Mazdak Farrokhzad edited b) Algorithm.tex  almost 10 years ago

Commit id: 898455fa785a819fa6f08d21313a795cf2f0c4d3

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\begin{subequations}  \begin{align*}  T_{\mathtt{min}}(p, k) &= \floor{\log_2(p)}^22^{\floor{\log_2(k)}-1}\left(2^{\floor{\log_2(k)}} \floor{\log_2(p)}^2 2^{\floor{\log_2(k)}-1}\left(2^{\floor{\log_2(k)}}  - 1\right)\\ &\geq \Big(\log_2(p)-1\Big)^2\frac{k}{2^2}\left(\frac{k}{2} - 1\right)\\  T_{\mathtt{max}}(p, k) &= \Big(\floor{\log_2(p)}+1\Big)^2 2^{\floor{\log_2(k)}}\left(2^{\floor{\log_2(k)}+1} - 1\right)\\  &\leq \Big(\log_2(p)+2\Big)^2 2k\left(2^2k - 1\right)