Research on key generation and security of quantum public keycryptosystems over number fields

我们扩展了OTU2000，它是一个背包密码系统，利用数域作为量子公钥密码系统的显式模型。我们提出了一种不受次数和整数基限制的密钥生成方法，给出了一个较弱的密钥生成条件，可以从更广的范围内得到密钥，并成功地生成了公钥。该方法已被制定并发表在JSIAM Letters上。其结果比我们一开始预期的要好，为OTU2000在任意数域上的扩展建立了一个很好的实用密钥生成方法。

We have extended OTU2000 which is a knapsack base cryptosystem utilizing number fields proposed as an explicit model of quantum public key cryptosystems. We have proposed a method of generating secret keys without any restriction on degrees or integral basis, given a weaker condition for secret keys to obtain them from wider area, and actually succeeded in generating public keys also. The method has beenformulated and published as a paper in JSIAM Letters. The result is more than what we expected at the beginning, and has established a good practical method of key generation for an extension of OTU2000 over arbitrary number fields.