Table 1 Cost of septuple formula for elliptic curves over binary fields
From: Efficient scalar multiplication of ECC using SMBR and fast septuple formula for IoT
Sub-expression | Intermediate value | Cost |
|---|---|---|
\(A\) | \(x^{2} ,x^{3} ,x^{4}\) | \(2\left[ s \right] + 1\left[ m \right]\) |
\(B\) | Â | \(1\left[ m \right]\) |
\(C\) | \(A^{2} ,A^{3} ,x^{4} B\) | \(1\left[ s \right] + 2\left[ m \right]\) |
\(D\) | \(B^{2} ,A(B^{2} + C)\) | \(1\left[ s \right] + 1\left[ m \right]\) |
\(E\) | \(A^{6} ,x^{4} B(A^{3} + B^{2} )\) | \(1\left[ s \right] + 1\left[ m \right]\) |
\(F\) | \(C{}^{2},A^{2} D\) | \(1\left[ s \right] + 2\left[ m \right]\) |
\(\frac{1}{E}\) | Â | \(1\left[ i \right]\) |
\(\frac{xF}{{E^{2} }}\) | \(\frac{1}{{E^{2} }},xF\) | \(1\left[ s \right] + 2\left[ m \right]\) |
\(u\) | \(xD,xD\left( {\frac{xF}{{E^{2} }}} \right)\) | \(2\left[ m \right]\) |
\(v\) | \(CF,\frac{CF}{E},(x^{2} + y)D,\left( {\frac{xF}{{E^{2} }}} \right)\left[ {\frac{CF}{E} + (x^{2} + y)D} \right]\) | \(4\left[ m \right]\) |
Total:\(1\left[ i \right] + 7\left[ s \right] + 16\left[ m \right]\) | ||