Let $\phi=1103481364240094378710324387523817552607307673089944349316644000826050949$ and $N=1050467212358431669174928621845479661$. I want to generate an integer $e=N^{\alpha}$ of $59$ bits and an integer $d=N^{\delta}$ satisfying $ed\equiv 1\bmod \phi$ and $\delta<2-\sqrt{\alpha}.$ How to do this rapidly ?
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