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I am studying a cryptography video on Coursera here titled: Modes of Operation: Many Time Key (CTR).

I have just two simple questions:

  1. At around 4:30 in the video they show 2^48 without saying where this number came from, perhaps it forms part of the AES specification?

  2. They then go on to explain that they plugged in the value 2^48 into the underlined equation on the line above, to calculate how many messages and of what size could be sent before a new key is required. How did they do this and what was the output?

Here is a picture from the video: Screen shot from video

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  • $\begingroup$ square-root square-root! $\endgroup$
    – kelalaka
    Jul 13, 2021 at 22:28
  • $\begingroup$ @kelalaka What did they square root? $\endgroup$
    – questioner
    Jul 13, 2021 at 22:58
  • $\begingroup$ Well, you have three numbers 128, 32 and 48 as powers of two... They have chosen 48 bit as margin, but remember the birthday bound! $\endgroup$
    – Maarten Bodewes ♦
    Jul 14, 2021 at 0:15
  • $\begingroup$ @MaartenBodewes Would you mind posting a reply to the question, because I did the square root of 128 and got a different answer... Then there is the case of the second question. $\endgroup$
    – questioner
    Jul 14, 2021 at 0:49
  • $\begingroup$ I think I can explain the slide, but I'm currently unsure about the term $|X|$... The squared q is needed because the nonce can collide otherwise. Basically you use 128 - 32 = 96 bits, and the square root of that is 48 bits. However, you still have to deal with the counter as well. However, I have too little context to create a readable answer - these slides are not the best readable without context - i.e. the presentation. $\endgroup$
    – Maarten Bodewes ♦
    Jul 14, 2021 at 11:07

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