can open the chest without having at least one pirate from the other group. How do they
set this up?
Problem C-2.5
A group of four pirates has a treasure chest and one unique lock and key for each pirate.
Using hardware that is probably already lying around their ship, they want to protect the
chest so that any subset of three of these pirates can open the chest using their respective
locks and keys, but no two pirates can. How do they set this up?
Problem C-2.6
A thief walks up to an electronic lock with a 10-digit keypad and he notices that all but
three of the keys are covered in dust while the 2, 4, 6, and 8 keys show considerable wear.
He thus can safely assume that the 4-digit code that opens the door must be made up of
these numbers in some order. What is the worst case number of combinations he must now
test to try to open this lock using a brute-force attack?
Problem C-2.9
A variation of the following biometric authentication protocol was experimentally tested
several years ago at immigration checkpoints in major U.S. airports. A user registers in
person by showing her credentials (e.g., passport and visa) to the registration authority
and giving her fingerprint (a “palmprint” was actually used). The registration authority
then issues to the user a tamper-resistant smartcard that stores the reference fingerprint
vector and can execute the matching algorithm. The checkpoint is equipped with a tamper
resistant admission device that contains a fingerprint reader and a smartcard reader.
The user inserts her smartcard and provides her fingerprint to the device, which forwards
it to the smartcard. The smartcard executes the comparison algorithms and outputs the
result (“match” or “no match”) to the device, which admits or rejects the user accord-
ingly. Clearly, an attacker can defeat this scheme by programming a smartcard that always
outputs “match.” Show how to modify the scheme to make it more secure. Namely, the ad-
mission device needs to make sure that it is interacting with a valid smartcard issued by the
registration authority. You can assume that the smartcard can perform cryptographic com-
putations and that the admission device knows the public key of the registration authority.
12