Nabil, are you looking for encryption or for using EC for authentication. This is a 2006 paper that shows that it is possible to implement an ECC processor on RFID tags with between 8500 and
14000 gates, depending on the implementation characteristics: An Elliptic Curve Processor Suitable For RFID-Tags
There may be more recent/efficient results, this paper should be a good starting point though.
Pascal sir and Karim sir, please provide some idea about chip designing for cryptography algorithm implementation. Which tool to be used for such implementation? I'm completely new to the designing of chip field. What are the basic steps for chip implementation? Please give some paper which had done the chip implementation of any cryptography algorithm or any simulation in this area.
You can implement an arithmetic unit/processor that performs the EC operations using Verilog or VHDL. I am not a chip designer myself, but I have enough background in EE to understand that these papers may be a starting point: