How random are TOTP codes?

Re:How random are TOTP codes? by yulle on Friday July 05, 2024 @03:48AM (#40880601)

For those curious on how to find that ~1200 values are needed before a 50% probability of collision, this is a generalized form of the birthday problem [0].

With a calculator [1], we can find the exact amount. plugging in D=10^6 (# of unique codes) with P=0.5 (odds of collision) gives you 1178 values.

[0] https://en.wikipedia.org/wiki/Birthday_problem

[1] https://www.bdayprob.com/

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Re:How random are TOTP codes? by codeflo on Friday July 05, 2024 @03:58AM (#40880664)

The very rough rule of thumb that I think one should remember is: You get a 50% chance of collision with sqrt(total) samples.

Sqrt(1 000 000) = 1 000, close enough to the exact number you calculated.

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Re:How random are TOTP codes? by ColinWright on Friday July 05, 2024 @05:52PM (#40886368)

More accurately, for 50% it's \sqrt(\ln(4))\sqrt(N) which is \sqrt( ln(4) N ).

That's about 1.17741 times \sqrt(N).

The reasons are explained here: https://news.ycombinator.com/item?id=40886363

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