4 ms·

For me it’s “I swear I feel like I’ve gotten the exact same TOTP code not that long ago!”. What’s the actual likelihood of seeing the same TOTP code from diffe

• masklinn 2y ago
  > What’s the actual likelihood of seeing the same TOTP code from different apps at different times? There’s only a million 6 digit TOTP codes, so I reckon you get to 50% odds of collision at ~1200 values.
  • yulle 2y ago
    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 https://en.wikipedia.org/wiki/Birthday_problem [1] https://www.bdayprob.com/ https://www.bdayprob.com/
    • codeflo 2y ago
      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.
      • ColinWright 2y ago
        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 https://news.ycombinator.com/item?id=40886363