Fast scalar multiplication method using change-of-basis matrix to prevent power analysis attacks on Koblitz curves

Abstract

We propose a fast scalar multiplication method using a change-of-basis matrix to prevent power analysis attacks on Koblitz curves. Our method assures the fastest execution time without offline computation compared with previous countermeasures against power analysis attacks. Using the change-of-basis matrix, the Frobenius endomorphism of Koblitz curves is executed in the normal basis representation, whereas point addition is executed in the polynomial basis. In addition, we restrict the range of the number of additions. Even though we do not conceal the number perfectly, the algorithm remains secure with a security parameter chosen carefully. These techniques enable our method to prevent SPA with little computational overhead. For DPA prevention, we introduce randomness with negligible overhead. Timings results show that the proposed method is as efficient as a sliding window method.