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Cake day: June 25th, 2024

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  • To get every password, you’d have to exploit the password manager process itself. The manager asks you to approve every single password it hands out and you would know something is wrong if the extension starts asking for lots of passwords.

    The separation keeps the memory where the passwords are stored away from the browser. No malicious code executing inside the browser can access it. Also, the protocol between the extension and the manager can be really simple and (hopefully) easy to get right without making exploitable mistakes.

    It’s the Swiss cheese principle. The attacker has to break out of the website sandbox, get into the extension to copy the secret keys that are needed to impersonate the extension in the connection to the password manager, and exploit the password manager through that connection in order to get to the passwords. If any step fails (the holes in the cheese slices don’t align), the attack doesn’t get through.














  • x = 15

    Denote the origin of the circle O and the points A, B, C clockwise starting from the left. From the isosceles triangle OAB we get 2 r sin(alpha/2) = 24, where alpha is the angle between OA and OB.

    Construct the line orthogonal to OB that goes through C. The length of the line, h, between C and the intersection is h = 7 sin(beta) = x sin(90 - alpha). Denote the lengths of the parts of OB a and b, where a is connected to B. We have a + b = r

    Use Thales circle theorem to find that the triangle ABA’ completes the red shape, with A’ on the circle opposite to A. That means that the angle between A’A and A’B is alpha/2, but A’OB is also an isosceles triangle. So the angle on the other side, beta, has to be the same. Thus, beta = alpha/2.

    Now, put everything together: a = 7 cos (alpha/2), b = h cot(90 - alpha) = 7 sin(alpha/2) tan(alpha), r = 12 / sin(alpha/2).

    a + b = r <=> cos(alpha/2) sin(alpha/2) + sin^2(alpha/2) tan(alpha) = 12 / 7

    1/2 sin(alpha) + 1/2(1 - cos(alpha)) tan(alpha) = 12/7 <=> tan(alpha) = 24/7

    From the identity for h we know that x = 7 sin(alpha/2) / cos(alpha). Insert alpha = arctan(24/7)