typos

Cryptography/RSA.md

@@ -12,24 +12,46 @@ common divisor](https://en.wikipedia.org/wiki/Greatest_common_divisor) via
 [euclidean
 algorithm](https://crypto.stanford.edu/pbc/notes/numbertheory/euclid.html)
 
-`d` is the modular inverse of e and phi
+$$
+\phi(n) = (p-1)(q-1)
+$$
 
----
+and further
 
 $$
 1 < \phi < n
 $$
 
-There is also
-$$
-\phi = (p-1) * (q-1)
-$$
 
 Encryption, public key `e` is a prime between 2 and phi  
 $$
 2 < e < \phi
 $$
 
+
+Decryption, private key `d`
+$$
+d\ e\ mod\ \phi(n) \equiv 1
+$$
+
+$$
+d\ e \equiv 1\ (mod\ \phi(n))
+$$
+
+`d` is the modular inverse of e and phi and makes the private key.
+
+$$
+Cipher = msg^{d}\ mod\ \phi
+$$
+
+$$
+Cleartext = cipher^{e}\ mod\ \phi
+$$
+
+---
+
+`e` and `d` may be found through the following Python snippets
+
 ```python
 possible_e = []
 for i in range (2, phi):
@@ -37,11 +59,6 @@ for i in range (2, phi):
         possible_e.append()
 ```
 
-Decryption, private key `d`
-$$
-d * e mod \phi = 1
-$$
-
 ```python
 possible_d = []
 for i in range (phi + 1, phi + foo):
@@ -49,14 +66,6 @@ for i in range (phi + 1, phi + foo):
        possible_d.append()
 ```
 
-$$
-Cipher = msg ** d mod \phi
-$$
-
-$$
-Cleartext = cipher ** e mod \phi
-$$
-
 ## Euklid
 
 Just a short excourse: