## mercredi, février 20, 2019

### ECC backdoors for dummies in 5 steps

It will be explained in the most simple and pragmatic way, what possible ECC backdoors look like and why choosing the right curve and the right prime number to build the cryptographic curve is important.

## 2nd step: Understand graphically how a scalar multiplication looks like when choosing the right base point with a good prime number on a good curve

We first takes a random base point (2,22) and scalar multiply from 1 to n until it reaches infinity or point (0,0), then we look for the next base point that was not part of previous loop and multiply it, and so on until there are no free untouched base points.

For [y2 = x3 + 0x + 7  Ordre 67  size 78] curve whatever base point you start with, the loop contains all points of the curve (plus(0,0)), Thus there is only one curve.

To decrypt some data, without knowing the key, using these parameters you have to do 78 tests.

## 4th step: choose a wrong curve

### ## 5th step: going further open points

`https://www.coindesk.com/math-behind-bitcoin/`
`https://crypto.stackexchange.com/questions/44304/understanding-elliptic-curve-point-addition-over-a-finite-field`
`https://fr.wikipedia.org/wiki/Courbe_elliptiquehttps://en.wikipedia.org/wiki/Elliptic_curve_point_multiplication#Point_addition`

`The code to draw these curves : https://github.com/emariacher/kebra/blob/master/elliptique_sbt/core/src/main/scala/FaisGaffeAuxBackDoors.scala`
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