2022/05/21 by Wei Yan, Sian-Jheng Lin, Yan, Wei +1
Computer Science · Engineering · #Coding theory and cryptography #Cryptography and Data Security #FOS: Computer and information sciences #Information Theory (cs.IT) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2205.10614
openalex publication_date 2022/05/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Evolving secret sharing schemes do not require prior knowledge of the number of parties n and n may be infinitely countable. It is known that the evolving 2-threshold secret sharing scheme and prefix coding of integers have a one-to-one correspondence. However, it is not known what prefix coding of integers to use to construct the scheme better. In this paper, we propose a new metric KΣ for evolving 2-threshold secret sharing schemes Σ. We prove that the metric KΣ≥ 1.5 and construct a new prefix coding of integers, termed λ code, to achieve the metric KΛ=1.59375. Thus, it is proved that the range of the metric KΣ for the optimal (2,∞)-threshold secret sharing scheme is 1.5≤ KΣ≤1.59375. In addition, the reachable lower bound of the sum of share sizes for (2,n)-threshold secret sharing schemes is proved.