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COMP 3334 – Computer Systems Security
创建日期：2024-07-06 16:11:25
标签： COMP 3334
Computer Systems Security

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COMP 3334 – Computer Systems Security 


Assignment

Submission requirements

Submit on Blackboard a single ZIP file containing:

1. A PDF file named as comp3334-studentid.pdf for your written answers. Change “studentid” with your actual student ID. The file must also include your name and student ID on the first page.

2. The three Python files as requested in the exercises below: exercise{1,3,4}.py.

Double check your submission. Any incorrect submission format may result in a zero mark for this assignment.

Exercise 1: Misusing AES [30 pts]

A website authenticates its users by asking for a login/password, and sends them a cookie C, valid for one minute, to keep track of their authentication status. The cookie C is formed such as C = Enc("user=username,tmstmp=timestamp"), with username = "anonymous" for unauthenticated users, or the name of the user when authenticated; and timestamp is a Unix-formated timestamp representing the time up to which the user is authenticated (current time plus one minute). Enc(·) designates the AES256 encryption in OFB-mode using iv as a random IV and k as a random key; both k and iv are unknown to us. The OFB mode of operation for encryption is described in Figure 1.

In this exercise, we consider cookies delivered on February 1st, 2024 at 00:00am UTC. At that time, an unauthenticated user coming to the website will receive a cookie:

CU = AES256-OFBk,iv("user=anonymous,tmstmp=1706745660")

The value 1706745660 corresponds to 00:01am on February 1st. We denote by PU the plaintext version of the cookie.

a) Give the plaintext cookie, denoted PA, that corresponds to the authenticated admin user if he logged in at the same time. Compare the length of PA and PU . [3 pts]

b) Describe how to modify the cookie CU into CA = AES256-OFBk,iv(PA) without knowing k nor iv. You may rethink about the value of PA so that PU and PA have the same length. Note that the cookie may authenticate the user admin for as long as you want (but at least the original one minute duration). [7 pts]

c) Implement in Python the attack that would turn CU into a valid CA for at least the original duration. Prepare a single Python file named exercise1.py that contains a function modifycookie() that takes as argument a base64-encoded cookie and returns the base64-encoded modified cookie. Your attack should work for different timestamps. You will get full marks if, given an encrypted cookie

Figure 1: Output Feedback (OFB) mode of operation (during encryption)

issued at any later date than February 1st this year, you are able to turn this cookie into a valid admin cookie for at least the original duration. Make sure your code uses meaningful variable names, consistent indenting scheme, and comments. [20 pts]

Exercise 2: Lan Manager hash [20 pts]

Back in the days, up to Windows XP, Windows account passwords were hashed using Microsoft’s LAN Manager (LM) hash function, which works as follows:

Step 1 The password is converted into upper case, null-padded to 14 characters (or truncated to 14 characters), and split into two 7-character halves.

Step 2 Each half is separately converted into a DES key. This key is used to encrypt the ASCII string “KGS!@#$%”, producing an 8-byte value.

Step 3 The two 8-byte values are concatenated, resulting in a 16-byte hash.

1. Suppose the attacker obtains a file with N hashed passwords. How much work would he need to do, at most, to crack these passwords by brute-force search? Show your calculations. Express the result in scientific notation (m × 10n, m ∈ R < 10, n ∈ N), and round it to two decimals. Assume that users could type any of the 95 printable characters found on a US keyboard i.e., letters, numbers, symbols, and punctuation marks, which are represented by codes 32 to 126 in the ASCII table. Passwords could be any length. [15 pts]

2. Knowing that a single modern NVIDIA GeForce RTX 4090 GPU can perform. 151.1 GH/s for LM, how long would it take an attacker with one such GPU to crack these N hashes? Assume that the overhead of matching a 64-bit string in a list of 2N 64-bit strings is negligible. [5 pts]

Exercise 3: PKCS#7 padding [20 pts]

The PKCS#7 padding scheme is commonly used to pad irregularly-sized plaintext messages to a specific block length before encryption, and is described in RFC5652. The algorithm simply consists in appending the required number of bytes up to nearest multiple of the block length. The value of each appended byte is equal to the number of bytes added. The maximum length of the pad is therefore 255. If the plaintext size is already a multiple of the block length, padding is still required. In this case, an entire block of padding bytes will be used. To remove the padding after decryption, the last byte of the decrypted ciphertext is read, which indicates how many bytes (of the same value) should be stripped from the end. For this exercise, do NOT use any library/package in your code.

1. Write a function pkcs(plaintext, length) in Python that takes a plaintext (plaintext) and a desired block length (length) as input and applies the PKCS#7 padding scheme. The function should return the padded input. An exception should be thrown if the block length is greater than the maximum pad length, using: raise Exception("Invalid block size")

For instance, for the message "YELLOW SUBMARINE" and a block size of 20, the output should be "YELLOW SUBMARINE\x04\x04\x04\x04". [5 pts]

2. Write a function validate_pkcs(plaintext, length) in Python that verifies the validity of the padding, and returns an unpadded string. The function should throw exceptions using raise Exception("Invalid padding") when: 1) the length of the plaintext indicates that no padding has been used; 2) the value for the pad length is incompatible with the block length; 3) the value of the padding bytes is incorrect. [15 pts]

Prepare a single Python file named exercise3.py that contains both functions.

Make sure to use the exact exception messages given above throughout this exercise; otherwise, your function will not be evaluated properly for assessment.

Exercise 4: Near collisions [30 pts]

Referring to the exercise given in Lecture 4 (slide 23), find a “near collision” on SHA-256 by hashing values that must contain your student ID. A near collision is defined as a pair of inputs which hash to values that share the same first n bits. We define n = 34 for this exercise.

One method of finding such collisions is to hash an increasing counter (concatenated to your student ID) and keep n-bit prefixes in a dictionary. If you encounter a prefix you have already seen, you found a near collision.

1. Provide a function find_near_collisions(studentid) that takes as input your student ID as a string in the format 12345678 (without letter) and outputs a tuple of binary strings (val1, val2) that are near collisions, and studentid is a substring of each value. Your program should terminate within one minute on a reasonably modern laptop and with a correct output.     [20 pts]

2. Provide a function get_values() that returns a tuple of binary strings (val1, val2) that you have previously computed and that satisfy the above criteria. Simply hardcode those values and return them.        [10 pts]

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CIVL2010 ECMT2150 CS 333 CP1406 KIT308 Economics 701 ECON3740 ECE 5759 BFC3340 FINC2012 COMP4500 MATH3871 FIT3080 18-819C Economic ECO202Y5Y PHY100 FINC-780 Econ 100B EC602 IE582 EE450 COMP9517 WRDS 150B ECON 570 LECTURE 2 ECA5101 ECE 4420 ADAD9311 FIT3031 CS 544 MF 703 CS 6140 KIT501 ENGSCI 344 CSC171 IE 332 FINM8007 21S2 COSC 1114 FE545 E471 SIT102 CSC108 MAT301 IAE 101 COP3503 STAT2004 EC 303 CS1026 STAT1203 MATH3171 ISOM5160 IFN657 FIT2014 ACCT2102 DSCI550 STATS 330 ELEC421 COMP3670 QBUS6840 MEES:698B MAST30027 MIET1077 Economics IFT 6758 FIT5122 BUSN5101 CptS 111 HRMT5502 Math2018 PP 312 INFS3200 CZ3005 CSSE1001 SENG 2011 MKTG 553Q BUFN 640 COMP507 ETF5952 DATA 311 ECE4043 BANK3011 finance M3H623544 HW1 INFS 7410 AI6103 STAT3888 INFS3208 ACCT7103 ECOS3013 PSYCH 20B F79MA STAT3006 ENGG952 2X MGSC 7000 ECE4132 MSF 526 MATH 3033 CDS 511 EEEE4120 EEET2465 ECA5103 MATH2070 ELEC3104 BU51019 EEE8147 ENGR20003 COSC 1107 ETF3200 FNCE 435 MSFI 435 ISyE6420 GENG4405 HW ETC5523 IE 7315 MOEC0021 STA 106 ENGG 1300A ENGG 1300 OLET1139 STAT 3503 STAT 206 FEM11149 ELEN 4720 COMP20003 SOLA1070 CS574 C11CS LINB29H3 MAST90083 ECON7200 STAT 610 LINB29 DSM-5 COMP3161 EEEN40010 MATH 4431 K353 STA 3386 IERG4300 COMS W4167 ENG5298 AMME 2302 CS3910 COMPSCI 320 STATS 369 GR5242 COSC 328 CSCI435 MGTS1301 INFS2200 COMP3900 CIS 375 Module AE03 COMP3121 CS260 HAM503 MGMT5050 INT3075 COSC 285 GEOL0029 GEGE2X01 STAT1201 MATH1061 MMF1941H STAT 5060 CS 520 COMP 4320 MSIN0104 000T FINS3648 ECMT2160 ECON4003 Phys 129L CSE 142 CS 3130 MGEB01 EECS 340 Finance (20443/20444) ECMM149 COMP5310 EEEN60180 CSC 111 AT2 CSCI 4430 STAB57 MA/CSC 427 MATH322 D100 CSCI544 CITS3004 CI6227 CSE 565 APCO 1P01 852L1 ELEC S411F COMP3207 STATS330 ECON7530 FIT5149 CSI4104 CMPT 371 COMP201 SEHS4696 FI4003 MATH6182 CG1 WS MATH401 MGT 205 QTM 110 COMP 0137 MACE12201 FIT5210 ECE 544 BISM7206 HUDM 6055 ECON3203 STATS 210 MSCI 570 MATH6173 COMPSCI4039 Accounting COM3503 AOE2024 ECON213 PSYC10004 Control Data 100/200A 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