Cryptography & Information Theory in Quantum Computing

Classical Cryptography

Classical cryptography involves using mathematical algorithms and techniques to secure communications by transforming readable messages into coded formats. This field has a rich history, dating back to ancient civilizations such as Egypt and Rome.

• Key Concepts:
  • Substitution Ciphers: Replace each letter with another letter or symbol. Examples include the Caesar Cipher and Vigenère Cipher.
  • Transposition Ciphers: Rearrange the letters of the plaintext.
  • Concealment Ciphers: Hide messages within other texts or images.
• Limitations: Classical ciphers are often easy to break using techniques like frequency analysis.

Summary: Classical cryptography laid the foundation for modern cryptographic techniques but is limited by its susceptibility to attacks.

Quantum Key Exchange I: The BB84 Protocol

The BB84 protocol is a quantum key distribution method that securely exchanges cryptographic keys using quantum states. It relies on the uncertainty principle, ensuring that any eavesdropping attempt can be detected.

• Key Concepts:
  • Uses four quantum states in two bases: rectilinear and diagonal.
  • Alice and Bob compare subsets of their keys to detect eavesdropping.
  • Privacy amplification ensures the security of the shared key.
• Example: Toshiba uses an efficient implementation of BB84 called T12 for secure key distribution.

Summary: The BB84 protocol provides secure key exchange by leveraging quantum mechanics to detect eavesdropping.

Quantum Key Exchange II: The B92 Protocol

The B92 protocol is a modified version of the BB84 protocol, using only two quantum states. It simplifies the process by eliminating the need for basis comparison.

• Key Concepts:
  • Uses two possible states of qubits.
  • Does not require comparing bases between Alice and Bob.
  • Detects eavesdropping without explicit basis comparison.
• Example: Proposed by Charles Bennett in 1992 as a simpler alternative to BB84.

Summary: The B92 protocol offers a streamlined approach to quantum key distribution with reduced complexity.

Quantum Key Exchange III: The EPR Protocol

The EPR protocol involves using entangled pairs (EPR pairs) for quantum key exchange. It is based on the principles of quantum mechanics and entanglement.

• Key Concepts:
  • Utilizes entangled particles to encode information.
  • Offers perfect forward secrecy by ensuring that any attempt to measure the state of one particle affects the other.
  • Can be used to implement Diffie-Hellman key exchange in a quantum context.