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Ramp Scheme Based on CRT for Polynomial Ring over Finite Field

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Abstract

Chinese Reminder Theorem (CRT) for integers has been widely used to construct secret sharing schemes for different scenarios, but these schemes have lower information rates than that of Lagrange interpolation-based schemes. In ASIACRYPT 2018, Ning, et al. constructed a perfect (r,n)-threshold scheme based on CRT for polynomial ring over finite field, and the corresponding information rate is one which is the greatest case for a (r,n)-threshold scheme. However, for many practical purposes, the information rate of Ning, et al. scheme is low and perfect security is too much security. In this work, the authors generalize the Ning, et al. (r,n)-threshold scheme to a (t,r,n)-ramp scheme based on CRT for polynomial ring over finite field, which attains the greatest information rate (r − t) for a (t,r,n)-ramp scheme. Moreover, for any given 2 ≤ r1 < r2 ≤ n, the ramp scheme can be used to construct a (r1,n)-threshold scheme that is threshold changeable to (r′, n)-threshold scheme for all r′ ∈ {r1 + 1, r1 + 2, ⋯, r2}. The threshold changeable secret sharing (TCSS) scheme has a greater information rate than other existing TCSS schemes of this type.

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Authors and Affiliations

  1. College of Computer and Cyber Security, Fujian Normal University, Fuzhou, 350007, China

    Jian Ding

  2. School of Mathematics and Big Data, Chaohu Univeristy, Hefei, 238024, China

    Jian Ding

  3. School of Mathematics and Statistics, and Fujian Provincial Key Lab of Network Security and Cryptology, Fujian Normal University, Fuzhou, 350007, China

    Pinhui Ke & Changlu Lin

  4. School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, 639798, Singapore

    Huaxiong Wang

Authors
  1. Jian Ding
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  2. Pinhui Ke
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  3. Changlu Lin
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  4. Huaxiong Wang
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Corresponding authors

Correspondence to Pinhui Ke or Changlu Lin.

Additional information

This paper was supported by the National Natural Science Foundation of China under Grant Nos. U1705264, 61572132, 61772292 and 61772476, the Natural Science Foundation of Fujian Province under Grant No. 2019J01275, University Natural Science Research Project of Anhui Province under Grant No. KJ2020A0779, the Singapore Ministry of Education under Grant Nos. RG12/19 and RG21/18 (S).

This paper was recommended for publication by Editor CHEN Shaoshi.

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Ding, J., Ke, P., Lin, C. et al. Ramp Scheme Based on CRT for Polynomial Ring over Finite Field. J Syst Sci Complex 36, 129–150 (2023). https://doi.org/10.1007/s11424-022-1292-4

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  • DOI: https://doi.org/10.1007/s11424-022-1292-4

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