs) that can detect impersonation attacks and/or substitution attacks. First, we derive lower bounds on the sizes of the shares and random number used in encoding for given correlation levels, which are measured by the mutual information of shares. We also derive lower bounds on the success probabilities of attacks for given correlation levels and given sizes of shares. Next we propose a strong (k, L, n) ramp SSS against substitution attacks. As far as we know, the proposed scheme is the first strong (k, L, n) ramp SSSs that can detect substitution attacks of at most k-1 shares. Our scheme can be applied to a secret S^L uniformly distributed over GF(p^m)^L, where p is a prime number with p≥L+2. We show that for a certain type of correlation levels, the proposed scheme can achieve the lower bounds on the sizes of the shares and random number, and can reduce the success probability of substitution attacks within nearly L times the lower bound when the number of forged shares is less than k. We also evaluate the success probability of impersonation attack for our schemes. In addition, we give some examples of insecure ramp SSSs to clarify why each component of our scheme is essential to realize the required security.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E100-A No.12 pp.2709-2719

Publication Date: 2017/12/01

Publicized

Online ISSN: 1745-1337

DOI: 10.1587/transfun.E100.A.2709

Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications)

Category: Cryptography and Information Security

Authors

Wataru NAKAMURA
  The University of Tokyo
Hirosuke YAMAMOTO
  The University of Tokyo
Terence CHAN
  University of South Australia

Keyword

ramp secret sharing schemes, cheating detection, impersonation attacks, substitution attacks, mutual information of shares

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Wataru NAKAMURA, Hirosuke YAMAMOTO, Terence CHAN, "A Cheating-Detectable (k, L, n) Ramp Secret Sharing Scheme" in IEICE TRANSACTIONS on Fundamentals, vol. E100-A, no. 12, pp. 2709-2719, December 2017, doi: 10.1587/transfun.E100.A.2709.
Abstract: In this paper, we treat (k, L, n) ramp secret sharing schemes (SSSs) that can detect impersonation attacks and/or substitution attacks. First, we derive lower bounds on the sizes of the shares and random number used in encoding for given correlation levels, which are measured by the mutual information of shares. We also derive lower bounds on the success probabilities of attacks for given correlation levels and given sizes of shares. Next we propose a strong (k, L, n) ramp SSS against substitution attacks. As far as we know, the proposed scheme is the first strong (k, L, n) ramp SSSs that can detect substitution attacks of at most k-1 shares. Our scheme can be applied to a secret S^L uniformly distributed over GF(p^m)^L, where p is a prime number with p≥L+2. We show that for a certain type of correlation levels, the proposed scheme can achieve the lower bounds on the sizes of the shares and random number, and can reduce the success probability of substitution attacks within nearly L times the lower bound when the number of forged shares is less than k. We also evaluate the success probability of impersonation attack for our schemes. In addition, we give some examples of insecure ramp SSSs to clarify why each component of our scheme is essential to realize the required security.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1587/transfun.E100.A.2709/_p

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@ARTICLE{e100-a_12_2709,
author={Wataru NAKAMURA, Hirosuke YAMAMOTO, Terence CHAN, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A Cheating-Detectable (k, L, n) Ramp Secret Sharing Scheme},
year={2017},
volume={E100-A},
number={12},
pages={2709-2719},
abstract={In this paper, we treat (k, L, n) ramp secret sharing schemes (SSSs) that can detect impersonation attacks and/or substitution attacks. First, we derive lower bounds on the sizes of the shares and random number used in encoding for given correlation levels, which are measured by the mutual information of shares. We also derive lower bounds on the success probabilities of attacks for given correlation levels and given sizes of shares. Next we propose a strong (k, L, n) ramp SSS against substitution attacks. As far as we know, the proposed scheme is the first strong (k, L, n) ramp SSSs that can detect substitution attacks of at most k-1 shares. Our scheme can be applied to a secret S^L uniformly distributed over GF(p^m)^L, where p is a prime number with p≥L+2. We show that for a certain type of correlation levels, the proposed scheme can achieve the lower bounds on the sizes of the shares and random number, and can reduce the success probability of substitution attacks within nearly L times the lower bound when the number of forged shares is less than k. We also evaluate the success probability of impersonation attack for our schemes. In addition, we give some examples of insecure ramp SSSs to clarify why each component of our scheme is essential to realize the required security.},
keywords={},
doi={10.1587/transfun.E100.A.2709},
ISSN={1745-1337},
month={December},}

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TY - JOUR
TI - A Cheating-Detectable (k, L, n) Ramp Secret Sharing Scheme
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2709
EP - 2719
AU - Wataru NAKAMURA
AU - Hirosuke YAMAMOTO
AU - Terence CHAN
PY - 2017
DO - 10.1587/transfun.E100.A.2709
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E100-A
IS - 12
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - December 2017
AB - In this paper, we treat (k, L, n) ramp secret sharing schemes (SSSs) that can detect impersonation attacks and/or substitution attacks. First, we derive lower bounds on the sizes of the shares and random number used in encoding for given correlation levels, which are measured by the mutual information of shares. We also derive lower bounds on the success probabilities of attacks for given correlation levels and given sizes of shares. Next we propose a strong (k, L, n) ramp SSS against substitution attacks. As far as we know, the proposed scheme is the first strong (k, L, n) ramp SSSs that can detect substitution attacks of at most k-1 shares. Our scheme can be applied to a secret S^L uniformly distributed over GF(p^m)^L, where p is a prime number with p≥L+2. We show that for a certain type of correlation levels, the proposed scheme can achieve the lower bounds on the sizes of the shares and random number, and can reduce the success probability of substitution attacks within nearly L times the lower bound when the number of forged shares is less than k. We also evaluate the success probability of impersonation attack for our schemes. In addition, we give some examples of insecure ramp SSSs to clarify why each component of our scheme is essential to realize the required security.
ER -