ECC Atomic Block with NAF against Strong Side-Channel Attacks on Binary Curves

Various side-channel attacks against elliptic curve cryptography (ECC) have been proposed so far, including simple power analysis, horizontal collision correlation analysis, improving the Big Mac attack, and differential power analysis.  Developing countermeasures against such attacks is considered as an important research task in cryptography. They are executed by analyzing power consumption while a device implemented in a cryptosystem performs cryptographic processing. To address this problem, we propose using three atomic blocks serving as the countermeasures against such attacks on ECC over finite fields of characteristic two. Two of them are basic atomic blocks, while the third one is an improved version of these two, having lower computational cost.  In this paper, concerning the possibility of more sophisticated side-channel attacks appearing in the future, we propose a threat model based on the atomic blocks that is constructed to be secure for strong side-channel attacks with more powerful abilities.