Authentication in quantum key growing

Jörgen Cederlöf

Quantum key growing, often called quantum cryptography or quantum key distribution, is a method using some properties of quantum mechanics to create a secret shared cryptography key even if an eavesdropper has access to unlimited computational power. A vital but often neglected part of the method is unconditionally secure message authentication. This thesis examines the security aspects of authentication in quantum key growing. Important concepts are formalized as Python program source code, a comparison between quantum key growing and a classical system using trusted couriers is included, and the chain rule of entropy is generalized to any Rényi entropy. Finally and most importantly, a security flaw is identified which makes the probability to eavesdrop on the system undetected approach unity as the system is in use for a long time, and a solution to this problem is provided.

Keywords:

Quantum key growing, Quantum key generation, QKG, Quantum key distribution, QKD, Quantum cryptography, Message authentication, Unconditional security, Rényi entropy.

• 1. Introduction
  • 1.1 Setup
  • 1.2 Running the system
  
  
• 2. QKG versus courier
  • 2.1 Manufacturing and transferring
  • 2.2 Unconditional security
  • 2.3 Denial of Service attacks
  • 2.4 Mobility
  • 2.5 Time and price
  • 2.6 Limited lifetime
  
  
• 3. Discrete random variables
  • 3.1 Discrete random variables
  • 3.2 Dependent random variables
  • 3.3 Jensen's inequality
  
  
• 4. Entropy
  • 4.1 Conventions
  • 4.2 Shannon entropy
  • 4.3 Guessing entropy
  • 4.4 Rényi entropy
    • 4.4.1 Conditional Rényi entropy
    • 4.4.2 Chain rule of Rényi entropy
    • 4.4.3 Spoiling knowledge
    • 4.4.4 Entropy holism
  
  
• 5. Unconditionally secure authentication
  • 5.1 Universal families of hash functions
  • 5.2 Examples
  • 5.3 Authentication
  • 5.4 Encrypted tags
  
  
• 6. Authentication with partially secret key
  • 6.1 Active and passive chance of forgery
  • 6.2 No message/tag pairs seen
  • 6.3 Encrypted tags
  • 6.4 A message/tag pair seen
    • 6.4.1 The problem
    • 6.4.2 The solution
  
  
• 7. Authentication in QKG
• A. Source code
• Bibliography