Below is an example of key generation, encryption, and decryption using RSA. Look at the example, then fill in the blanks to indicate what each part is or answer the question. You do not have to do any math for this. Here are the words to select from to fill in the blanks. Modulus, encrypt key, decrypt key, factor, plaintext, ciphertext Public key is (23, 11) What is 23 called?_ Private key is (23, 13) What is 23 called? 23 can be part of the public key because it is very hard to ENCRYPT (m) = m^e mod n What is m? DECRYPT (c) = c^d mod n What is c? What is 11 called?_ What is 13 called?_ what is n? large prime numbers. (generic name, not a number)

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
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Below is an example of key generation, encryption, and decryption using RSA. Look at the example, then fill in the blanks to indicate what each part is or answer the question. You do not have to do any math for this. Here are the words to select from to fill in the blanks.

Modulus, encrypt key, decrypt key, factor, plaintext, ciphertext

Public key is (23, 11) What is 23 called? ____________, What is 11 called?____________

Private key is (23, 13) What is 23 called?____________, What is 13 called?____________

23 can be part of the public key because it is very hard to ____________ large prime numbers.

ENCRYPT (m) = m^e mod n   What is m? ____________, what is n? ____________ (generic name, not a number)

DECRYPT (c) = c^d mod n   What is c? ____________

Search for the following.

What does "mod" mean?
Transcribed Image Text:Below is an example of key generation, encryption, and decryption using RSA. Look at the example, then fill in the blanks to indicate what each part is or answer the question. You do not have to do any math for this. Here are the words to select from to fill in the blanks. Modulus, encrypt key, decrypt key, factor, plaintext, ciphertext Public key is (23, 11) What is 23 called? ____________, What is 11 called?____________ Private key is (23, 13) What is 23 called?____________, What is 13 called?____________ 23 can be part of the public key because it is very hard to ____________ large prime numbers. ENCRYPT (m) = m^e mod n What is m? ____________, what is n? ____________ (generic name, not a number) DECRYPT (c) = c^d mod n What is c? ____________ Search for the following. What does "mod" mean?
**Example: Generating an RSA Public-Key/Private-Key Pair**

An RSA public-key/private-key pair can be generated by the following steps:

**1. Generate a pair of large, random primes p and q. Note:** For examples, we use small prime numbers due to the size of the number generated.

- **p = 3, q = 5**

**2. Compute the modulus n as n = pq.**

- **n = p * q, 15 = 3 * 5**

**3. Select an odd public exponent e between 3 and n-1 that is relatively prime to p-1 and q-1.**

- \( e \) is between 3 and 14, \( e \) is relatively prime to 2 (3-1) and 4 (5-1)

- \( \phi(n) = 2 * 4 = 8 \)

- **e = 7, could also be 9 or 11 or 13**

**4. Compute the private exponent d from e, p, and q.**

- **\( e \times d \equiv 1 \pmod{\phi(n)} \)**

- **\( 7 \times d \equiv 1 \pmod{8} \)**

**5. Calculate d:**

- **\( 7 \times d \equiv 1 \pmod{8} \)**  
- What number multiplied by 7 and then divided by 8 equals 1?

  | Multiples of 8 | **8** | 16 | 24 | 32 | 48 | 56 | 64 | 72 | 80 | 88 | 96 | 104 |  
  | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |  
  | Multiples of 7 | **7** | 14 | 21 | 28 | 35 | 42 | **49** | 56 | 63 | 70 | 77 | 84 | 91 |98 | 105 |

  - **\( 7 \times 15 \equiv 1 \pmod{8} \) = 105/8 = 13 remainder 1**

- **d = 15**

**6. Output (n, e) as the public key and (
Transcribed Image Text:**Example: Generating an RSA Public-Key/Private-Key Pair** An RSA public-key/private-key pair can be generated by the following steps: **1. Generate a pair of large, random primes p and q. Note:** For examples, we use small prime numbers due to the size of the number generated. - **p = 3, q = 5** **2. Compute the modulus n as n = pq.** - **n = p * q, 15 = 3 * 5** **3. Select an odd public exponent e between 3 and n-1 that is relatively prime to p-1 and q-1.** - \( e \) is between 3 and 14, \( e \) is relatively prime to 2 (3-1) and 4 (5-1) - \( \phi(n) = 2 * 4 = 8 \) - **e = 7, could also be 9 or 11 or 13** **4. Compute the private exponent d from e, p, and q.** - **\( e \times d \equiv 1 \pmod{\phi(n)} \)** - **\( 7 \times d \equiv 1 \pmod{8} \)** **5. Calculate d:** - **\( 7 \times d \equiv 1 \pmod{8} \)** - What number multiplied by 7 and then divided by 8 equals 1? | Multiples of 8 | **8** | 16 | 24 | 32 | 48 | 56 | 64 | 72 | 80 | 88 | 96 | 104 | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | Multiples of 7 | **7** | 14 | 21 | 28 | 35 | 42 | **49** | 56 | 63 | 70 | 77 | 84 | 91 |98 | 105 | - **\( 7 \times 15 \equiv 1 \pmod{8} \) = 105/8 = 13 remainder 1** - **d = 15** **6. Output (n, e) as the public key and (
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Follow-up Question
Suppose we have 1G x 16 RAM chips that make up a 32G x 64 memory that uses high-order
interleaving. (This means that each word is 64 bits in size and there are 32G of these words.)
a) How many RAM chips are necessary?
b) Assuming four chips per bank, how many banks are required?
c) How many lines must go to each chip?
d)
How many bits are needed for a memory address, assuming it is word addressable?
e)
For the bits in part d, draw a diagram indicating many and which bits are used for chip select,
and how many and which bits are used for the address on the chip.
Transcribed Image Text:Suppose we have 1G x 16 RAM chips that make up a 32G x 64 memory that uses high-order interleaving. (This means that each word is 64 bits in size and there are 32G of these words.) a) How many RAM chips are necessary? b) Assuming four chips per bank, how many banks are required? c) How many lines must go to each chip? d) How many bits are needed for a memory address, assuming it is word addressable? e) For the bits in part d, draw a diagram indicating many and which bits are used for chip select, and how many and which bits are used for the address on the chip.
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