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Applications of Cryptography CSCE 4050/5050 (Spring 2024)
Homework 4
Due
on Feb 16 (Mon), 11:59pm
Grading remarks:
CSCE 4050 (undergraduate) students will receive extra 10 bonus points, as long as the assignment sheet (with attempted solutions) will be submitted.
Total points (the actual grade will not exceed 100 points):
CSCE 4050: 120 points.
CSCE 5050: 110 points.
1.
[
Advantage (distinguishing)
] Let G : K
{0,1}
n
be a PRG that outputs the keystream of RC4 (stream cipher). We know from Lecture 2-2 that G has the following weakness: the probability that the second byte in the output of G takes a value 0x00 (that is an all-zero byte) is 2/256. Define a statistical test for distinguishing the output of G from a uniformly random sequence and compute the respective advantage.
Hint: Follow the example of Slide 20, Lecture 3-1.
[20 points]
2.
[
Definition of semantic security
] Consider Slide 18 of Lecture 4-1 and suppose that the adversary B selects the messages as follows: m
0
such that lsb(m
0
) = 1 and m
1
such that lsb(m
1
) = 0. Compute the advantage Adv
SS
[B,E] in this case. Explain your answer.
[20 points]
3.
[
DES S-boxes
] For DES, suppose that the S-box S
1
has input “000001” and the S-box S
2
has input “100000”. Provide the respective outputs.
Tip: The description of S-boxes can be found, e.g., here:
https://csrc.nist.gov/csrc/media/publications/fips/46/3/archive/1999-10-25/documents/fips46-3.pdf
[10 points] Rubric: 5 points for each correct answer.
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Related Questions
Chapter 8: Problem 9
Previous Problem
Problem List
Next Problem
Results for this submission
Entered
49
146
Answer Preview
Result
49
146
incorrect
incorrect
At least one of the answers above is NOT correct.
(1 point) Alice and Bob are using the ElGamal cipher with the parameters p = 193 and a = = 5.
=
=
Alice makes the mistake of using the same ephemeral key for two plaintexts, x1 and x 2. The eavesdropper
Eve suspects that x1 146. She sees the two ciphertexts y1
= 141 and y2 = = 167 in transit; these are the
encryptions of x1 and x2, respectively.
a) What is the masking key kм?
49
b) What is the plaintext x2 ?
146
arrow_forward
Quest A
Problem 3:
Not y
ans ared
A small private club has only 100 members. Answer the following questions:
a.
How many secret keys are needed if all members of the club need to send secret messages to each
other?
b.
How many secret keys are needed if everyone trusts the president of the club? If a member needs to
send a message to another member, he first sends it to the president; the president then sends the
message to the other member. Justify your answer.
Note: For numerical questions above, show formulas used and calculation details.
arrow_forward
3. Students are required to create 6-character long passwords to access the library. The letters must be from
lowercase letters or digits. Each password must start with "a" or "b", it also must contain at most three lowercase-
letters (including the first letter) and contains no repeated digits (letters can be repeated). How many valid
passwords are there? You are required to show your work step-by-step. [10 marks]
10 points
arrow_forward
8-1 Discussion: Cryptography V
Available on Jun 18, 2022 11:59 PM. Submission restricted before availability starts.
As you learned this week, RSA is the most widely used public key cryptosystem. In
this discussion, you will apply RSA to post and read messages. For this reflection
discussion, use the prime numbers p = 3 and q = 11.
Using the public key e = 3, post a phrase about something that you found
interesting or relevant in this course. Include only letters and spaces in your phrase.
Represent the letters A through Z by using the numbers 01 through 26, and
represent a space by the number 32. Treat upper case and lower case letters as the
same.
Optional: If you want to include punctuation characters, you can use the numbers
27 through 31 for that, but you must inform your classmates that you did.
How did you calculate your value for d? As a check, the phrase "A CAB" would be
represented by "01 32 03 01 02" and would be encrypted as "01 32 27 01 08".
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provide the correct answer and show all steps
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im not sure whats wrong
arrow_forward
Question 1
Study the scenario and complete the question(s) that follow:
Ceasar Cipher
The Caesar Cipher technique is one of the earliest and simplest method of encryption technique. It's
simply a type of substitution cipher, i.e., each letter of a given text is replaced by a letter some fixed
number of positions down the alphabet. For example with a shift of 1, A would be replaced by B, B
would become C, and so on. The method is apparently named after Julius Caesar, who apparently
used it to communicate with his officials.
1.1 Write a Ceasar cipher algorithm in such a way that a character D is changed to N. Derive
the encryption of the other characters accordingly.
1.2 Based on your algorithm, what will be the encrypted code of the message “my mother is not
home".
End of Question 1
arrow_forward
In the use of RSA Cryptography, if the public key under RSA Cryptography is (11, 65), find the private key You must show all the detailed steps.
arrow_forward
Network Security problem
Q1] Consider the RSA encryption algorithm. Suppose that a malicious user
intercepts the ciphertext C = 18 that is being sent to Alice. If Alice's public key
PUa = {5,35) is known by the malicious user, show how the malicious user will
recover the plaintext M?
[Hint: find M=?]
Note: C stands for Ciphertext,
M stands for Message (Plaintext),
PUa stand for Alice's public key.
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Provide the correct answers
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Problem 1
Which of the following statements about digital signature is CORRECT:
A. Digital signature should be unforgeable, but can be valid by anyone who sees it.
B. In digital signature, the algorithms GenerateKey, Sign, and Verify should be randomized algorithms.
C. In digital signature, public key is used to encrypt a message.
D. In digital signature, private key is used to decrypt a message.
Problem 2
Which of the following statements about Goofycoin is INCORRECT:
A. A designated entity called Goofy can create new coins whenever he wants and these newly created coins belong to him.
B. Whoever owns a coin can transfer it on to someone else.
C. Goofycoin can address the double spending issue.
Problem 3
Which of the following statements about ScroogeCoin is INCORRECT:
A. A designated entity called Scrooge publishes an append‐only ledger containing the history of all the transactions that have happened.
B. Scrooge can build a block chain, which is a series of data blocks,…
arrow_forward
RSA
Using python script:
Attacker obtains Q(n) = 15000 and knows public key is
(en) = (19,15251). He is able to calculate decryption private
key (d,n) and use it to decrypt the following:
ciphertext: 9794-3241-9862
Find plaintext: "
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Answer the given question with a proper explanation and step-by-step solution.
cryptography
Keys:
cryptographic
networksecurity
. Using the two keys (memory words) cryptographic and network security, encrypt the following message: Be at the third pillar from the left outside the lyceum theatre tonight at seven. If you are distrustful bring two friends.
Make reasonable assumptions about how to treat redundant letters and excess letters in the memory words and how to treat spaces and punctuation. Indicate what your assumptions are.
Note: The message is from the Sherlock Holmes novel, The Sign of Four.
b. Decrypt the ciphertext. Show your work.
c. Comment on when it would be appropriate to use this technique an\d what its advantages are.
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6. In a Rivest, Shamir and Adleman (RSA) cryptosystem, a particular user uses two prime
numbers P and Q to generate the public key and the private key. If P is 23 and Q is 29,
using RSA algorithm, find the following:
e) public key
f) private key
g) Encrypted data (Assume the original message, M=7)
h) Decrypted data
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The following parameters are chosen to generate the public and private keys for the RSA cryptosystem.
p = 7q = 11e = 13d = 37
If the plaintext is m = 4, then what is the ciphertext c?
c =
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Cryptography is the study of protecting information. A cipher is a pair of algorithms
―the first algorithm encrypts a message and the second algorithm decrypts the
message. In most cases, a unique key is also required to encode or decode plaintext.
The Caesar cipher is one of the simplest and most widely known ciphers. It is named
after Julius Caesar who allegedly used it to protect important military directives.
Every letter in the plaintext is replaced by a letter N positions down the alphabet. For
example, if N = 3, then a => d and b => e.
While the idea is remarkably simple, it appeared to work in Ancient Rome. Most
people there couldn't read, and those who could simply assumed it was a foreign
language.
Write a program that implements the Caesar cipher. You program will get from
standard input the key N, followed by a line of plaintext.
.
.
The key N should be any integer between 0 and 26 inclusive. If this isn't the
case, print an error message and quit.
Any numbers or…
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(**no chatGPT and feel free to provide the reference link)
Scenario:
Recent EY’s Global Information Security Survey 2021 - finds Chief Information Security Officers (CISOs) and security leaders battling against a new wave of threats unleashed by COVID-19 highlighted the current state of cybersecurity and the challenges that organisations face in protecting their data and systems. The growing vulnerability of an IT risk has received a lot of attention in the survey report. Overall, the 2021 EY Global Information Security Survey report provides valuable insights into the current state of cybersecurity, the challenges that organizations face, and strategies for improving cybersecurity resilience and preparedness in the face of emerging threats.
a) Briefly explain the nature of EY's Global Information Security Survey.
b) Identify any TWO(2) key challenges faced by CISOs to balance the competing demands of cybersecurity while preserving business innovation and growth.
arrow_forward
(**no chatGPT and feel free to provide the reference link)
Scenario:
Recent EY’s Global Information Security Survey 2021 - finds Chief Information Security Officers (CISOs) and security leaders battling against a new wave of threats unleashed by COVID-19 highlighted the current state of cybersecurity and the challenges that organisations face in protecting their data and systems. The growing vulnerability of an IT risk has received a lot of attention in the survey report. Overall, the 2021 EY Global Information Security Survey report provides valuable insights into the current state of cybersecurity, the challenges that organizations face, and strategies for improving cybersecurity resilience and preparedness in the face of emerging threats.
a) Identify any TWO(2) key challenges faced by CISOs to balance the competing demands of cybersecurity while preserving business innovation and growth. (Give me around more than 150 words)
arrow_forward
1.
In the use of RSA Cryptography, if the public key under RSA Cryptography is
(11, 65), find the private key.
arrow_forward
1. Asymmetric Encryption and Message Authentication:
a) The primitive root of a prime number is the basic principle of Diffie-Hellman.
i) Is 3 the primitive root of 11? Show the proof with your calculation.
ii) What are the important criteria for selecting a prime number in cryptography? Is 11 a good choice for such a purpose?
b) Find the parameters stated using the Diffie-Hellman methods, given the user A and B shared a prime number and its primitive root of 23 and 5, respectively.
i) If user A public key value is 8, find the A’s private key.
ii) If user B public key value is 19, what is the common secret key?
c) In the following scenario, we will compare the security services that are given by digital signatures (DS) and message authentication codes (MAC). We assume that James can read all messages send from Chan to Badrul and the other way around, too. James has no knowledge of any keys but the public one in the case of DS. State whether and…
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7.
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Cryptography problem mathematics
Suppose Alice and Bob are using a cryptosystem with a 128-bit key, so there are 2128possible keys. Eve is trying a brute-force attack on the system.(a) Suppose it takes 1 day for Eve to try 264 possible keys. At this rate, how long willit take for Eve to try all 2128 keys? (b) Suppose Alice waits 10 years and then buys a computer that is 100 times fasterthan the one she now owns. Will she finish trying all 2128 keys before or after whatshe does in part (a)?
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Cryptography is the area of mathematics intended for the study of techniques and principles for transforming information from its original form to another, unintelligible form, so that it can be used only when authorized.
Based on the presented cryptographic definition, mark the correct alternative that corresponds to the Hash cryptographic system definition:
A) Cryptographic process that does not guarantee the non-repudiation of communication;
B) Computer file that contains a set of information regarding the entity to which the certificate was issued;
C) Standard-length cryptographic digest generated by math functions and hash tables
D) Public/private key pair that are shared and used for encryption and decryption;
E) Single private key that is shared and used for encryption and decryption.
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Part 1: Please answer the following questions about the fundamental of cryptography. Each question has only one correct answer.
1, Which description about block ciphers is NOT correct?
Block ciphers encrypt the message block by block.
A block cipher with a small block is vulnerable to the codebook attack.
The encryption and decryption algorithms in block ciphers use the same secret key.
The key length for block cipher should be very short to defend against the exhaustive key search attacks.
2, If the key length of a block cipher is 64 bits, what is the size of the key space?
Hint: The key space consists of all possible keys.
64
264
232
2128
3, Modern block ciphers combine substitution S and permutation P operations to improve security. Based on the security rule, the cipher should not use consecutive substitutions or consecutive permutations. In the following combinations, which one violates the above security rule?
?1?1?2?2
B. ?1?1?2?2
C. ?1?1?2?2
4, Which…
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Q2: Based on Diffie-Hellman protocol, if the public key is g = 23, p = 797, and c =
512. Find the value of private key a.
%3D
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Computer Science
Information Security
Decode simple ciphering puzzles
Solve the followings:
(HINT: This code uses base64 and the Caesar cipher)
UGRhIGx3b29za256IGJrbiBwZGEgeWR3aGhhamNhIGx3Y2EgZW86IHludWxwaw==
Decode the following : Vigenere Code – Key Word
Ym pyi kqw bbgy ckrbwkqutk xf cbiymswbt as r uqcnpv eijzi kjii dlzep xz xyg xgvhleb dm wvxmghp, rpl ioi dcrdymka wu vyi ewcavfxmgzmvu kdti wtwb alrv.
Upyglu Ijyickch
Decode the following substitution cipher
S W M B X M B Q X S Q E X E H Q X T H I B M D X B R J G X H R S S S
X S J J L T C B K A E Q, L K Q X B R J G X H R S O X S J J L T
C B K A E Q X S Q E D Q S Y W D H M G D Q B M T D.
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Do not exceed three lines in length while writing your notes on any of the following subjects:(what/why/advantage(s)/disadvantage(s)) Manchester codes
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Please written by computer source
Your employer, SGA (Secretive government Agency) want you to develop an encryption program. After doing some research you have two candidate algorithms. According to your research, Algorithm 1 has cost Θ(n3), while algorithm 2 is listed as Ο(n4) and Ω(n2). Which one do you choose? How do you decide? What would you have to know to choose the other one? Please walk through the process of how you would decide.
arrow_forward
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Related Questions
- Chapter 8: Problem 9 Previous Problem Problem List Next Problem Results for this submission Entered 49 146 Answer Preview Result 49 146 incorrect incorrect At least one of the answers above is NOT correct. (1 point) Alice and Bob are using the ElGamal cipher with the parameters p = 193 and a = = 5. = = Alice makes the mistake of using the same ephemeral key for two plaintexts, x1 and x 2. The eavesdropper Eve suspects that x1 146. She sees the two ciphertexts y1 = 141 and y2 = = 167 in transit; these are the encryptions of x1 and x2, respectively. a) What is the masking key kм? 49 b) What is the plaintext x2 ? 146arrow_forwardQuest A Problem 3: Not y ans ared A small private club has only 100 members. Answer the following questions: a. How many secret keys are needed if all members of the club need to send secret messages to each other? b. How many secret keys are needed if everyone trusts the president of the club? If a member needs to send a message to another member, he first sends it to the president; the president then sends the message to the other member. Justify your answer. Note: For numerical questions above, show formulas used and calculation details.arrow_forward3. Students are required to create 6-character long passwords to access the library. The letters must be from lowercase letters or digits. Each password must start with "a" or "b", it also must contain at most three lowercase- letters (including the first letter) and contains no repeated digits (letters can be repeated). How many valid passwords are there? You are required to show your work step-by-step. [10 marks] 10 pointsarrow_forward
- 8-1 Discussion: Cryptography V Available on Jun 18, 2022 11:59 PM. Submission restricted before availability starts. As you learned this week, RSA is the most widely used public key cryptosystem. In this discussion, you will apply RSA to post and read messages. For this reflection discussion, use the prime numbers p = 3 and q = 11. Using the public key e = 3, post a phrase about something that you found interesting or relevant in this course. Include only letters and spaces in your phrase. Represent the letters A through Z by using the numbers 01 through 26, and represent a space by the number 32. Treat upper case and lower case letters as the same. Optional: If you want to include punctuation characters, you can use the numbers 27 through 31 for that, but you must inform your classmates that you did. How did you calculate your value for d? As a check, the phrase "A CAB" would be represented by "01 32 03 01 02" and would be encrypted as "01 32 27 01 08".arrow_forwardprovide the correct answer and show all stepsarrow_forwardim not sure whats wrongarrow_forward
- Question 1 Study the scenario and complete the question(s) that follow: Ceasar Cipher The Caesar Cipher technique is one of the earliest and simplest method of encryption technique. It's simply a type of substitution cipher, i.e., each letter of a given text is replaced by a letter some fixed number of positions down the alphabet. For example with a shift of 1, A would be replaced by B, B would become C, and so on. The method is apparently named after Julius Caesar, who apparently used it to communicate with his officials. 1.1 Write a Ceasar cipher algorithm in such a way that a character D is changed to N. Derive the encryption of the other characters accordingly. 1.2 Based on your algorithm, what will be the encrypted code of the message “my mother is not home". End of Question 1arrow_forwardIn the use of RSA Cryptography, if the public key under RSA Cryptography is (11, 65), find the private key You must show all the detailed steps.arrow_forwardNetwork Security problem Q1] Consider the RSA encryption algorithm. Suppose that a malicious user intercepts the ciphertext C = 18 that is being sent to Alice. If Alice's public key PUa = {5,35) is known by the malicious user, show how the malicious user will recover the plaintext M? [Hint: find M=?] Note: C stands for Ciphertext, M stands for Message (Plaintext), PUa stand for Alice's public key.arrow_forward
- Provide the correct answersarrow_forwardProblem 1 Which of the following statements about digital signature is CORRECT: A. Digital signature should be unforgeable, but can be valid by anyone who sees it. B. In digital signature, the algorithms GenerateKey, Sign, and Verify should be randomized algorithms. C. In digital signature, public key is used to encrypt a message. D. In digital signature, private key is used to decrypt a message. Problem 2 Which of the following statements about Goofycoin is INCORRECT: A. A designated entity called Goofy can create new coins whenever he wants and these newly created coins belong to him. B. Whoever owns a coin can transfer it on to someone else. C. Goofycoin can address the double spending issue. Problem 3 Which of the following statements about ScroogeCoin is INCORRECT: A. A designated entity called Scrooge publishes an append‐only ledger containing the history of all the transactions that have happened. B. Scrooge can build a block chain, which is a series of data blocks,…arrow_forwardRSA Using python script: Attacker obtains Q(n) = 15000 and knows public key is (en) = (19,15251). He is able to calculate decryption private key (d,n) and use it to decrypt the following: ciphertext: 9794-3241-9862 Find plaintext: "arrow_forward
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