I am very new to cryptography and so I am looking for feedback on this question on RSA. Please let me know if I have made any mistakes, Thank you!
-choose two primes p,q
-compute n = p * q
-compute phi = (p-1)*(q-1)
-choose e such that 1 < e < phi and gcd(e,phi) = 1 where gcd is greatest common divisor
-e is the public key
-calculate d such that d = phi * k + 1 / e for some integer k
-d is private key
-cipher text c for plain text
-m is computed as: c = m^e mod n
-plain text m for cipher text c is computed as m = c^d mod n
p = 83 ; q = 89 then, n = 7387 phi = 7216 e = 193 d = 4811 c = 4336 => 2^193 mod 7387
No, 11 is not a valid private key
Cipher text using 11 as private key is "2048".
Where as decrypting using d = 4811 is 2404 which is not equal to original 2
private key "d = 4811" for public key 25