The Key Establishment Problem

The combinatorics of cryptographic key establishment

“…A good survey of some of the topics considered in this paper is [72]. More generally, [10] provides an excellent survey on key establishment that goes beyond areas of combinatorial interest and [18] is probably the definitive work on cryptographic protocols relating to key establishment. Finally we note that both [7] and [26] include good reviews of other combinatorial applications to problems arising in information security.…”

“…Note that the precise meaning of property (2) in Definition 5.1 depends on the security model within which we are operating. If a KPS is unconditionally secure then these conditions can be stated information theoretically (see, for example [10]). The literature contains a wide variety of key predistribution schemes.…”

On Unconditionally Secure Robust Distributed Key Distribution Centers

“…More precisely, the user gets from S 1 the value 4 + 3 × 3 = 6 and the value 6 + 6 × 3 = 3 from S 2 . Using the public identifiers of S 1 and S 2 , the user sets up the two pairs of values (3,6), (2,3), and by applying the Lagrange Formula, he interpolates the polynomial P (x) = 3 × x − 3 mod 7. It is easy to see that P (0) = 4, and hence the user recovers κ 3 .…”

“…Several kinds of Key Distribution Schemes have been considered in the literature: Key Pre-Distribution Schemes (KPS, for short), Key Agreement Schemes (KAS, for short) and Broadcast Encryption Schemes (BES, for short) among others. The reader can consult [20] for a survey on unconditionally secure schemes, [19,11] for a general and detailed description of a variety of protocols for the Key Establishment Problem and related issues, and [3] for a simple introduction.…”