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A "One Time Pad" can be thought of a Vigenere cipher with...

  1. An infinitely long key
  2. A secure symmetric key
  3. Multiple ciphertext alphabets
  4. A columnar transposition

I had this question come up today in one of my mid-terms and to be honest it caught me off guard a little, I chose (2) but I'm having doubts and now thinking its (3). I'm pretty sure i'll get a quick response to this because its quite a basic question, this is from an initial test on intro to cryptography and I felt I did pretty well on the rest of the test but this is bugging me.

I know one time pad can have infinite period and can be truly unbreakable but that doesn't mean it has an infinitely long key! (does it). (4) is surely a null consideration which leads me to think its (2) or (3)!

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    $\begingroup$ What does "a secure symmetric key" mean? If (1) were worded "a random key as long as the plaintext", I would have chosen (1). $\endgroup$ – mikeazo Nov 11 '15 at 18:58
  • $\begingroup$ I'd say definitely not 3 or 4. You could easily argue that 2 is correct if you say that you define "secure symmetric key" as "a random key as long as the plaintext". $\endgroup$ – mikeazo Nov 11 '15 at 19:20
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    $\begingroup$ I think that (1) is clearly the the intended answer, but it's a badly formulated question. $\endgroup$ – CodesInChaos Nov 11 '15 at 19:33
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    $\begingroup$ @CodesInChaos, that's my guess too. I think that due to the wording you could argue (2). $\endgroup$ – mikeazo Nov 11 '15 at 19:35
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    $\begingroup$ @pi-e to me "multiple ciphertext alphabets" means polyalphabetic cipher. Vigenere is a polyalphabetic cipher by itself, so (3) doesn't really add anything to the sentence. $\endgroup$ – mikeazo Nov 11 '15 at 19:37
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(1) is the correct answer. The Vengiere cipher phrase is a distractor. Basically all alphabets are in the cipher.

Note that the key does not need to be infinite, merely the same length as the plaintext and random. So in that regard, all of the answers are incorrect... But (1) is the "best" answer as it is the answer with the most entropy or randomness, which is the point of a one-time pad. You cannot draw any conclusions about entropy from the other answers.

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  • $\begingroup$ There is no one-time pad implementation with an infinitely long key, as generating such a key would require an infinite computation and thus infinite energy. $\endgroup$ – Simon Johnson Nov 12 '15 at 21:54
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    $\begingroup$ I think I agree with you (1) is now the best answer either way i will consult with my professor regarding the ambiguity of the question (but these academics can often be staunch in their opinions). I think my fundamental understanding of a one time pad was my undoing in this question. $\endgroup$ – pi-e Nov 12 '15 at 22:25
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    $\begingroup$ @SimonJohnson They didn't say it had an infinitely long key, just that it can be thought of as a cipher with an infinitely long key. $\endgroup$ – Reid Rankin Nov 13 '15 at 12:40

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