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pedroalbanese authored Nov 28, 2024
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Expand Up @@ -638,7 +638,7 @@ Module-lattice-based algorithms, such as KEM (Key Encapsulation Mechanism) and D

### NUMS
**Microsoft Nothing Up My Sleeve Elliptic curves**
[NUMS](http://www.watersprings.org/pub/id/draft-black-numscurves-01.html) (Nothing Up My Sleeve) curves, which are supported in the MSRElliptic Curve Cryptography Library (a.k.a. MSR ECCLib).
[NUMS](http://www.ietf.org/archive/id/draft-black-numscurves-01.txt) (Nothing Up My Sleeve) curves, which are supported in the MSRElliptic Curve Cryptography Library (a.k.a. MSR ECCLib).

These curves are elliptic curves over a prime field, just like the NIST or Brainpool curves. However, the domain-parameters are choosen using a VERY TIGHT DESIGN SPACE to ensure, that the introduction of a backdoor is infeasable. For a desired size of $s$ bits the prime $p$ is choosen as $p = 2^s - c$ with the smallest $c$ where $c>0$ and $p$ mod 4 = 3 and $p$ being prime.

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