一种基于多项式的可追踪秘密共享方案
A Polynomial-Based Traceable Secret Sharing SchemeLuxiang Ping1,2, Keke Huang3,4, Changlu

Goyal 等在 CRYPTO’21 首次提出了可追踪秘密共享方案。该方案通过识别参与重构过程的参与者来限制诸如出售份额等恶意行为。Boneh 等在 CRYPTO’24 提出了分别基于 Shamir 和 Blakley 方法的两种可追踪秘密共享方案。在基于 Shamir 的方案中，假设有 f (f < t) 个参与者将份额出售，追踪者需要对黑盒进行 2f 次访问，通过黑盒返回的输出值分析出售份额的参与者的部分信息。随着 f 的增大，所需的黑盒访问的次数也相应增加，这将导致方案的效率降低。为了解决上述问题。本文引入带权重的秘密共享方案，提出了一种新的基于多项式的可追踪秘密共享方案，提升了追踪效率。实现了只要出售份额的参与者人数小于门限值 t，追踪者只需要对黑盒进行 2 次访问即可得到出售份额的参与者的信息。
Goyal et al. ？rst proposed the concept of traceable secret sharing scheme in CRYP- TO’21. This scheme restricts malicious behaviors such as selling shares by identifying participants involved in the reconstruction process. Boneh et al. introduced two trace- able secret sharing schemes based on Shamir’s and Blakley’s methods respectively in CRYPTO’24. In the Shamir-based scheme, assuming f (f < t) participants sell their shares, the tracer needs to query the black box 2f times to analyze partial information of the participants who sold their shares based on the outputs returned by the black box. As f increases, the number of black box accesses required also increases accord- ingly, which reduces the e？ciency of the scheme. To address this issue, this paper introduces a weighted secret sharing scheme and proposes a new polynomial-based traceable secret sharing scheme to improve tracing e？ciency. It is achieved that as long as the number of participants selling shares is less than the threshold t, the tracer only needs to query the black box twice to obtain the information of the participants who sold their shares.