How to determine the shift key to decrypt a ciphertext which was encrypted using Caesar cipher? So I found this question in a model paper,


  Break ciphertext ”BJJY GPXF DI TJPM ZSYH” which is encrypted by a
  Caesar Cipher.


This gives a meaningful plaintext if we use 21 as the shift key. So the answer is 


  "GOOD LUCK IN YOUR EXAM"


Do we have to find the shift key by guessing all the possible keys until we find the correct one, or is there any other way to find it?
There are only 26 possible shifts with the Caesar cipher, so you can check them all pretty quickly with a computer, or by hand for fun.

You could also get one step more sophisticated and do a frequency analysis: make histograms of ciphertext letters and compare those to the frequencies of English (e is the most common single letter; followed by t, a...just remember Etaoin Shrdlu and you'll be fine). Then you can do a $\chi$-squared test to compare your ciphertext frequencies to the expected ones from English.



Usual warning: because of how easy this is to break, make sure you only use it for fun: it offers no real security. Here's a longer discussion about cracking ciphers by hand.