Security as a Game – Decisions from Incomplete Models

Securing a computer system is always a battle of wits: the adversary tries to locate holes to sneak in, whereas the protector tries to cl ose them. Transmitting messages through a publicly accessible medium whilst having the content concealed from the adversary’s eyes is traditionally accomplished using mathematical transformatio ns. These are practically irreversible, unless some additional information – called the key – is available, making the secret accessible for the legitimate holder(s) of the key. Ever since the concept of perfect secrecy has rigorously been formalized by Shannon (1949), it has been known that unbreakable security is bought at the cost of keys that equal the message in terms of length. In addition, the key is required to be random and must be discarded immediately after usage. This pushed the concept of unconditional security out of reach for implementation in computer networks (though diplomatic and military applications existed), until 1984, where the idea of quantum cryptography was born by Bennett & Brassard (1984). The unique feature of this novel type communication is its usage of information carriers other than electrical pulses. By encoding bits in the polarization plane of single photons, the information becomes essentially not cloneable, as Wootters & Zurek (1982) have shown, and any attempt can be detected. This rendered the one-time pad practical in real-life electronic networks and unconditional security no longer needed to remain a dream. Classical cryptography widely relies on unprov en conjectures regarding the difficulty of solving computational problems. The field of public key cryptography draws its power from the infeasibility of reverting simple algebraic operations within large finite groups, but no proof has yet been discovered that rules out the existence of efficient algorithms to solve those problems. The sole indicator of security is thus the absence of any publication proving the assumptions wrong. But there is yet no othe r indication than pure hope for this to be true. Symmetric techniques, although conceptually different, come with no better arguments to support their security. Although these may lack much of the structure that public key systems enjoy and are thus harder to analyze, a rigorous proof of security or mathematical framework for proving security is also not available. In this work, we attempt taking a step towards providing a rigorous and easy-to-use decision-theoretic framework for proving security. Results are formulated with applications to quantum networks, but we emphasize that the framework is in no way limited to these.