Smudge Attack

April 11, 2025

Jackson is trying to crack your iPhone passcode. When you enter your password to unlock your device, you may leave a fingerprint smudge on the screen. Jackson can crack the code by detecting these oily smudges, finding the numbers that composes your password and then brute-forcing it through trials and errors. (This is called a smudge attack) For example, if your password is 1123, one can tell that your passcode contains "1", "2", and "3" from your smudges. For a 4-digit code, is it more secure to set your code with 4 distinct numbers, or 3, 2, or even 1? Please find the # of combinations for each cases and the most secure # of combinations. What about a 6-digit code?

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