A Novel SPA Attack on ECC Using MMM's Conditional Subtraction

摘要

Elliptic curve cryptosystems (ECCs) are becoming more popular because of the reduced number of key bits required in comparison to other cryptosystems such as RSA. They are especially suited to smartcards because of the limited memory and computational power available on these devices. However, the side-channel attacks especially simple side-channel analysis (SPA) can obtain information about the cryptosystem by measuring power consumption and processing time. To resist this attack there appear a number of countermeasures and the most widely used methods are Montgomery ladder and double-and-add-always algorithm. This paper proposes a novel simple power analysis attack to these countermeasures. Experimental results on smart cards demonstrate that this attack method can retrieve secret keys by distinguishing the conditional subtraction of Montgomery modular multiplication (MMM). Several countermeasures that can resist this kind of SPA attack are also demonstrated in this paper.