Improvement Of Twisted Edwards Curve Digital Signature Algorithms And Their Application To Mobile Security

It is well-known that the development of computer network technology hasbrought the fastest development, the keenest competition, and the most activeinnovation to the Mobile Internet. The security issues of mobile terminals havebeen explored as the mobile applications increase exponentially. As a novelscheme used for Mobile Internet Digital Signature, Elliptic curve DigitalSignature is playing an extremely vital role in mobile security field. This paperfirst analyzes all the main Digital Signature schemes used for mobile intelligentterminals and summarizes their merits and drawbacks. Then it introduces theElliptic curve Digital Signature, studies its efficiency, and puts forward animproved algorithm using addition and double based on Montgomery. And italso achieves better than the scalar multiplication NAFw algorithm bycombining the sliding window technology, which improves the speed of thecurve signature. The contributions are as follows:First of all, this paper puts forward an improved algorithm using additionand double based on Montgomery, which not only keeps the merit of not usingmultiplication in computing, but also reduces the times of commonmultiplication. Addition operation and mixing operation can reduce four times ofmultiplication in the coordinate system of standard projection, and three times inthe inverse coordinate system. Double operation an reduce two times ofmultiplication both in the coordinate system of standard projection and theinverse coordinate system. The experiments have shown that the improvedaverage efficiency rates of bettered addition operation and double operation are16.3%and27%respectively.Secondly, this paper applies the sliding window technology to the scalarmultiplication NAFw algorithm. The improved algorithm allows to change thesize of window w in the cycle of operation, which greatly solve the problem ofRepetitive operation. The experiments have shown that the improved algorithm’sperrfernance is efficient, which can reach at most27%when the window size is4, and26%when window size is3.Last, this paper implement s the improved Twisted Edward Curve DigitalSignature Algorithm, and applies it to the middleware project of mobile internetintelligent terminal application. This project implements the identityauthentication of developers, the level authentication of developers, and thesecurity authentication of mobile applications.