Choose the best answer (one) and give reason in a few sentences for your choice or not choosing others.

Assignment Brief

INFA 640 Homework 2

Choose the best answer (one) and give reason in a few sentences for your choice or not choosing others. Please give a reference. To get full credit the reason should be in your own words, not a copy from any reference. Without reason in your own words you will not get full credit.

1. Claude Shannon presented the encryption design principles of _________________.

1. multiplication and factoring
2. exponentiation and Logarithms
3. confusion and diffusion
4. perplexion and reflection

Reason: how and why those principles guide the encryption?

2. A good hash function creates _________ mapping between the source string and the output string.

1. complex
2. as many as needed
3. divisional
4. one to one

Reason why is it considered good?

3) To create a digital signature, a sender needs the plain text, the asymmetrical encryption algorithm, and ___________.

1. his/her public key
2. the receiver’s public key
3. his/her private key
4. the receiver’s private key

Reason How is it used?

4) A number is relatively prime to another if they _____________.

1. have only each other as factors
2. have no prime factors in common
3. only have one prime factor in common
4. are both divisible by 7

5) Repudiation means

1. Faking one’s identity
2. Uproot
3. Deny ownership
4. Plant clues in the text

Reason: Why it is important?

6) (25 pts) The following is a ciphertext:

ZQ GDH LMJ XHBIG JODHAC PD CLUJ XZUJF ZO KLMZV LV L GDHOA RLO, PCJO ECJMJUJM GDH AD QDM PCJ MJVP DQ GDHM XZQJ ZP VPLGV EZPC GDH, QDM KLMZV ZV L RDUJLNXJ QJLVP

JMOJVP CJRZOAELG

1. What kind of cipher text is this? Mono- or Poly alphabetic; [Hint: assume one and when that does not work look for the other] [2 points]
2. Describe your cryptanalysis process. List all the steps you went through to decrypt the message. The steps should be in sufficient details so that a reader would be able to decrypt the encrypted text without needing any help from you.

[If you find solution online or use online tools please give reference. However, you should describe the steps as if you are working without the tool, (Hint consider starting with the frequency analysis) to get full credit]

[If you list partial steps you will get partial credit]

[15points]

• State the plain text message in readable form i.e. separating words if required

[the solution worked without the help from online tools will be given full credit] [2 pts]

• List features of the cipher- text that hindered and helped your decryption process. mention of helpful and hindering features [6 pts]

Note: Only a decrypted message even if it is correct one without the methodology and the detailed description of the self-explanatory steps used to decrypt, would not get points.

Sample Answer

1. Claude Shannon presented the encryption design principles of:

Answer: Confusion and diffusion

Reason:

Claude Shannon introduced confusion to make the relationship between the encryption key and ciphertext as complex as possible, and diffusion to spread the plaintext information throughout the ciphertext so that changing a single plaintext bit affects many ciphertext bits. These principles ensure strong encryption by making it harder for attackers to find patterns and reverse-engineer the key.

Why not the others: Multiplication/factoring and exponentiation/logarithms are mathematical techniques used in specific cryptosystems, but they are not Shannon’s general design principles. “Perplexion and reflection” is not a recognised cryptographic concept.

Reference: Shannon, C.E. (1949). Communication Theory of Secrecy Systems, Bell System Technical Journal.

2. A good hash function creates:

Answer: One-to-one

Reason:
A strong cryptographic hash aims for a unique output (hash) for each unique input, effectively making it appear one-to-one in practice (even though collisions are mathematically possible due to the pigeonhole principle). This ensures that small changes in the source string produce vastly different outputs, making reverse-engineering nearly impossible.

Why not the others: “Complex” is too vague, “as many as needed” is meaningless in hashing, and “divisional” is unrelated to the mapping property.

Reference: Stallings, W. (2017). Cryptography and Network Security.

3. To create a digital signature, a sender needs:

Answer: His/her private key

Reason:
In digital signatures, the sender encrypts the message hash with their private key. This allows anyone with the sender’s public key to verify the signature’s authenticity and integrity. Only the rightful owner should have access to the private key, ensuring non-repudiation.

Why not the others: The sender’s public key cannot create the signature, the receiver’s public key is used for encryption in confidentiality (not signing), and the receiver’s private key is never used by the sender.

Reference: Menezes, A., van Oorschot, P., & Vanstone, S. (1996). Handbook of Applied Cryptography.

4. A number is relatively prime to another if they:

Answer: Have no prime factors in common

Reason:
Two integers are relatively prime (coprime) when their greatest common divisor (GCD) is 1, meaning they share no prime factor. This property is crucial in public-key algorithms like RSA, where choosing numbers with this relationship ensures key generation works correctly.

Why not the others: Having only each other as factors is incorrect wording, “only one prime factor in common” contradicts the definition, and divisibility by 7 is irrelevant.

Reference: Rosen, K.H. (2012). Discrete Mathematics and Its Applications.

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