计算机工程 ›› 2014, Vol. 40 ›› Issue (12): 78-82.doi: 10.3969/j.issn.1000-3428.2014.12.014

• 安全技术 • 上一篇    下一篇

基于REESSE1+公钥密码体制的概率加密

孙国栋1,苏盛辉1,2,徐茂智1,3   

  1. 1.北京工业大学计算机学院,北京 100124; 2.扬州大学信息工程学院,江苏 扬州 225009;
    3.北京大学数学科学学院,北京 100871
  • 收稿日期:2013-11-29 修回日期:2014-02-20 出版日期:2014-12-15 发布日期:2015-01-16
  • 作者简介:孙国栋(1985-),男,博士研究生,主研方向:信息安全,公钥密码学;苏盛辉、徐茂智,教授。
  • 基金项目:
    国家“863”计划基金资助项目(2009AA01Z441);国家“973”计划基金资助项目(2007CB311100)。

Probabilistic Encryption Based on REESSE1+ Public Key Cryptosystem

SUN Guodong1,SU Shenghui1,2,XU Maozhi1,3   

  1. 1.College of Computer,Beijing University of Technology,Beijing 100124,China;
    2.College of Information Engineering,Yangzhou University,Yangzhou 225009,China;
    3.School of Mathematics Sciences,Peking University,Beijing 100871,China
  • Received:2013-11-29 Revised:2014-02-20 Online:2014-12-15 Published:2015-01-16

摘要: 针对确定性公钥密码体制不能抵抗选择明文攻击的弱点,基于REESSE1+公钥密码体制设计2种概率加密方案,使同一明文对应的密文具有不确定性。方案1在明文比特序列的奇数位置插入相同长度的随机比特串,产生新的随机明文序列,并对该序列进行加密;方案2对公钥序列进行重新排列,使用新的公钥序列对明文进行加密。证明2种方案的正确性,并对其安全性和性能进行分析,结果表明,2种方案均可抵抗选择明文攻击,密码强度至少等价于基于离散对数问题的密码方案,同时,其加解密运行时间均少于基于RSA和剩余问题的概率密码方案。

关键词: 概率加密, REESSE1+公钥密码体制, 多变量组合问题, 非范子集积问题, 选择明文攻击, 互素序列

Abstract: In order to overcome the weakness that deterministic public key cryptosystem can not resist the chosen plaintext attack,two probabilistic encryption schemes are proposed based on REESSE1+ public key cryptosystem.The first scheme inserts a random bit sequence into the odd position of the bit sequence of plaintext,and produces a new random plaintext sequence which is encrypted.The second scheme generates a random permutation of the public key sequence,which is used to encrypt the plaintext.According to the two schemes,the ciphertext of a plaintext is uncertain.The correctness of the schemes is proved,and the security and performance of the schemes are also analyzed.Results show that,the two schemes can resist chosen plaintext attack and the cipher intensity of them is not lower than that of the scheme based on discrete logarithm problem.Besides,the encoding and decoding running time of the schemes are less than that of the scheme based on RSA and residuosity problem.

Key words: probabilistic encryption, REESSE1+ public key cryptosystem, multivariate permutation problem, anomalous subset product problem, chosen plaintext attack, coprime sequence

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