Asymmetric Cryptography#

Asymmetric cryptography relies on one-way mathematical functions.

One-Way Functions#

Regular arithmetic is reversible:

  • If $3^x=81$, then $x=log_{3}(81)$.

Modular arithmetic is not:

  • Solving $3^x \mod{7} = 1$ is non-trivial
  • The discrete logarithm problem is hard

Core Idea#

  • Encryption and decryption use different keys
  • Encryption key is public
  • Decryption key is private
  • Eliminates the key distribution problem

Public-Key Concept#

Anyone can encrypt a message using the public key. Only the private key holder can decrypt it.

Historical Development#

  • Diffie–Hellman introduced key exchange
  • Ellis conceptualized public-key cryptography (classified)
  • Cocks derived RSA internally at GCHQ
  • RSA publicly introduced the first practical system

RSA#

  • Based on integer factorization
  • Security relies on computational hardness
  • Initially limited to governments and industry

Hybrid Cryptography#

  • RSA encrypts symmetric keys
  • Symmetric cipher encrypts message
  • Used in systems like PGP

Summary#

Asymmetric cryptography enables secure communication over open channels by exploiting mathematical asymmetry rather than secrecy.

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