Asymmetric Cryptography and RSA Overview

Asymmetric Cryptography

• Asymmetric cryptography uses key pairs, one private and one public.
• The private key is kept secret and personal, not shared.
• The public key is available to everyone.
• Asymmetric cryptography allows for confidentiality without prior secret exchange.
• It enables authentication of data content and origin.
• Cryptographic operations for confidentiality and authenticity are illustrated.
• Use case examples of confidential and authenticated communication are detailed.

Asymmetric Ciphers

• Advantages: Fundamental authentication mechanism; enables features not possible with symmetric ciphers.
• Disadvantages: Much slower than symmetric ciphers (performance 2-3 orders lower than AES). Large keys increase memory usage.
• Problems: Trustworthy public key distribution; managing lost/deprecated/compromised keys.

RSA

• RSA, a prominent algorithm, was developed in 1978.
• RSA uses keys: Private (d, n), Public (e, n).
• It enables public-key encryption (confidentiality) and private-key encryption (authenticity).
• Mathematical formulas for these operations are defined.
• Computational complexity relies on discrete logarithm and integer factorization.
• Key selection involves generating large prime numbers (p and q) and calculating d corresponding to e modulo calculation.

Playing with RSA

• Example RSA key generation and encryption/decryption using specific numbers (p, q, e, n) is shown.
• Example demonstrating encryption (P = 26, C = 31) and decryption (C = 31, P = 26, using the specific key).

Hybrid Encryption

• Combines the best aspects of both symmetric and asymmetric cryptography.
• Typically uses a fast symmetric cipher to encrypt data and an asymmetric cipher to (more securely) transmit the symmetric key.
• A method for hybrid encryption is described:
  • Obtain public key.
  • Generate a random symmetric key.
  • Encrypt the message with the symmetric key.
  • Encrypt the symmetric key with the public key of the receiver.
  • Transmit both encrypted portions.

Randomization of Asymmetric Encryptions

• RSA is deterministic; equal messages yield identical outputs.
• Non-deterministic asymmetric encryption is crucial to preventing trial and error attacks.
• Approaches to making asymmetric encryption non-deterministic (e.g.concatenation, fixed value, random value) are listed.

OAEP (Optimal Asymmetric Encryption Padding)

• OAEP enhances asymmetric encryption to be more robust against attacks.
• Specific components including the Hash function, seed, zeros (PS), and plaintext (M) are described.
• The Mask Generation Function (MGF) component functions similarly to a digest function, but in a flexible manner.

Diffie-Hellman Key Agreement

• A method to securely establish a shared secret key over an insecure channel.
• Requires the selection of a large prime (q) and its primitive root (a).
• Procedures for each party are defined mathematically and illustrated with an example.

Elliptic Curve Cryptography (ECC)

• ECC utilizes elliptic curves, a different mathematical approach, for cryptographic operations.
• Key sizes in ECC are generally smaller than in RSA for the same security level.
• NIST's and other specific elliptic curves are listed.
• ECC key agreement (ECDH) operations are illustrated with mathematical formulas.
• An ECC public key encryption method is given, combining ECDH with symmetric encryption.
• The steps involved in the process are presented mathematically.

Digital Signatures

• Digital signatures are used to authenticate and verify the authenticity of data.
• They verify the integrity and authorship of documents.
• Digital signatures are essentially asymmetric encryption with the sender's private key.
• Various approaches/methods are detailed with algorithms (e.g. Hash, asymmetric encryption, info, keys).
• Methods for verifying digital signatures are presented mathematically.

Practical Considerations

• Sending secure, authenticated data requires two asymmetric cryptography operations (encryption, signature).
• Encrypting the hash of a message, a more efficient approach for producing digital signatures, avoids this issue.

This quiz explores the concepts of asymmetric cryptography, detailing the mechanisms of key pairs, including their roles in confidentiality and authentication. It also delves into the RSA algorithm, outlining its development, advantages, and challenges compared to symmetric ciphers. Test your understanding of these fundamental cryptographic principles and practices.