RSA(Rivest, Shamir and Adleman)is being used as a public key exchange and key agreement tool for many years. Due to large numbers involved in RSA, there is need for more efficient methods in implementation for public key cryptosystems. Elliptic Curve Cryptography(ECC) is based on elliptic curves defined over a finite field. Elliptic curve cryptosystems(ECC) were discovered by Victor Miller and Neal Koblitz in 1985.This paper comprises of five sections. Section I is introduction to ECC and its components. Section II describes advantages of ECC schemes and its comparison with RSA. Section III is about some of the applications of ECC. Section IV gives some embedded implementations of ECC. Section V contains ECC implementation on fixed point Digital Signal Processor(TMS320VC5416). ECC was implemented using general purpose microcontrollers and Field Programmable Gate Arrays (FPGA) before this work. DSP is more powerful than microcontrollers and much economical than FPGA. So this implementation can be efficiently utilized in low-power applications.