Update for 31-01-22 15:00

This commit is contained in:
Tyler Perkins 2022-01-31 15:00:01 -05:00
parent 277d624613
commit da31d1ec7a
5 changed files with 49 additions and 6 deletions

9
math/Eliptic_Curve.wiki Normal file
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= eliptic Curve =
An eliptic curve is a curve of form:
```
y^2 = x^3 + ax + b
```
They often curve around the origin

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@ -10,7 +10,4 @@ alpha^3 mod q = x,,3,,
alpha^q-1 mod 1 = x,,(q-1),,
```
Where x,,n,, is
```
1, 2, 3, 4, etc
```
Where x,,n,, is *the set of values from 1 through q-1*

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@ -9,5 +9,28 @@ created between two parties via an unsecure channel.
== algorithm ==
1) For some prime `q`
2) Select some `alpha` such that `alpha < q` and `alpha` is a [[../math/primative_root]] of
`q`
2) Select some `alpha` such that `alpha < q` and `alpha` is a
[[../math/primative_root|Primative root]] of `q`
* known as global elements
3) X,,a,, and X,,b,, are the private keys of alice and bob respectively
* known as private elements/keys
4) Y,,a,, is `alpha^x,,a,, mod q`
* Same for Y,,b,,
* Known as public elements/keys
5) Both parties then calculate the shared secret via
`K,,a,, = Y,,b,,^X,,a,, mod q`
* same for K,,b,,
* K,,a,, should be same as K,,b,,
== example ==
```
q = 7
alpha = 5
X,,a,, = 3
Y,,a,, = 5^3 mod 7 = 6
X,,b,, = 4
Y,,b,, = 5^4 mod 7 = 2
```

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= Eliptic Curve Cryptography =
ECC is an algorithm that solves the same problem as [[RSA]], but with smaller
key sizes. It is asymetric and based on [[../math/Eliptic_Curve]]s and based on
the difficulty of inding a curve given points on said curve.
== algorithm ==

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@ -49,3 +49,7 @@ For example Encrypt B
Decrypt value
`4^11 mod 14 = 2` or our original `B`
== Also see ==
* [[Eliptic_Curve]]