As introduced from the story, they are three basic methods of coding or also known as encryption techniques. The methods are Caesar code, Atbash code, and Polialphabet code.

1. Caesar code

Caesar cide is a sinple way of encryption. All you have to do just replace a letter with its fit number. First, you have to write the alphabet starting from A to Z. Second, under the alphabet you have to write numbers starting from 0 to 25. So, A will fit with 0, B will fit with 1, until Z will fit with 25. Let's say the original plaintext is BUSAN, so we'll have 1 20 18 0 13. Then, to turn into ciphertext (code) we could only choose one letter as a key. For example, we choose N which fit the number 13. Then, we added 13 to every each of previous numbers (1 20 18 0 13). So, it will become 14 33 31 13 26. For every number that more than 25 should be reduced by 26. The numbers will become 14 7 5 13 0. From this you can have your final ciphertext by turn the numbers back to its fit letters. So, 14 will fit with O, 7 with H, and so on. So, the final ciphertext is OHFNA.

2. Atbash code

Atbash code is the simplest way of encryption. We just have to write two rows of alphabet. First row, contains an alphabet from A to Z. Second row, contains an alphabet from Z to A, so it reversed alphabet. A will fit with Z, B will fit with Y, until Z will fit with A. Let's say the original plaintext is TYPHON, so we just have to turn it to its fit reversed alphabet. The final ciphertext we have iz GBKSLM.

3. Polialphabet code

Polialphabet code basically has the same way as Caesar code, the different is on the key. If Caesar only use one letter as a key, in Polialphabet we're allowed to use more than one letter as the key. For example, we have DAEGU as an original plaintext. If we turned it to its fit numbers, we'll have 3 0 4 6 20. Then we choose T and Y as the keys, so we will add 19 and 24 to the previous numbers (3 0 4 6 20), it will be 3+19, then 0+24, until 19, in the end we have 22 24 23 30 39. For every numbers which more than 25 should be reduced by 26, so we have 22 24 23 4 13 and WYXEN as the plaintext.

How Aeri and Baekhyun broke the codes? It would be a super duper long time if we discussed it since the culprit made the ciphertext from combination of two or even three methods at once. So, instead of working forward from ciphertext to plaintext, I'll tell you backward instead and from that you'll know the sweat and hardwork Aeri and Baekhyub did, also how smart they are.

First plaintext: DAEGU

Methods: Atbash and Polialphabet code

Turned DAEGU into WZVTF. Turned WZVTF to its fit numbers 22 25 21 19 5. Used T (19) and P (15) as the keys and added to previous numbers, final result is 41 40 40 34 24, then reduced by 26 become 15 14 14 8 24. So the final ciphertext is POOIY.

Second plaintext: BUSAN

Methods: Caesar and Atbash code

Turned BUSAN to its fit numbers 1 20 18 0 14. Used N (13) as the key then added to the previous numbers, final result is 14 33 31 13 26, then reduced by 26 become 14 7 5 13 0. Turned the numbers back to its fit letters which become OHFNA. Final step was using Atbash code and the final ciphertext is LSUMZ.

Third plaintext: TYPHON

Methods: Atbash, Polialphabet, and Caesar code

Turned TYPHON to its reversed letter, GBKSLM. Then turned it to its fit numbers, 6 1 10 11 13 and added H (7) and Y (24) as the key and added to previous numbers becone 13 25 17 16 18 10. Then we used Caesar code used O (14) as the key and added to previous numbers, and in the end we have 27 39 31 30 32 24 which next reduced by 26, and the final result is 1 13 5 4 6 24. The final ciphertext is BNFEGY.