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Thinking about unlocking as an application of the Birthday Problem (or Paradox), can someone with better math skills than me calculate the # of iPhone X users i
by ballenf 9y ago
Thinking about unlocking as an application of the Birthday Problem (or Paradox), can someone with better math skills than me calculate the # of iPhone X users in a room necessary to get to 50% chance that someone can unlock someone else's phone? This would ignore the problem in the article and assume 1 in 1e6 odds.
https://en.wikipedia.org/wiki/Birthday_problem https://en.wikipedia.org/wiki/Birthday_problem
- tedunangst 9y agoThere's a formula in the article you linked.
- ballenf 9y agoYes, but I didn't think to use Wolfram and couldn't figure out how to reduce the formula to avoid having to calculate 1e6!
- The_Double 9y agoAbout 1250 people. http://www.wolframalpha.com/input/?i=plot++1-((n!+*+bin(1000000,n))%2F1000000%5En)+from+0+to+2000 http://www.wolframalpha.com/input/?i=plot++1-((n!+*+bin(1000...
- tedunangst 9y agosqrt(1400000) is about 1183.
- ballenf 9y agoWhere does the 1400000 come from?
- tedunangst 9y agoFrom the wikipedia formula. 2 ln 2 is about 1.4.
- ryanmonroe 9y agoR has a function for this qbirthday(prob = 0.5, classes = 1e6, coincident = 2) # 1178 You could also just calculate a bunch of the probabilities and find the minimum more "maunually" in.room <- 1000:1500 probs <- sapply(in.room, function(x) prod(((1e6 - (x - 1)):1e6)/1e6)) in.room[which.min(abs(probs - .5))] # 1178
- crindy 9y agoThis seems like a silly way to think about FaceID. You’d need 1000+ people to all try their faces on each other’s 1000+ phones to get the 50% chance of unlocking. That’s not the scenario biometric authentication is built for, which is why the phone would require a password after 5 failed attempts.
- mjevans 9y agoThe problem with that is the ease with which anyone can compare their input to the 'key'; externally. You could very quickly rule out 95% of the field with little effort, and people already do things like say "you look so much like X": we have a short list of collisions already.
- katastic 9y agoExactly. I'm more worried about if someone can make a mask of someone's face (or even a print out) and get it to work. But at least it's not like people have pictures of their faces plastered across every social network... ... crap.
- mikeash 9y agoApple specifically mentioned testing with high-end masks, and there have been videos made about people attempting it. It doesn’t work.
- zwily 9y agoWired gave it a pretty good go: https://www.wired.com/story/tried-to-beat-face-id-and-failed-so-far/ https://www.wired.com/story/tried-to-beat-face-id-and-failed...
- gnicholas 9y agoAs others have said, those who have tried masks haven't worked. But I wonder if normal masks have different heat signatures than real faces, which an IR array can detect. It's possible that something as simple as standard mask + heat would fool the system. Hopefully not!
- tzs 9y agoWhen they say that the probability of Face ID accepting the wrong person is 1 in N, what do they actually mean? Does it mean that if some random person who is not you tries to repeatedly unlock you phone, that person will succeed on average once every N tries? Or does it mean that the set of all people can be sorted into two groups, (1) those who can unlock your phone almost all the time, and (2) those who cannot unlock your phone, with 1/Nth of the population being in the first group?
- giovannibajo1 9y agoIt means that if 1 million strangers tried to unlock your phone, one of them on average would succeed. Obviously the phone requires a pin after 5 failures, but that’s another matter.