Electromagnetic Analysis on Elliptic Curve Cryptosystems: Measures and Counter-Measures for Smart Cards

Although the possibility of attacking elliptic curve cryptosystems (ECC) by power analysis repeatedly appears in research papers, there were few electromagnetic analysis papers and conclusive experiments where actual elliptic curve cryptosystems were successfully attacked and prevented. In this paper we describe electromagnetic (EM) analysis experiments conducted on 3 implementations of elliptic curve cryptosystems. They are respectively binary, double-and-add-always and Montgomery methods of point multiplication. The experimental results indicate that using simple electromagnetic analysis (SEMA), the complete key material could be successfully retrieved from binary method, but not from double-and-add-always and Montgomery method.