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Lets say the key is a string of length 10, perfectly random.
We use the key to xor a large quantity of perfectly random length 10 strings.
Can the key be recovered if the encrypted strings are compromised?
No.
If the input data are completely random, then applying a completely random key via XOR doesn’t produce any meaningful patterns. The result is still random, and no information can be gleaned from randomness.
The reason XOR isn’t used as an encryption mechanism is generally known-plaintext attacks, which do not apply against a random corpus.