【作者】 张瑛瑛；

【导师】 曾吉文；

【作者基本信息】 厦门大学 ， 基础数学， 2018， 博士

【摘要】 随着互联网信息时代的到来,电子信息已经成为当今社会沟通与交流的主要载体。在这种环境和现实需求下,对电子信息的数字签名也开始变得尤为重要。数字签名技术由于具有身份认证性、数据完整性、不可抵赖性等等优势,使得它在信息安全领域扮演着重要角色。数字签名也随着用户的具体需求而产生各种特殊签名。比如代理签名方案是原始签名者因某种原因不能签名而将签名权利委托给代理签名者的数字签名方案。环签名方案是签名者想要达到匿名签名目的的数字签名方案。对称密码体制的优点是计算成本低,算法简单,加密速度快。可是由于对称密码体制中加密密钥和解密密钥都是完全相同的,导致它的开放性差,通讯双方需要在通信前就把这个密钥通过非常可靠的信道进行传递,并且这个密钥也必须妥善的保管。而数字签名需要公开的密钥进行身份的认证,所以对称密码体制就不能用于数字签名。Diffie和Hellman在1976年密码学新方向一文中首次打破了对称密码体制的局限,提出了公钥密码体制的概念([1])。公钥密钥体制中用户的密钥成对出现,分为公钥(公诸于众)和私钥(用户自己保存)。自此公钥密码体制也就成为密码学者设计数字签名方案的基础。2003年,Al-Riyami和Paterson二人提出了无证书公钥密码体制([3])。由于无证书公钥密码体制没有证书,故其可以解决传统公钥密码体制中的证书管理成本问题。而且无证书公钥密码体制的密钥生成中心(KGC)只能为用户产生部分私钥,所以也就成功避免了基于身份密码体制中私钥生成中心(PKG)生成用户全部私钥而导致权利过大的问题。本文首先是在无证书公钥密码体制下设计了一个新的环签名方案。在安全方面,我们在随机预言模型下,在计算性Diffie-Hellman(CDH)问题和计算性co-Diffie-Hellman(co-CDH)问题是难解的假设前提下,证明了我们的无证书环签名在适应性选择消息攻击下是不可伪造的。在效率方面,我们的无证书环签名方案只在签名验证阶段使用三个双线性运算,它的操作效率比较高。其次本文对代理环签名方案也做出了新的构造。在安全方面,我们在随机预言模型下,在椭圆曲线群的离散对数问题(DLP)是难解的假设前提下,证明了我们的代理环签名在适应性选择消息攻击下是不可伪造的。在效率方面,我们的代理环签名方案的最大的特点是没有使用双线性对运算,在签名的验证阶段我们使用运算耗时很少的哈希函数(Hash)来进行,这样以来我们方案的效率就会大大提高。我们知道数字签名技术的安全性是基于数学上的困难问题的难解程度来完成的,比如大数分解问题、离散对数问题等等。但是量子计算的理论会严重威胁这些困难问题的安全性,因而传统的数字签名技术的安全性受到了严峻的挑战。为了抵制量子计算机带给数字签名的危机,量子密码理论诞生([86])。量子签名方案是利用量子力学基本原理,结合密码学的知识产生的。目前设计的量子签名方案,从理论上都被证明是无条件安全的。最后本文设计了一个仲裁量子签名方案(AQS)。思路过程如下:Liu等人在文[113]中将量子一次一密算法(QOTP)改进成新的量子一次一密算法(T-QOTP),并用T-QOTP算法设计了一个AQS方案。Xu和Zou在文献[115]中指出Liu等人的AQS方案中存在签名者的抵赖和接收者的存在性伪造攻击。Xu和Zou分析认为Liu等人的方案遭到安全性攻击的主要原因是由于仲裁者Trent无法判断消息的可靠性。我们的方案结合QOTP算法和T-QOTP算法对量子消息进行加密可以解决这一关键问题,从而可以弥补Liu等人的AQS方案中存在的安全性攻击。我们的AQS方案还保留了原来Liu等人方案中的所有的特点。更多还原

【Abstract】 With the arrival of the Internet Information Age,electronic information has become the main carrier of communication and interaction in today’s society.Under such environment and actual need,the digital signature for electronic information has gradually become more and more important.Because of its advantages of identity authentication,data integrity,non-repudiation,etc.,digital signature technology plays an important role in the field of information security.The digital signature also generates various special signatures in order to meet the special needs of users.For instance,proxy signature scheme is a kind of digital signature scheme that the original signer delegates his signing right to the proxy signer for some reason.Ring signature scheme is another kind of digital signature scheme that the signer wants to achieve the purpose of anonymous signing.Symmetric cryptosystem has its advantages of low computational cost,simple algorithm,and fast encryption speed.However,since both the encryption key and the decryption key in the symmetric cryptosystem are identical,resulting in poor openness,the two parties need to pass this key through a very reliable channel before communication and the key must also be kept properly.Digital signature schemes require public keys for ident.ity authentication.Naturally,symmetric cryptosystems can not be used for digital signatures.Diffie and Hellman broke the limitation of symmetric cryptosystem for the first time in an article about the new direction of cryptography in 1976,and put forward the concept of public key cryptosystem([1]).The user’s key in the public key cryptosystem appears in pairs and is divided into a public key(public)and a private key(stored by the user).Then public key cryptosystem has become the basis for cryptographers to design digital signature schemes.In 2003,Al-Riyami and Paterson proposed a certificateless public key cryptosystem([3]).The certificateless public key cryptosystem has no certificate,so it can solve the problem of certificate management cost in the traditional public key cryptosystem.Moreover,the key generation center of the certificateless public key cryptosystem can only generate part of the private key for the user,thus avoiding the problem that the private key generation center of the identity-based public key cryptosystem generates all the private keys of the user and thus leads to excessive rights.This paper first designs a new ring signature scheme under the certificateless public key cryptosystem.In terms of safety,with the random oracle model,we show that our certificateless ring signature is unforgeable against adaptive chosen message attacks under the assumption that the computational Diffie-Hellman(CDH)problem and computational co-Diffie-Hellman(co-CDH)are intractable.In terms of efficiency,our certificateless ring signature scheme uses only three bilinear operations during the signature verification phase,and its design is more efficient.Secondly,this paper also makes a new structure for the proxy ring signature scheme.In terms of safety,with the random oracle model,we prove that our proxy ring signature is unforgeable against adaptive chosen message attacks under the assumption that the discrete logarithm problem(DLP)of an elliptic curve group is intractable.In terms of efficiency,the biggest feature of our proxy ring signature scheme is that it does not use bilinear pairings.In the stage of signature verification,we use hash function which has little operation time to complete.In this way,the efficiency of our scheme will be greatly improved.We know that the security of digital signature technology is based on the difficult degree of hard problems about mathematics,such as the factorization problems of large numbers,discrete logarithm problems and so on.However,the theory of quantum computing can seriously threaten the security of these difficult problems.Therefore,the security of traditional digital signatures has been severely challenged.In order to resist the crisis that quantum computers bring to digital signatures,the theory of quantum cryptography came into being([86]).Quantum signature scheme makes use of the basic principle of quantum mechanics and is combined with the knowledge of cryptography.The current quantum signature schemes have been proved to be unconditionally safe in theory.Finally,this paper designs a new arbitration quantum signature scheme(AQS).The thinking process is as follows.Liu et al.improved the quantum one-time pad algorithm(QOIP)into a new quantum one-time pad algorithm(T-QOTP)in the text[113],and designed an arbitration quantum signature scheme using the new quantum one-time pad algorithm(T-QOTP).Xu and Zou pointed out in the literature[115]that Liu et al.’s AQS scheme had a denial of the signer and receiver’s existence forgery attack.The analysis of Xu and Zou showed that the main reason for the security attacks of Liu et al.’s scheme was that the arbitrator Trent could not judge the reliability of the message.Our paper combining QOTP algorithm with T-QOTP algorithm to encrypt the quantum message can deal with this key problem.Thus it can make up for the security attacks that exist in Liu et al.’s AQS scheme.Our AQS scheme also remains all the features of the original Liu et al.’s scheme.更多还原