| In a variety of security applications such as authentication and payment of the certificate, USBKey as a personal security module technology to provide users many security features such as authentication, access control, key storage and safe handling. Compared to the smart card, USBKey is a more light and compact plug-and-play information security equipment, which can set USB card reader and smart cards in one.As USBKey allowing only a smaller storage space to achieve a reliable security guarantee, this requires that we can improve related technologies and algorithms as much as possible. Along with the communication and the integrated circuit technology's development, the important individual information and the sensitive information's security on-line transaction is getting more and more common, such as: online banking, home office, Internet video conferencing, e-government, e-commerce, etc. This not only make a harsher demands of safety equipment, but also provide an opportunity for combination of IC technology, smart card technology and USBKey technology.RSA and ECC cryptography is the most practical and significance public-key cryptosystem at persent, both are important theoretical bases for USBKey's reliable security. Based on integer factorization, RSA algorithm had shown good efficiencies to be achieved as encryption and decryption. Based on elliptic curve discrete logarithm problem, ECC algorithms have characteristics of small storage space, short key length and system parameters in the digital signature and authentication.To raise the operation efficiency, Montgomery in 1985 proposed a effective method about calculating the modular multiplication algorithm. He transformed the ordinary modular multiplication to a special modular multiplication to substitute the shift operation for the very complex division operation, calculating modn of a·b(modn) based on complete residue system. This provided an important solution idea of improving the RSA operational efficiency. Along with it, B.S.Kaliski, Walter Colin and others proposed one after another the improvement Montgomery modular multiplication algorithm. Koc compared the various algorithms and concluded them for different hardware environments. In improving the efficiency of elliptic curve operations, coordinate conversion and point of operation is the key. Heri Cohen proposed a "modified Jacobian coordinate projection", its advantage is to use the least calculation time of modular multiplication operations when calculating point-multiplication. In dealing with elliptic curve point multiplication, Gordon drew on he skills and methods of calculatingαn. Using the features that calculating the negative element of a point on elliptic curve is not time-consuming, he made a tape symbol ofκ(NAF format) instead of the binary to gain a higher computational efficiency.This article unifies the USBKey correlation theories knowledge, has made a brief introduction to the public-key cryptosystem, and given the public key cryptographic algorithm in-depth analysis. It focused on the improvement Montgomery modular multiplication algorithm from the Stephen R. Dusse and Burton S. Kalisli Jr. and carrying on a detailed analysis and consideration about its concrete implementation.At ECC algorithm, this article comes up with JSF sliding window multi-point multiplication algorithm based on the ideas of Brickell, Gordon's sub-blocks and sliding window. This article have an important theoretical significance in enriching public-key cryptographic algorithms and perfecting the public key cryptography technology in the field of application of USBKey. |
PDF Full Text Request