Power Analysis to ECC Using Differential Power Between Multiplication and Squaring

Power analysis is a serious attack to implementation of elliptic curve cryptosystems (ECC) on smart cards. For ECC, many power analysis attacks and countermeasures have been proposed. In this paper, we propose a novel power analysis attack using differential power between modular multiplication and modular squaring. We show how this difference occurs in CMOS circuits by counting the expectation of signal transition frequency, and present a simulation result on our ECC co-processor. The proposed attack is applicable to two efficient power analysis countermeasures based on unified addition formulae and elliptic curves with Montgomery form.