Quantum key growing, referred to as quantum cryptography or quantum key distribution, is a technique using some attributes of quantum mechanics to create a secret shared cryptography key even if an eavesdropper has access to unlimited computational power. An important but often overlooked part of the technique is unconditionally secure message authentication. This dissertation looks at the security facets of authentication in quantum key growing. Crucial 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. Lastly and above all, a security flaw is identified that 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.
Contents: Authentication in quantum key growing
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 R´ enyi entropy
4.4.1 Conditional R´ enyi entropy
4.4.2 Chain rule of R´ enyi 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…
Source: Linköping University
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