A threshold secret sharing apparatus, a threshold secret sharing scheme, a secret information recovery apparatus a secret information recovery method, and a program thereof are provided using XOR computation, thereby offering a general (k,n) threshold secret sharing scheme with high computation speed. Secret information K is divided into (np−1) divided pieces of secret information Kq (np is a prime number which is equal to or greater than a secret distribution number n). Furthermore, dummy secret information K0 is generated. Moreover, random numbers R, which are pairwise independent are generated. Then, pieces of shares are created using exclusive-OR (XOR) operations based upon the dummy secret information K0, the divided piece of secret information Kq, and the random numbers R. The pieces of shares thus generated are concatenated so as to generate n shares Si, thereby providing a (k,n) threshold secret sharing scheme.
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机译：使用XOR计算来提供阈值秘密共享设备，阈值秘密共享方案，秘密信息恢复设备，秘密信息恢复方法及其程序，从而提供具有高计算速度的通用（k，n）阈值秘密共享方案。 。秘密信息K分为（n p -1）个分割的秘密信息K q （n p 是一个质数等于等于或大于秘密分配数n）。此外，生成伪机密信息K 0 。此外，生成成对独立的随机数R。然后，根据虚拟机密信息K 0 ，分割后的机密信息K q 和随机数，使用异或（XOR）操作创建股份将这样生成的股份进行级联以生成n个股份S i ，从而提供（k，n）门限秘密共享方案。
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