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Please refer the document at NIST site pointing to the document (800-22-rev 1a ) updated on April 2010 (http://csrc.nist.gov/publications/nistpubs/800-22-rev1a/SP800-22rev1a.pdf). The list of special published (SP) documents are available at (http://csrc.nist.gov/publications/PubsSPs.html) It involves some reading, but should get your answers. Since it ...


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What you are doing is the following: Choose a random number $r$ in $[1,2^n-1]$. Check if $r$ is invertible $\bmod n$ (should be with probability $\approx1-2^{-1000}$, because by random luck you'd have to hit $p$ or $q$), if not go to 1. Check if $(\frac{r}{p})=(\frac{r}{q})=1$($(\frac{a}{n})$ denotes the jacobi symbol), if not go to 1. So in order to ...



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