Abstract:

The McEliece Public Key Cryptography （PKC） based on Quasi-Cyclic Moderate-Density Parity-Check （QC-MDPC） code is a promising scheme to resist quantum attack with small key size， so it is easy to storage. However， a reaction attack has a great threat to its security currently. The attacker selects some special error patterns to encrypt numerous messages to obtain the decoding failure feedback from the receiver， and then cracks the private key by analyzing the relationship between the decoding failure rate and the private key structure. This attack is called key recovery attack. In response to this attack， a new public key scheme cascading QC-MDPC code and fountain code was proposed. In the scheme， the “rateless characteristic” of fountain code was used to generate abundant encrypted packets which were used to substituted for the Automatic Repeat-reQuest （ARQ） structure， so that the attacker was not able to achieve the feedback information. The analysis results show that the proposed scheme can effectively resist key recovery attack and guarantee the security under other attacks as well.

Key words: Quasi-Cyclic Moderate-Density Parity-Check (QC-MDPC) code, quantum attack, key recovery attack, fountain code, Public Key Cryptography (PKC)

摘要：

基于中密度准循环奇偶校验（QC-MDPC）码的McEliece公钥密码（PKC）方案具有较小的密钥量，利于存储，是一类在抵抗量子攻击上发展前景良好的公钥密码体制。然而目前存在一种反应攻击对其安全性产生了较大威胁。攻击者选取特殊的错误图样对大量消息进行加密以获得接收者反馈的译码失败情况，然后通过分析译码失败率与私钥结构的关系从而破解出私钥，该攻击被称为密钥恢复攻击。为应对此攻击，提出了一种将QC-MDPC码与喷泉码进行级联的公钥方案。该方案利用喷泉码的“无码率性”生成大量的加密包来取代反馈重发（ARQ）结构，使攻击者无法获取反馈信息。分析结果表明，所提出的方案能有效抗击密钥恢复攻击，同时还能保证在其他攻击下的安全性。

关键词: 中密度准循环奇偶校验码, 量子攻击, 密钥恢复攻击, 喷泉码, 公钥密码体制