Unified point addition for computing elliptic curve point addition and doubling is considered to be resistant to simple power analysis. Recently, new side-channel attacks, such as recovery of secret exponent by triangular trace analysis and horizontal collision correlation analysis, have been successfully applied to elliptic curve methods to investigate their resistance to side-channel attacks. These attacks turn out to be very powerful since they only require leakage of a single power consumption trace. In this paper, using these side-channel attack analyses, we introduce two vulnerabilities of unified point addition on the binary Huff curve. Also, we propose a new unified point addition method for the binary Huff curve. Furthermore, to secure against these vulnerabilities, we apply an equivalence class to the side-channel atomic algorithm using the proposed unified point addition method.
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