Question

2) (25 pts) Consider a brute force attempt to crack keys for the following scenario. You have in your possession a wireless emulator the size of a 6" cube (i.e., 6" x 6" x 6) with a weight of less than 5 pounds which you can take to a parking lot containing 1,000 new cars. Each car has a four-digit wireless door key (between "0000" and "9999 using wireless symbols) as well as a three-digit engine key (between "000" and "999" including the endpoints, i., "O00" is a legitimate engine key as is "999). a (10 pts.) The first step is to open the door of one of the cars. In order to not lock out a customer due to others using wireless keys nearby, there is no limit on the number of attempts. Assume that cach attempt takes one second and is broadcast to the nearest 10 cars which have not yet been opened. Furthermore, assume that the parking lot is not monitored between 3am and 3:30am, and that the attack occurs during this half hour. How many cars can be broken into by the wireless emulator during this half hour, ignoring the time it takes to walk around the parking lot and ignoring any "reset" time (in other words, a wireless break-in attempt is made every second without delay between attempts)? b. (10 pts.) The second step is to emulate the wireless engine key. However, this involves pressing one's foot on the brakes and pressing a button which takes 5 seconds per attempt. Furthermore, after 10i failed attempts the engine locks itself, refuses to accept further attempts and triggers an alarm. Therefore, the thief with the wireless emulator makes at most 100 attempts per car engine. Assuming all 1,000 cars have been broken into (i.e, their doors are open providing access to the brake and to the ignition button), how many car engines can be started in a half hour of malicious effort? (5 pts.) Did you need to make any assumptions in answering either of the above two parts of this problem, problem 1 on homework I of ECE 3894 CHES? If you did not have to make any assumptions, please explain one way you could have changed the problem, e.g., by adding a limit on failed attempts for question 1.a, and explain how this change would have possibly affected (or not affected) car customers. If you did have to make at least one assumption, please reexplain one of the assumptions you made here (in your answer to 1c) as well as an alternative to the assumption (i.e., explain what could have been a different resolution to the lack of clarity which presumably would have changed your answer). Please note that Professor Mooney made up this question a few days before assigning this homework; therefore, please do not ask if assumptions are needed or not because Professor Mooney and the Graduate Teaching Assistant, Yu Cheng Chen, are not certain c.

Answer 1

crack four-sligit a) from quien Anila (ss) ampermalient a het Breaking into the car you should wireless doo key. gay is Between "oooo" to ccagga? so gey is from "oood" to "agas" Setol fossililitiey are 9998. 99 , 0880xx 398 яная артизан - the dool key for a car = 1998 rniss » 40 so, trobability of opening, 10x In -> Gaas e sal in a second १९१8 in 30 minutos so, numbee of sors that can be Broken : 10 x 1800 30 minutes : 30x6 osecane 1 minuta = 60 seconds 9998 18000 9998 ~ 1-8 so an average of 1.8 cars can be Broken in 30 minutes b) three digit enginee bey: 000-999 Number of possibilities = 1000 It takes 5 seconde for attempt Probability that the key generated by emulated matches engine key 1000 - De fet sooscanels 1000 i Lot for so o attemps = 2006

we have 1800 seconds to start the car engine so, average Number of sales that som be stated = 0.36 cals