It is required to invent the public-key cryptosystem (PKC) that is based on an {it NP/}-hard problem so that the quantum computer might be realized. The knapsack PKC is based on the subset sum problem which is {it NP/}-hard. In this paper, we propose a knapsack PKC with a cyclic code over $GF(2)$ using the Chinese remainder theorem. The proposed scheme is secure against Shamir's attack and Adleman's attack and invulnerable to the low-density attack. Furthermore, the proposed scheme can reduce the size of public key by almost $25% sim 50%$ of the conventional scheme using a linear code.
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机译：需要发明基于{ it NP /}-hard问题的公钥密码系统（PKC），以便可以实现量子计算机。背包PKC基于{ it NP /}困难的子集和问题。在本文中，我们使用中国余数定理提出了一个循环码超过$ GF（2）$的背包PKC。提出的方案可以安全地抵御沙米尔（Shamir）和阿德曼（Adleman）的攻击，并且不受低密度攻击的影响。此外，与使用线性码的传统方案相比，所提出的方案可以将公钥的大小减少近$ 25 ％ sim 50 ％$。
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