Abstract
Scalar multiplication is a major operation in an elliptic curve cryptosystem. It is the mostly costly and time consuming operations. This study proposes a new signed-digit {0,1,3}-NAF scalar multiplication algorithm for elliptic curve over binary field with the scalar multiplier in base 2 and using digits {0, 1, 3}. The digit 3 requires tripling operations in the execution of the scalar multiplication algorithm. Thus, a tripling formula is also proposed and the proof of the formula is presented in this study. Complexity analysis is carried out to compare the proposed scalar multiplication algorithm with the addition-subtraction algorithm. At average case analysis, the proposed scalar multiplication algorithm has better performance than the addition-subtraction algorithm exceptionally when only one digit 3 occurs in the scalar multiplier. When compared with traditional NAF scalar, the proposed scalar has better performance except when the Hamming weight and the bit-length of the proposed scalar and the traditional NAF are the same.
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