电子学报 ›› 2006, Vol. 34 ›› Issue (10): 1892-1895.

• 论文 • 上一篇    下一篇

REESSE1加密方案中杠杆函数的充分必要性分析

苏盛辉1, 杨义先2, 杨炳儒1   

  1. 1. 北京科技大学信息工程学院,北京 100083;2.
  • 收稿日期:2005-05-13 修回日期:2006-07-28 出版日期:2006-10-25 发布日期:2006-10-25

The Necessity and Sufficiency Analysis of the Lever Function in the REESSE1 Encryption Scheme

SU Sheng-hui1, YANG Yi-xian2, YANG Bing-ru1   

  1. 1. School of Information Engineering,University of Science & Technology Beijing,Beijing 100083,China;2. School of Information Engineering,Beijing University of Post & Telecom,Beijing 100876,China
  • Received:2005-05-13 Revised:2006-07-28 Online:2006-10-25 Published:2006-10-25

摘要: 文章介绍了REESSE1公钥体制的加密方案,包括密钥生成、加密和解密3个算法.通过对密钥变换公式中杠杆函数(.)为常数或不存在的假设,讨论了连分式攻击,因而从逆否命题的角度证明了(.)对REESSE1体制私钥安全的必要性.作者通过不确定推理、反例列举和参数归约的方法论述了(.)存在时,REESSE1的私钥安全性等价于多变量排列难题、明文安全性大于离散对数难题,从而证明了(.)对REESSE1体制私钥与明文安全的充分性.最后,指出了私钥中包含三个独立参数的REESSE1体制与私钥中仅包含一个或两个参数的MH、RSA和ElGamal体制相比,复杂性得到了显著提高.

关键词: 公钥密码体制, 安全性, 杠杆函数, 连分式, 加密

Abstract: This paper presents the REESSE1 public key cryptosystem including three algorithms for keys,encryption and decryption,discusses the continued fraction attack by presuming that the lever function (.) in the key transform is one constant or does not exists,and proves that (.) is necessary to the private key security of REESSE1 from the contrapositive assertion.The authors argue that the private key security is equivalent to the multivariate arrangement hardness,and the plaintext security is greater than the discrete logarithm hardness when (.) exists in the transform by expounding the indeterminate reasoning,giving counterexamples and reducing parameters,and so show that (.) is sufficient for the private key and the plaintext securities.At last,point out that the complexity of REESSE1 whose private key contains three independent parameters is far higher than those of MH,RSA and ElGamal whose private keys contain only one or two parameters respectively.

Key words: public key cryptosystem, security, lever function, continued fraction, encryption

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