ITPEC FE Subject A October 2024 Question 28
Which of the following bitwise logical operation can be applied in stream cipher between a plain-text and a keystream to produce a cipher-text, and between a ciphertext and the keystream to recover the plaintext?
Explanation
XOR — the only one of the four operations that undoes itself, so the same keystream both encrypts and decrypts.
A stream cipher combines each plaintext bit P with a keystream bit K: C = P ⊕ K. Applying the same keystream again gives C ⊕ K = P ⊕ K ⊕ K = P, because K ⊕ K = 0 and P ⊕ 0 = P.
Example: plaintext 1010 XOR keystream 0110 gives ciphertext 1100, and 1100 XOR 0110 gives 1010, the plaintext again.
Answer (d)
Why not others:
- •(a) AND — wherever the key bit is 0 the output is 0 whatever the plaintext bit was, so that bit cannot be recovered
- •(b) NAND — wherever the key bit is 0 the output is always 1, so again the plaintext bit is lost (it only inverts the bits where the key is 1)
- •(c) OR — wherever the key bit is 1 the output is 1 whatever the plaintext bit was, so that bit is lost
Key rule: A combining operation works as a cipher only if it is reversible for every key bit; XOR flips a bit where the key is 1 and keeps it where the key is 0, so applying it twice restores the original.
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