【作者】 李继红；

【导师】 肖国镇；

【作者基本信息】 西安电子科技大学 ， 密码学， 1999， 博士

【摘要】 本论文主要研究了基于离散对数的ElGamal型数字签名方案的安全性关系和它们的一些应用。作者取得的主要研究成果如下：（1）对Nyberg等人提出的强等价进行了推广，提出一个新的概念-概率转换，它 是对ElGamal型方案进行安全性研究的一个基本工具；（2）对广义ElGamal数字签名方案进行安全性等价分类，利用这个分类，可以很 容易选择性能较好的签名方案；（3）给出了ElGamal方案与相应的MR（P）方案的安全性关系；（4）提出了一个不等式验证方式的数字签名方案；（5）指出Nyberg-Ruppel可认证加密方案中的一个多余参数；（6）提出了一个可以很容易检测多个欺骗者的改进Pinch方案；（7）形式化地描述了一些高级秘密共享技术，从而很容易在广义ElGamal签名方 案上构造门限签名方案；（8）提出了一个具有完善零知识特性的可转换不可否认签名方案；（9）成功地攻破了最近由Z.Shao提出了两个增强型的数字签名方案；（10）提出了一个可以抵抗Tiersma攻击的修改He-Klesler方案。更多还原

【Abstract】 This dissertation mainly discusses the security relations between ElGamal-type digital signatures based on discrete logarithm problem and their applications, the main results obtained are as follows: (1) Probability transformation, a new extended concept for strong equivalence proposed by Nyberg etc. is given. It is a basic tool to analysis the security relation among ElGamal -type schemes. (2) Some classifications on the security among generalized ElGamal schemes are given with probability transformation, thus some better schemes in performance may be selected very easily. (3) The security relation between ElGamal scheme and the corresponded MR(P)-type scheme is given: (4) A digital signature scheme with an inequation verification is proposed: (5) An unnecessary parameter in Nyberg-Ruppel authentic message encrypt scheme is pointed out; (6) A modified Pinch scheme is proposed which may check many cheater very easily; (7) Some advanced technology about secret sharing is formalized. So that thresh signature schemes may be constructed very easily; (8) A convertible undeniable signature scheme with perfectly zero-knowledge feature is proposed. (9) Two signature schemes recently proposed by Z.Shao are broken successfully. (10) A modified He-Klesler scheme which can withstand Tiersma attack is proposed.更多还原