Abstract
In the Russian cards problem, Alice, Bob and Cath draw a, b and c cards, respectively, from a publicly known deck. Alice and Bob must then communicate their cards to each other without Cath learning who holds a single card. Solutions in the literature provide weak security, where Alice and Bob’s exchanges do not allow Cath to know with certainty who holds each card that is not hers, or perfect security, where Cath learns no probabilistic information about who holds any given card. We propose an intermediate notion, which we call varepsilon -strong security, where the probabilities perceived by Cath may only change by a factor of varepsilon . We then show that strategies based on affine or projective geometries yield varepsilon -strong safety for arbitrarily small varepsilon and appropriately chosen values of a, b, c.
Highlights
Consider the following scenario: Bob is the commander of a team of a + b + c agents and must coordinate a covert operation
Claude Shannon was one of the first to formalize the study of cryptography
The solutions we present here will provide an intermediate level of security between weak and perfect, controlling the amount of probabilistic information that may be acquired by the eavesdropper, while having the advantage of being much easier to construct than perfectly secure solutions
Summary
Consider the following scenario: Bob is the commander of a team of a + b + c agents and must coordinate a covert operation. To do this, he must choose a + c of his agents to each carry out an individual mission and rendezvous with Alice behind enemy lines. For the safety of the operation, none of the agents know who else is involved before meeting Alice, and the only information they can provide her with is their own identity When they reach the rendezvous point, only a of them show up and the other c are assumed captured by the enemy leader, Cath. The use of a random deal of cards is convenient in that it allows Alice and Bob to share information with unconditional security, as described below
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