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密钥共享方案是现代密码学的一个重要分支,是信息安全和数据保密中的重要手段,在数字签名、安全多方计算、纠错码等领域也有着重要的应用.现有的很多方案都是利用拉格朗日插值多项式而构造,且各参与者的密钥份额由分发者选取并且只能使用一次,需要秘密信道传输信息,在秘密重构时不具有可验证性,一次只能共享一个密钥.针对这些问题,利用非齐次线性递归构造两个可验证门限多重密钥共享方案.在初始化阶段,参与者的密钥份额由自己选取;在分发阶段,根据密钥的重数k与门限值t的大小关系考虑方案的两种情形k?t、k?t,并将共享的多重密钥置于t阶非齐次线性递归的等式中;在验证阶段,改进Dehkordi-Mashhadi的验证算法,使得公开参数的个数从2n+k-t+4降低为n+k+5;在恢复阶段,参与者只须提供伪份额而不会暴露密钥份额,使得重复利用密钥份额成为安全.提出的方案具有可验证性、可以共享多重密钥、密钥份额可以多次使用、只需要公开信道、基于椭圆曲线密码学等特点,同时具有公开参数少、重构多项式次数小的优点,这使得方案更加高效实用.
Key sharing scheme is an important branch of modern cryptography and an important means of information security and data confidentiality. It also has important applications in the fields of digital signature, secure multi-party computation, error correction code, etc. Many of the existing schemes are Constructed using Lagrange interpolation polynomials, and each participant’s key share is selected by the distributor and can only be used once. The secret channel is required to transmit information. In confidential reconstruction, the key share is not verifiable. Only one Key.In order to solve these problems, two verifiable threshold multiple key sharing schemes are constructed by nonhomogeneous linear recursion. At the initial stage, the key share of the participants is selected by themselves. During the distribution phase, And the threshold t the size of the relationship between the two cases consider the program k? T, k? T, and the shared multiple key placed t-order inhomogeneous linear recursive equation; in the verification phase, improve the Dehkordi- Mashhadi’s verification algorithm reduces the number of public parameters from 2n + k-t + 4 to n + k + 5. During the recovery phase, participants only need to provide a pseudo-share without exposing the key share, so that the reuse of the secret Key share becomes secure. Presented Case has verifiability, can share multiple keys, the key share can be used many times, only need to open the channel, based on elliptic curve cryptography and other characteristics, but also has the advantages of fewer public parameters and fewer reconstruction polynomials, which makes the program More efficient and practical.