Public-Key Cryptography Overview

Public-Key Cryptosystems

• Public-key cryptography was developed to solve two key problems associated with symmetric encryption:
  • Key distribution: How to securely share keys between two parties without a pre-established method.
  • Digital signatures: How to verify the authenticity and integrity of digital messages.

Asymmetric Encryption

• Asymmetric encryption uses two related keys: a public key and a private key.
• Public key: Can be shared freely and is used for encryption.
• Private key: Kept secret and used for decryption.
• Computationally infeasible to derive the private key from the public key.

Public-Key Encryption Scheme

• Plaintext: The original, readable message to be encrypted.
• Encryption algorithm: The mathematical function used to transform plaintext into ciphertext using the public key.
• Public and private keys: The key pair, where one key is public and the other is private.
• Ciphertext: The scrambled message produced by encryption, which can only be decrypted using the matching private key.
• Decryption algorithm: The mathematical function used to recover plaintext from ciphertext using the private key.

Implementing Public-Key Cryptography

• Each user creates a unique key pair.
• The public key is made available to others.
• The private key is kept secret by the user.
• To send a confidential message to Alice, Bob encrypts the message using Alice's public key.
• Alice can decrypt the message using her private key, as only she knows this key.

Public-Key Encryption for Authentication

• Public-key encryption can provide authenticity, ensuring message integrity and sender identity.
• The sender signs the message using their private key.
• The receiver verifies the signature using the sender's public key.

Applications of Public-Key Cryptosystems

• Encryption/decryption: Securely exchanging confidential messages.
• Digital signatures: Verifying message authenticity and integrity.
• Key exchange: Securely exchanging session keys for symmetric encryption.

RSA Encryption Algorithm

• Developed in 1977 by Rivest, Shamir, and Adleman.
• Widely used in web browsers and e-commerce applications.

RSA Key Generation

• Choose two large prime numbers, p and q.
• Calculate n = p * q and z = (p - 1)(q - 1).
• Choose a public key exponent 'e' that is relatively prime to z.
• Calculate the private key exponent 'd' such that (d * e) % z = 1.
• The public key is (e, n), and the private key is (d, n).

RSA Encryption and Decryption

• Encryption: To encrypt message m, calculate ciphertext c = m^e % n.
• Decryption: To decrypt ciphertext c, calculate plaintext m = c^d % n.

Explore the fundamentals of public-key cryptography, including key distribution and digital signatures. Understand how asymmetric encryption works using public and private keys, and the processes involved in encrypting and decrypting messages. This quiz will test your knowledge on the principles and applications of public-key encryption schemes.