A case study in almost-perfect security for unconditionally secure communication

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 ε-strong security, where the probabilities perceived by Cath may only change by a factor of ε. We then show that a mild variant of the so-called geometric strategy gives ε-strong safety for arbitrarily small ε and appropriately chosen values of a, b, c. *

Perfectly secure data aggregation via shifted projections

“…But it may be the case that Eve has a very high probability of guessing correctly who holds c. To this end, [13] introduced the stronger notion of perfect safety, where Eve's perceived probability that an agent holds c does not change after executing the protocol. Perfectly safe solutions for a wider number of cases were later reported in [12], and [8] proposed an approximate notion which led to 'almost-perfectly' safe solutions.…”

A Distributed Computing Perspective of Unconditionally Secure Information Transmission in Russian Cards Problems

“…[54], about stronger security requirements e.g. [40], about fault-tolerant solutions [36], and more than two parties e.g. [22].…”

“…The design consists of seven triples, which are precisely the lines that form the projective geometric plane. Particularly for perfect security notions, designs are important, as demonstrated in [40,53,54]. Such notions require C not gaining any probabilistic advantage in guessing the fate of some set of δ cards, perfect δ-security.…”

“…Many instances of the generalized Russian cards problem have been studied, included where the cards are dealt over more than three agents and work on cryptography. The generalized Russian cards problem has close ties to the field of combinatorial designs, particularly for perfect security notions [40,54]. The traditional security requirement of the Russian cards problem, which is the one we consider, C may not know with certainty who holds any given card, that does not mean that she may not have a high probability of guessing this information correctly.…”

“…The problem has received a fair amount of attention since then 1 e.g. [3,4,12,13,14,21,22,40,53,54], in its generalized form of signature (a, b, c), and other variants, including multiround, multiplayer, and different security requirements. Solutions are based either on modular arithmetic or on combinatorial designs.…”