Research And Application Of NTRU

Fast public-key cryptosystems find more applications than the traditional public-key cryptosystems and the design of fast public-key cryptosystem has been an interesting topic in the literature of public-key cryptographic community.NTRU public-key cryptosystem is a typical kind of fast public-key cryptosystem.It has solved the problem of speed which limits the development of PKCS.Because of its characteristics such as small size private key and easy-operated,NTRU can widely used in domains of e-commerce,communication, Embedded Systems and so on.This paper studies on NTRU public-key cryptosystems.It provides the detail description and the mathematical foundation of the NTRU algorithm, and discusses the security of NTRU.The first chapter introduces the actuality of public-key cryptosystems,and analyses the algorithm of NTRU briefly;The second chapter elaborates on the mathematical foundation of NTRU,discusses the hard problems SVP,CVP and so on in lattice theory.The third chapter explains the traditional NTRU algorithm and enhanced NTRU algorithm in detail.Our contributions are given in the last three chapters:1,In chapter four.the causes of NTRU decryption failures have been studied and analysed roundly.According to the characteristic of decryption failures,a mothed which can reduce the probability of decryption failures has been given to the traditional NTRU algorithm and enhanced NTRU algorithm respectively.2,In chapter five,the existing motheds of attacking to NTRU have been introduced and compared.Base on the existing attacking motheds and the study on NTRU decryption failures in chapter four.a new mothed of attacking NTRU have been presented.3,The sixth chapter studies on NTRU digital signatures such as NSS,R-NSS and NTRUSign.In this chapter,a new conception of cyclic basis has been imported. Combineing CVP with cyclic basis,a new digital signature scheme based on NTRU lattice has been presented.