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Concept
Stream cipher attacks
Summary
Stream ciphers, where plaintext bits are combined with a cipher bit stream by an exclusive-or operation (xor), can be very secure if used properly. However, they are vulnerable to attacks if certain precautions are not followed:
keys must never be used twice
valid decryption should never be relied on to indicate authenticity
Stream ciphers are vulnerable to attack if the same key is used twice (depth of two) or more.
Say we send messages A and B of the same length, both encrypted using same key, K. The stream cipher produces a string of bits C(K) the same length as the messages. The encrypted versions of the messages then are:
E(A) = A xor C
E(B) = B xor C
where xor is performed bit by bit.
Say an adversary has intercepted E(A) and E(B). They can easily compute:
E(A) xor E(B)
However, xor is commutative and has the property that X xor X = 0 (self-inverse) so:
E(A) xor E(B) = (A xor C) xor (B xor C) = A xor B xor C xor C = A xor B
If one message is longer than the other, our adversary just truncates the longer message to the size of the shorter and their attack will only reveal that portion of the longer message. In other words, if anyone intercepts two messages encrypted with the same key, they can recover A xor B, which is a form of running key cipher. Even if neither message is known, as long as both messages are in a natural language, such a cipher can often be broken by paper-and-pencil methods. During World War II, British cryptanalyst John Tiltman accomplished this with the Lorenz cipher (dubbed "Tunny"). With an average personal computer, such ciphers can usually be broken in a matter of minutes. If one message is known, the solution is trivial.
Another situation where recovery is trivial is if traffic-flow security measures have each station sending a continuous stream of cipher bits, with null characters (e.g. LTRS in Baudot) being sent when there is no real traffic. This is common in military communications. In that case, and if the transmission channel is not fully loaded, there is a good likelihood that one of the ciphertext streams will be just nulls.
Official source
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