Are standards compliant elliptic curve cryptosystems feasible on RFID?

Sandeep Kumar, Chris­tof Paar

Workshop on RFID Security 2006, Graz, Austria, Juli 2006.


Abstract

With elliptic curve cryptography emerging as a serious al- ternative, the desired level of security can be attained with signi¯cantly smaller key sizes. This makes ECC very attractive for small-footprint de- vices with limited computational capability, memory and low-bandwidth network connections. However ECC is still considered to be impractica- ble for very low-end constrained devices like sensor networks and RFID tags. We present a stand-alone highly area optimized ECC processor de- sign for standards compliant binary ¯eld curves. We use the fast squarer implementation to construct an addition chain that allows inversion to be computed e±ciently. Hence, we propose an a±ne co-ordinate ASIC im- plementation of the ECC processor using a modi¯ed Montgomery point multiplication method for binary curves ranging from 113¡193 bits. An area between 10k and 18k gates on a 0.35um CMOS process is possi- ble for the di®erent curves which makes the design very attractive for enabling ECC in constrained devices.

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Tags: ecc, Fermat's little theorem