Abstract
We study security functions which can serve to establish semantic security for the two central problems of information-theoretic security: the wiretap channel, and privacy amplification for secret key generation. The security functions are functional forms of mosaics of combinatorial designs, more precisely, of group divisible designs and balanced incomplete block designs. Every member of a mosaic is associated with a unique color, and each color corresponds to a unique message or key value. Every block index of the mosaic corresponds to a public seed shared between the two trusted communicating parties. The seed set should be as small as possible. We give explicit examples which have an optimal or nearly optimal trade-off of seed length versus color (i.e., message or key) rate. We also derive bounds for the security performance of security functions given by functional forms of mosaics of designs.
Highlights
1.1 Two problems of information-theoretic securityA channel W : X → Z is a stochastic matrix W with rows indexed by the finite input alphabet X and columns indexed by the finite output alphabet Z
Our goal in this paper is to systematically study security functions where every preimage f −1(α) is the incidence relation of a balanced incomplete block design (BIBD) or a group divisible design (GDD) with point set X and block index set S
We investigate the optimal trade-off of the color rate vs. the block rate for functional forms of mosaics of BIBDs and GDDs
Summary
A channel W : X → Z is a stochastic matrix W with rows indexed by the finite input alphabet X and columns indexed by the finite output alphabet Z. All distributions are fixed in this setting, it makes sense to require semantic security It guarantees that even if Eve has the a priori knowledge that the key generated in the privacy amplification process has one of only two possible values, she is unable to tell which of these two is the one chosen. The physical channel from Alice to Bob will generally be noisy as well, and an error-correcting code needs to be applied first to make the error probability on this channel as small as possible In this case, the input alphabet X is the message set of the error-correcting code. An important feature of information-theoretic security is that it provides provable security even against attacks per-
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