基于LCD码的可验证多秘密共享方案

Verifiable Multi-Secret Sharing Scheme Based on LCD Code

摘要: 为了解决基于线性码的秘密共享在区块链数据隐私保护中容易受到Tompa-Woll攻击以及子秘密只能单次使用的问题，本文提出了一种基于LCD码的可验证多秘密共享方案。该方案旨在应对不诚实用户通过提供错误子秘密而导致诚实用户无法获取秘密的情况。考虑到秘密重构函数的线性特性和其易受Tompa-Woll攻击的特点，本文采用双变量单向函数进行验证，从而有效抵御不诚实用户的恶意行为，并实现子秘密的多次使用。与其他方案的比较结果表明，该方案在性能上优于现有解决方案。

Abstract: To address the vulnerability of linear code-based secret sharing in blockchain data privacy protection-specifically its susceptibility to Tompa-Woll attacks and the single-use limitation of sub-secrets-this paper proposes a verifiable multi-secret sharing scheme based on LCD codes. The scheme targets the issue where dishonest users can cheat by submitting incorrect sub-secrets, preventing honest users from successfully reconstructing the secret. Given the linear nature of the secret creconstruction function and its vulnerability to Tompa-Woll attacks, this paper utilizes a two-variable one-way function for verification, effectively countering malicious behavior from dishonest users. Additionally, the use of the two-variable one-way function enables the reuse of sub-secrets. Comparative results show that this scheme outperforms existing solutions in terms of performance.