base things for rsa notes, still missing last example in rsa.md

312/notes/math.bc

@@ -16,3 +16,11 @@ define gcd(a,b) {
 	return a;
 }
 
+define euclid(a, b) {
+	while(b != 0) {
+		t = b;
+		b = a % b;
+		a = t;
+	}
+	return a;
+}

312/notes/rsa.md

@@ -1,23 +1,23 @@
 # Procedure
 
+We have 4 primary values that we deal with:
 
-Example using 3 values:
-
-* p = 3 
-* q = 17
-* e = 15
-* m = 3
+* p
+* q
+* e
+* m
 
 There are a few components which must be calculated before we can safely determine a cipher text:
 
 `n = p * q` : note that `p` and `q` values should be primes in this case.
 
-`O(n) = (p - 1) * (q - 1)` is used later to verify that we have a value `d` which is the inverse of `e`. _We call this the quotient function_.
+`Φ(n) = (p - 1) * (q - 1)` is used later to verify that we have a value `d` which is the inverse of `e`. _We call this the quotient function_.
+
 
 
 ## Encryption
 
-To produce a cipher text `C` we take `m` and raise it to the power of `e`(from earlier) then take the modulor of it by `n`:
+To produce a cipher text `C` we take `m` and raise it to the power of `e`(from earlier) then take the modulo of it by `n`:
 
 ```
 C = (m^e) % n
@@ -38,3 +38,16 @@ The reverse of this is the following:
 ```
 M = (c^d) % n
 ```
+
+## E inverse e^1
+
+To find `d` the following _must_ be true: `GCD(e, Φ(n)) == 1`. 
+If this is not the case then there is no `d` or `e^-1`.
+
+
+> how do i actually this trash tho???
+
+Let's say we have `e=17` and `Φ(n)=60`:
+
+We know the GCD(17,60) == 1 [17 is prime] so we can find an `e` inverse.
+_Check the notes at the bottom for an easy to rationalize method of verifying this_.