Is HJXDDUDAYIZQRFGSJJ a valid one-time pad encryption of WESTERNENGINEERING?

Question

How we can check this is valid or not? As I know in one time pad, we have key to make cipher text from plain-text.

WESTERNENGINEERING

HJXDDUDAYIZQRFGSJJ

Answer 1

If they have the same length: yes. That's the point of one-time pad. Any ciphertext can be decrypted to everything. You must know the correct key to decide which decryption is the correct one.

That's why bruteforcing is useless against a one time pad.

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In partcular the key: LFFKDQWLCRDNBPKWD should do the trick for the pair of plaintext/ciphertext you provided.

Answer 2

If a one-time pad was used, then

HJXDDUDAYIZQRFGSJJ

could legitimately decrypt to any of these, or 1.0314425e+28 other strings;

WESTERNENGINEERING
HARRYPOTTERFOREVER
CHECKPOINTFIREWALL
INSERTYOURTEXTHERE
ANYTHINGWORKS1TIME

Without the key there is no way to know what the mapping is. Even if you reverse a key from what you believe the text to be, unless that key was used twice you cannot know if that's the correct key (which is why they're called one-time pads).