CALCULATE RSA ENCRYPTION FORMULA

Select two prime numbers
prime numbers are represented by "P" & "Q"
Calculate product of prime numbers
"P" x "Q" = "N"
Calculate totient of "N"
totient is product of 1 subtracted from each prime number represented by "T"
"T" = ("P"-1) x ("Q"-1)
Select Public Key
Public key value is represented by "E" and must match following requirements:
must be a prime number
must be less than totient ("T")
must not be a factor of totient ("T")
a factor is a number you can multiple to get another number
e.g factors of 12 are 1, 2, 3, 4, 6, and 12
Calculate Private Key
product of public key multipled by private key when divided by totient must result in remainder of 1
represented by "D"
(D x E) MOD T = 1
MOD is modulus which calculates remainders i.e. 16 MOD 3 = 1 (3 into 16 goes 5 times with 1 remaining)


RSA encryption formula
cipher text = M ^ E MOD N
RSA decryption formula
plain text = M ^ D MOD N
where "M" is the "message"


Simple Encryption/Decryption Example
Variables
P=7
Q=11
N=77
T=60 (7-1 x 11-1)
E=23 (meets the 3 public key criteria)
D=47 (meets the private key criteria)
(47 x 23) MOD 60 = 1
Encrypt Plaintext "65" (ASCII codepoint "A")
(65 ^ 23) MOD 77 = 32
32 is the ciphertext of "65" plaintext (i.e."H")
Decrypt CipherText of "32"
(32 ^ 47) MOD 77 = 65
65 is the plaintext of the ciphertext of "32"