本文選題：圓錐曲線 + 數(shù)字簽名　； 參考：《西安電子科技大學(xué)》2014年博士論文

【摘要】：公鑰密碼學(xué)的提出是密碼科學(xué)史上的一次重要改革,它解決了對稱密碼中最困難的兩個問題:密鑰分配和數(shù)字簽名。公鑰密碼算法的最大特點是采用兩個相關(guān)密鑰將加密和解密能力分開,而該算法在已知密碼算法和加密密鑰,求解解密密鑰在計算上是不可行的。消息認證的作用是保護通信雙方以防第三方的攻擊,然而卻不能保護通信雙方中的一方防止另一方的欺騙或偽造。通信雙方之間也可能存在多種形式的欺騙,因此在收發(fā)雙方未建立起完全的信任關(guān)系且存在厲害沖突的情況下,單純的消息認證就顯得不夠,數(shù)字簽名技術(shù)則可有效地解決這一問題。數(shù)字簽名是一種實現(xiàn)消息或文件認證性的密碼技術(shù),其主要目的是用來保證信息的真實性和信息來源的可靠性,并且一個有效的簽名能夠使消息接收方驗證簽名者的身份、簽名日期和被簽名的消息。數(shù)字簽密技術(shù)是一種集加密和簽名兩種功能于一體的密碼體制,即在網(wǎng)絡(luò)信息傳輸中同時保證了信息的機密性和可認證性。在簽密技術(shù)出現(xiàn)以前,用來同時實現(xiàn)保密性和認證性的傳統(tǒng)方法是先簽名再加密。但是這帶來兩個問題:效率較低以及有可能降低方案的安全性。簽密作為一種新技術(shù),它巧妙地將加密和簽名整合到一起,以小于先簽名再加密的代價同時實現(xiàn)了對消息的保密性和認證性,同時在計算時間和存儲空間上,代價都有所降低。將具有特殊性質(zhì)的數(shù)字簽名和簽密結(jié)合起來便可以得到一些具有特殊性質(zhì)的數(shù)字簽密,因而目前簽密技術(shù)的發(fā)展已經(jīng)引起了眾多密碼學(xué)者的極大興趣�；谡麛�(shù)環(huán)Zn上的圓錐曲線是一個新型的代數(shù)曲線,其特點是明文容易嵌入,同時也易于從曲線中恢復(fù)明文,點的運算簡單,尤其是求逆簡單快速,曲線群的階容易計算。結(jié)合這些特點,在近幾年的密碼學(xué)中圓錐曲線的密碼特征逐漸得到了發(fā)展和完善,不但一些著名的數(shù)字簽名可在圓錐曲線上得以實現(xiàn),而且還表明圓錐曲線上的這些方案相比于有限域上的數(shù)字簽名方案具有更加完善的密碼特征。例如,圓錐曲線上的RSA簽名相比有限域上的RSA能抵抗小私鑰攻擊�；诖�,各種性質(zhì)的數(shù)字簽名和數(shù)字簽密在圓錐曲線上相繼都得到了實現(xiàn)和數(shù)字模擬。本論文對正整數(shù)環(huán)Zn上的圓錐曲線的密碼性質(zhì)進行了進一步研究,結(jié)合圓錐曲線上的密碼技術(shù)設(shè)計了一些高效安全的具有特殊性質(zhì)的數(shù)字簽名和數(shù)字簽密,具體的內(nèi)容包括以下成果:1.利用圓錐曲線上的公鑰密碼設(shè)計了一個高效的同時生效簽名方案。與有限域上的同時生效簽名方案相比,所提方案具有運算簡單快速,計算量小,有效提高了運算效率,而且在隨機預(yù)言模型下證明了方案在基于圓錐曲線上的離散對數(shù)和大整數(shù)分解困難問題下滿足不可偽造性、模糊性、公平性。2.利用圓錐曲線上的公鑰密碼設(shè)計了一個高效的完美同時生效簽名方案。方案的優(yōu)勢在于利用協(xié)議雙方建立一個共享的私密鑰,并將該私密鑰和消息進行綁定,克服了單純的同時生效簽名方案中因起始簽名者利用主私鑰所引發(fā)的不公平因素。3.利用無證書簽名思想提出了一個有效的指定驗證者的簽名方案。與現(xiàn)有的方案相比,方案在保證安全性的同時,減少了信息運算量,改進了方案的運算效率,并在隨機預(yù)言模型下證明方案滿足存在性不可行偽造。4.利用圓錐曲線上的公鑰密碼簽名技術(shù)提出了一個公平的無可信第三方的電子信息交換協(xié)議。與現(xiàn)有方案相比,方案將信息的交互次數(shù)由n+1次降到了3次,有效提高了網(wǎng)絡(luò)運算效率,降低了通信代價。5.利用圓錐曲線上的公鑰密碼技術(shù)提出了廣播簽密方案和高效的多重簽密方案。和現(xiàn)有的方案相比,所提方案均在運算效率上實現(xiàn)了極大的改進,并在隨機預(yù)言模型下證明了消息的保密性和不可偽造性。
[Abstract]:The presentation of public key cryptography is an important reform in the history of cryptography. It solves two most difficult problems in symmetric ciphers: key distribution and digital signature. The largest feature of public key cryptography is to separate the encryption and decryption capabilities by using two related keys, and the algorithm is used to solve decryption in known cryptographic algorithms and encryption keys. The key is not feasible in computing. The function of message authentication is to protect the two parties to prevent the attack of third parties, but it can not protect one party from the two parties to prevent the other from cheating or forgery. There may be many forms of deception between the two parties. Therefore, there is no complete trust relationship between the two parties in the transceiver and the existence of the two parties. In the case of severe conflict, simple message authentication is not enough, and digital signature technology can effectively solve this problem. Digital signature is a cryptographic technology that implements message or document authentication. Its main purpose is to ensure the authenticity of information and the reliability of the source of information, and an effective signature can make a message. The receiver verifies the identity of the signer, the signature date and the signed message. The digital signcryption technique is a cryptographic system that combines two functions of encryption and signature, that is, to ensure the confidentiality and authentication of the information in the transmission of network information. The traditional method is to sign and then encrypt. But this brings two problems: low efficiency and possibility of reducing the security of the scheme. As a new technique, signcryption combines encryption and signature ingeniously to realize the confidentiality and authentication of the message at the cost of less than the first signature and reencryption, while calculating the time and storage. With the combination of digital signatures and signatures with special properties, some digital signatures with special properties can be obtained. Therefore, the development of signcryption technology has aroused great interest of many cryptography scholars. The conic curve based on the positive integer ring Zn is a new algebraic curve. The characteristic is that the plaintext is easy to be embedded, and it is easy to recover the plaintext from the curve, and the operation of the point is simple. In particular, the order of the curve group is easy to calculate. Combining these characteristics, the cryptographic features of the conical curve have been developed and perfected in the cryptography in recent years, and not only some famous digital signatures can be conic in conical curves. It is realized on the line and also shows that these schemes have more perfect cryptographic features compared to the digital signature schemes on the finite field. For example, the RSA signature on the conic curve can resist the small private key attack compared to the RSA on the finite field. Based on this, the digital signatures and digital signatures of various properties are successively on the conic curve. In this paper, the cryptographic properties of the conic curve on the positive integer ring Zn are further studied in this paper. Some efficient and secure digital signatures and digital signatures with special properties are designed with the cryptographic technique on the conic curve. The specific contents include the following results: 1. the public key on conic curves is used. A efficient signature scheme with effective simultaneous signature is designed. Compared with the simultaneous effective signature scheme on the finite field, the proposed scheme has simple and fast computation, less computation and efficient operation. Moreover, under the random oracle model, the scheme is proved under the difficult problem of discrete logarithm and large integer decomposition based on the conic line. To satisfy the non forgery, fuzziness and fairness,.2. uses the public key cryptography on the conic curve to design an efficient and perfect simultaneous signature scheme. The advantage of the scheme is to use the two parties to establish a shared private key, and bind the secret key and message, and overcome the beginning of the simple simultaneous signature scheme. The unfairness factor.3. caused by the main private key is used by the signer to use the idea of certificateless signature to propose an effective signature scheme for the designated verifier. Compared with the existing scheme, the scheme reduces the amount of information operation while ensuring the security, improves the operational efficiency of the scheme, and proves that the scheme satisfies the scheme under the random oracle model. A fair and untrusted third party electronic information exchange protocol is proposed by the public key cryptosystem on the conic curve. Compared with the existing scheme, the scheme reduces the number of information interacts from n+1 times to 3 times, effectively improves the efficiency of the network operation and reduces the communication cost.5. using the conic curve, and reduces the communication cost.5.. Public key cryptography proposes the broadcast signcryption scheme and the efficient multiple signcryption scheme. Compared with the existing schemes, the proposed schemes have greatly improved the operational efficiency and proved the confidentiality and the non Forgability of the message under the random oracle model.
【學(xué)位授予單位】：西安電子科技大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2014
【分類號】：TN918.4

【參考文獻】

相關(guān)期刊論文 前1條

1 杜紅珍;溫巧燕;;一個高效的基于身份的聚合簽名方案[J];四川大學(xué)學(xué)報(工程科學(xué)版);2011年01期

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本文編號：2006386