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Oct 22, 2014 at 21:17 comment added fgrieu Addtion: If $2^n-1$ is prime, it becomes easier to ascertain that the feedback of a LFSR of order $n$ makes it maximum-length: it is then enough to show that the LFSR loops after $2^n-1$ steps, which is easy (otherwise, we would also need to show that it does not loops after $2^n-1\over p$ steps for each prime divisor $p$ of $2^n-1$). $\;$ That observation is not so useful, though: LFSR by themselves are poor keystream generators (we need to combine them, see the ASG).
Oct 22, 2014 at 20:47 comment added CodesInChaos Some ECC implementation use extension fields with characteristic $2^{127}-1$. One example is snowshoe.
Oct 22, 2014 at 20:00 history edited poncho CC BY-SA 3.0
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Oct 22, 2014 at 19:29 history answered poncho CC BY-SA 3.0