Asymmetric Encryption Algorithms 🔐

RSA (Rivest-Shamir-Adleman) 🔑

• Introduction: One of the first practical asymmetric cryptography systems.

• Development: Patented in 1983, released to the public domain in 2000.

• Key Features:

  • Key Generation: Based on choosing two large, random prime numbers.

  • Usage: Key generation, encryption, and decryption operations.

• Security Note: High-level mathematics involved; detailed math not covered here.

DSA (Digital Signature Algorithm) ✍️

• Introduction: Used for signing and verifying data.

• Development: Patented in 1991, part of the US federal information processing standard.

• Key Features:

  • Key Generation: Includes a random seed value; security depends on this randomness.

  • Historical Issue: Sony PlayStation 3 (2010) - compromised due to non-randomized seed value, leading to unauthorized software signing and game piracy.

Diffie-Hellman (DH) Key Exchange 🔄

• Introduction: Used for securely exchanging keys over an unsecured channel.

• Process:

  • Agree on a large random starting number (not secret).

  • Each person selects a secret random number.

  • Combine the starting number with the secret number and exchange results.

  • Compute the final shared value without disclosing secrets.

• Usage: Primarily for key exchange; adaptations exist for encryption and Public Key Infrastructure (PKI) systems.

Elliptic Curve Cryptography (ECC) 🔍

• Introduction: Public-key encryption system using elliptic curves over finite fields.

• Concept:

  • Elliptic Curves: Defined by equations such as ( y^2 = x^3 + ax + b ).

  • Properties: Horizontal symmetry and intersection properties facilitate encryption.

• Advantages:

  • Efficiency: Achieves security with smaller key sizes compared to traditional systems.

  • Example: 256-bit ECC key is comparable to a 3072-bit RSA key.

• Variants:

  • ECDH (Elliptic Curve Diffie-Hellman): Key exchange.

  • ECDSA (Elliptic Curve Digital Signature Algorithm): Signing.

• Recommendations: NIST endorses ECC; NSA permits use up to top-secret data with 384-bit keys.

• Concerns: Potential vulnerability to quantum computing.

Summary 📈

• RSA: Pioneering asymmetric encryption with large prime numbers.

• DSA: For data signing and verification, with historical security issues.

• Diffie-Hellman: Key exchange mechanism for secure communication.

• ECC: Efficient encryption with smaller key sizes and elliptic curves, facing future quantum computing challenges.

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