Resourch On Algorithms And Applications Of Public Key Cryptography Used In Ubiquitous Computing Systems

With the growth of E-Business and wireless communication, a trusted WPKI( Wireless Public Key infrastructure) must be established on ubiquitous computing systems to enable the privacy of private information and implemention of E-Business, while the PKC(Public Key Cryptosystem) is the inevitable technology of this framework. ECC HCC and XTR are all excellent candidates for constructing PKC because of their high efficiency and security together with much smaller key sizes. They are so-called lightweight PKC algorithms. The ubiquitous computer only has scarce computational and restore resources(such as mobile station. Smart card, RFID), and their power is also limited. We should make a necessary choice and improvement of PKC to fit for their shortage. So it's very important but difficult for constructing WPKI with HCC, ECC and XTR which has independent intellectual property of our country.This paper focuses on the techniques related to ECC, HCC, XTR cryptosystem with the emphasis on the fast software implementation and application obtained by the author and another resourchers, and the goal is to get a efficient solution for WPKI on ubiquitous computer. The paper consists of 7 chapters and is organized as follows:Chapter 1 is a general overview, including background, status quo and advance to ECC , HCC and XTR. The motivations and intentions of the research work, and the main framework of the paper have also been proposed in this chapter.Chapter 2 provides certain algebraic and geometrical principles of ECC and some necessary mathematical materials used in the paper, including notation and representation of mathematical objects.Chapter 3 describes and discusses all kinds of fast software algorithms for high-security elliptic curve and emphasis on the key opertation of point addition and scalar multiplication. Firstly an uncomplete reduction method in modular arithmetic is introduced, and we give a improved method for it to fit for the whole field. And then we propose the fast point scalar multiputation algorithm-Double-Base Chain. At the end we make a experiment to run the code of ECDSA on a mobile development platform(MSM 6025) and prove that ECC can work well on ubiquitous computer.Chapter 4 discusses the cryptosystems based on bilinear pairing. A notable success in this area was the elegant solution by Boneh and Franklin of the problem of efficient identity-based encryption. The security standard is provided in this chapter to make certain the security of this technique for the users. A VSS scheme based on bilinear pairing is also proposed.Chapter 5 exploits the Hiperelliptic Cryptosystems theory. Because the HCC is far from practice, we give a theoretical resourch in this chapter. And then we discuss three topic: the first is the divor addition and scalar multiplication;The second desicrbe cryptographic schemes for confidentiality services and non-repudiation services, such as ElGamal and Nyberg-Rueppel signature, and the last one is the implementation of HCC to get the high security levels. The discussion may be contribute to the standardization of HCC.Chapter 6 discussed the XTR cryptosystems and gives a new cryptosystem based on eclliptic field, which uses trace isomorphism to achieve the redeuction of the size of elements as XTR. Atfirst we discuss the cyclotomic subgroups crytopsystems and make sure XTR is the efficient one of them. Then the fast trace compution algorithms are given in this chapter to achieve a good proformence of XTR. At last we proposed a cryptosystem name ECC-XTR as told before andmake a experiment of EXTR to prove that XTR can work well on ubiquitous computer.The last chapter give a direct proposition of the construction of WPKI based on the PKC algorithms discussed in the before chapter. We give two technices to improve the proformance of traditional WPKI. One can delete CA role in WPKI using IBE proposed by Boneh and Franklin, another can achieve the XTR advantage by put XTR cryptosystem in WPKI certificate.This paper summarize the research works of the author in three study years, and the author believes that the works of this paper has greatly promoted the applications of ECC ^ HCC and XTR cryptosystems on ubiquitous computer.