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

利用数字域作为量子公钥密码系统的显式模型，我们扩展了OTU2000这个背包基密码系统。我们提出了一种不受度数和积分基限制的密钥生成方法，给出了密钥从更广的区域获得密钥的较弱条件，并实际成功地生成了公钥。该方法已在《JSIAM Letters》上发表。结果超出了我们最初的预期，并为OTU2000在任意数目字段上的扩展建立了一个很好的实用的密钥生成方法。

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.