1.2 KiB
Procedure
We have 4 primary values that we deal with:
- 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.
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 modulo of it by n:
C = (m^e) % n
m is the desired message to encrypt.
The public and private keys are using the above cipher text functions whose unknown parameters are passed as follows
PublicKey(e, n)
PrivateKey(d, n)
Decryption
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.