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# RSA Cryptography: Encryption and Decryption

Created by
@LighterVerisimilitude

## Questions and Answers

### What is the primary principle behind RSA cryptography?

• Modular arithmetic
• Cyclic groups
• Prime number generation
• Prime factorization (correct)
• ### What is the purpose of the public key in RSA?

• To encrypt the plaintext (correct)
• To generate prime numbers
• To decrypt the ciphertext
• To compute the private key
• ### What is the output of the encryption process in RSA?

• Private key
• Plaintext message
• Ciphertext (correct)
• Public key
• ### What is the role of the padding scheme in RSA?

<p>To convert plaintext to numerical values</p> Signup and view all the answers

### What is the decryption process in RSA?

<p>Computing the plaintext using the private key</p> Signup and view all the answers

### What is the relationship between 'n' in the public and private keys?

<p>They are the same</p> Signup and view all the answers

### What is the security aspect of RSA relying on?

<p>Difficulty of factoring large composite numbers</p> Signup and view all the answers

### What is the output of the decryption process in RSA?

<p>Plaintext message</p> Signup and view all the answers

### What is the role of the private key in RSA?

<p>To decrypt the ciphertext</p> Signup and view all the answers

### What is the significance of the condition gcd(e, φ(n)) = 1 in the RSA key generation process?

<p>It ensures that <code>e</code> and <code>φ(n)</code> are coprime, guaranteeing that <code>d</code> can be computed such that <code>d * e ≡ 1 (mod φ(n))</code></p> Signup and view all the answers

### How does the modulus n relate to the prime numbers p and q in the RSA key generation process?

<p>The modulus <code>n</code> is the product of the two prime numbers <code>p</code> and <code>q</code>, i.e., <code>n = p * q</code></p> Signup and view all the answers

### What is the purpose of the Euler's totient function φ(n) in the RSA key generation process?

<p>It is used to compute the public exponent <code>e</code> and the private exponent <code>d</code></p> Signup and view all the answers

### What is the mathematical operation used to encrypt a message m in the RSA encryption process?

<p>The encryption formula is <code>c = m^e (mod n)</code></p> Signup and view all the answers

### What is the range of values that the ciphertext c can take in the RSA encryption process?

<p>The ciphertext <code>c</code> is a number between <code>0</code> and <code>n-1</code></p> Signup and view all the answers

### How does the decryption process in RSA recover the original message m from the ciphertext c?

<p>The decryption formula is <code>m = c^d (mod n)</code></p> Signup and view all the answers

### What is the relationship between the public exponent e and the private exponent d in the RSA key pair?

<p>They satisfy the equation <code>d * e ≡ 1 (mod φ(n))</code></p> Signup and view all the answers

### Why is it necessary to convert the message m into a numerical value before encryption in the RSA algorithm?

<p>To enable the mathematical operations required for encryption and decryption</p> Signup and view all the answers

## Study Notes

### RSA Cryptography: Encryption and Decryption

#### Overview

• RSA (Rivest-Shamir-Adleman) is an asymmetric encryption algorithm used for secure data transmission.
• It's based on the principle of prime factorization, which makes it computationally infeasible to factorize large composite numbers.

#### Key Components

• Public Key (e, n): A pair of integers, where 'e' is the public exponent and 'n' is the modulus (product of two large prime numbers, p and q).
• Private Key (d, n): A pair of integers, where 'd' is the private exponent and 'n' is the modulus (same as public key).

#### Encryption

• Encryption Process:
1. Convert plaintext message (M) to a numerical value (m) using a padding scheme (e.g., PKCS#1).
2. Compute the ciphertext (c) using the public key: c = m^e mod n.
• Example: If M = "Hello", m = 123456789 (after padding), e = 17, and n = 3233, then c = 123456789^17 mod 3233.

#### Decryption

• Decryption Process:
1. Compute the plaintext (m) using the private key: m = c^d mod n.
2. Convert the numerical value (m) back to the original plaintext message (M) using the padding scheme.
• Example: If c = 2819 (from encryption), d = 2753, and n = 3233, then m = 2819^2753 mod 3233 = 123456789, and M = "Hello".

#### Security Aspect

• RSA's security relies on the difficulty of factoring large composite numbers (n) into their prime factors (p and q).
• Given the public key (e, n), it's computationally infeasible to determine the private key (d, n) without knowing the prime factors (p and q).

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## Description

Understand the basics of RSA cryptography, including key components, encryption and decryption processes, and the security aspect of this asymmetric encryption algorithm.

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