Research On Some Algorithms For Public-Key Cryptosystems

Public-key cryptosystems play a important role in digital signatures, authentication protocols, electronic payment protocols, which are crucial techniques for electronic commerce security. Public-key cryptosystems are based on some difficult problems in number theory and algebra. Therefore, most public-key algorithms involve complicated operations with long integers or polynomials over algebraic structures such as groups, rings and fields, which are less efficient and require more memory space. Now, the problem of low computational efficiency is still a serious obstacle to widespread deployment of public-key cryptosystems. Furthermore, so-called side channel attacks, which exploit leakage information by cryptographic devices such as computational time, faults and power traces, can obtain the critical information on secret cryptographic keys or reduce the computational cost of cryptanalysis by combining other cryptanalysis methods. Indeed, side channel attacks become a new serious threat to implementation of public-key cryptosystems. Therefore, to design efficient algorithms with better computational efficiency and lower memory space against side channel attacks has become an active research topic in the cryptographic field.In this dissertation, we try to investigate several efficient algorithms for public-key cryptosystems and countermeasure algorithms against novel side channel attacks. The related problems are described as follows:(1) Efficient algorithms for public-key cryptosystems. The most famous public-key cryptosystems, such as RSA cryptosystem, ElGamal-like cryptosystems, elliptic curve cryptosystems, and bilinear pairing based cryptosystems, are founded over various algebraic structures such as the ring of integers modulo n, the prime field of integers modulo p, elliptic curves over finite fields GF(q), and bilinear pairings (Weil and Tate) on supersingular elliptic,curves. Therefore, it is an important task to...