From da31d1ec7ac918d7f826ff32dc462daa853e7df4 Mon Sep 17 00:00:00 2001
From: Tyler Perkins <tperki17@kent.edu>
Date: Mon, 31 Jan 2022 15:00:01 -0500
Subject: [PATCH] Update for 31-01-22 15:00

---
 math/Eliptic_Curve.wiki  |  9 +++++++++
 math/primative_root.wiki |  5 +----
 tech/Diffie_Hellman.wiki | 27 +++++++++++++++++++++++++--
 tech/Eliptic_Curve.wiki  | 10 ++++++++++
 tech/RSA.wiki            |  4 ++++
 5 files changed, 49 insertions(+), 6 deletions(-)
 create mode 100644 math/Eliptic_Curve.wiki

diff --git a/math/Eliptic_Curve.wiki b/math/Eliptic_Curve.wiki
new file mode 100644
index 0000000..c51807a
--- /dev/null
+++ b/math/Eliptic_Curve.wiki
@@ -0,0 +1,9 @@
+= eliptic Curve =
+
+An eliptic curve is a curve of form:
+
+```
+y^2 = x^3 + ax + b
+```
+
+They often curve around the origin
diff --git a/math/primative_root.wiki b/math/primative_root.wiki
index 5a67dbb..e3edb3d 100644
--- a/math/primative_root.wiki
+++ b/math/primative_root.wiki
@@ -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*
diff --git a/tech/Diffie_Hellman.wiki b/tech/Diffie_Hellman.wiki
index 9092da1..394d3c7 100644
--- a/tech/Diffie_Hellman.wiki
+++ b/tech/Diffie_Hellman.wiki
@@ -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
+```
diff --git a/tech/Eliptic_Curve.wiki b/tech/Eliptic_Curve.wiki
index b6f348b..ed4c82a 100644
--- a/tech/Eliptic_Curve.wiki
+++ b/tech/Eliptic_Curve.wiki
@@ -1 +1,11 @@
 = 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 ==
+
+
+
+
diff --git a/tech/RSA.wiki b/tech/RSA.wiki
index fe178b7..3489c10 100644
--- a/tech/RSA.wiki
+++ b/tech/RSA.wiki
@@ -49,3 +49,7 @@ For example Encrypt B
 Decrypt value
 
 `4^11 mod 14 = 2` or our original `B`
+
+== Also see ==
+
+* [[Eliptic_Curve]]