Why do stream ciphers repeat and how is that a threat?

functionEqualsM

6/16/23, 4:38 AM

If you have to generate a sufficiently long keystream, why would the keystream eventually repeat?

If the keystream repeats does it pose the threat of being decrypted by a hacker? How could one use it to that advantage?

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cryptanalysis

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Crypto

DannyNiu

6/16/23, 4:54 AM

why would the keystream eventually repeat?

Because all stream ciphers have a finite state.

... does it pose the threat ... How could one use it to that advantage?

If the repetition period of the stream cipher is known, the adversary can choose to carry out chosen ciphertext attack (make the user decrypt) or chosen plaintext attack (make the user encrypt).

Once decrypted plaintext (CCA), or encrypted ciphertext (CPA) is obtained, the attacker can overlap the periods, xor them, and extract distinguishable patterns.

That's just a rough idea, I'm more of a coder than mathematician, so I'm not sure if I've explained completely and correctly.

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fgrieu

6/16/23, 6:44 AM

Obvious addition: this is a practical threat only if the known repetition period is small enough that (together with the _modus operandi_ of the stream cipher) repetition can practically occur.

functionEqualsM

6/18/23, 9:00 PM

@fgrieu, I'm a bit new to Cryptography could you explain your addition in lamens terms? I apologize.

DannyNiu

6/19/23, 1:26 AM

“only if the known repetition period is small enough”, for example, the counter mode of blockciphers with a 8-bit counter. @functionEqualsM

fgrieu

6/19/23, 5:27 PM

@functionEqualsM: for example: DES-OFB has a large period (expected to be in $[2^{64}\ldots2^{64}$ bytes for most keys), and that's not a practical security issue, because a given key won't be used for nearly that many bytes. The short size of the key, the risk of leak of the key, and the possibility that an IV repeats, are more practical security issues.

functionEqualsM

6/20/23, 2:13 AM

Oh okay thanks this helped me better understand. Yeah I'm struggling to understand the concept in cryptography so you have any reference material you would recommend?

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EN: Why do stream ciphers repeat and how is that a threat?

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RU: Почему поточные шифры повторяются и чем это грозит?

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