Elliptic Curves Cryptosystems approaches

This paper take in discussion an important area of security: Elliptic Curves Cryptosystems (ECC) are the next frontier in the use of security mechanisms by providing good security margins with lower computational cost. ECC´s domain is an important field emerged in information security. The elliptic curves (EC) are used for conceiving efficient factorization algorithms and for proving the primality. They are used in public key cryptosystems and in pseudorandom bit generators, too. The elliptic curves were also applied in Codes Theory, where they were used to create very good error protected codes. ECC is more and more considered as an attractive public-key cryptosystem for mobile/wireless environments. Compared to traditional public-key cryptosystems like RSA or Diffie-Hellman, ECC offers equivalent security with smaller key sizes; these result in faster computations, lower power consumption, as well as memory and bandwidth savings. ECC is especially useful for mobile devices, which are typically limited in terms of their CPU, power and network connectivity. In this paper, we aim to examine the security, implementation and performance of ECC applications on various mobile devices. Also, our goal is to compare ECC and conventional PKC performances. Doing these, we want to prove that ECC will become the next-generation of PKC.