Information-theoretic Physical Layer Security for Satellite Channels

Shannon introduced the classic model of a cryptosystem in 1949, where Eve has access to an identical copy of the cyphertext that Alice sends to Bob. Shannon defined perfect secrecy to be the case when the mutual information between the plaintext and the cyphertext is zero. Perfect secrecy is motivated by error-free transmission and requires that Bob and Alice share a secret key. Wyner in 1975 and later I.~Csisz\'ar and J.~K\"orner in 1978 modified the Shannon model assuming that the channels are noisy and proved that secrecy can be achieved without sharing a secret key. This model is called wiretap channel model and secrecy capacity is known when Eve's channel is noisier than Bob's channel. In this paper we review the concept of wiretap coding from the satellite channel viewpoint. We also review subsequently introduced stronger secrecy levels which can be numerically quantified and are keyless unconditionally secure under certain assumptions. We introduce the general construction of wiretap coding and analyse its applicability for a typical satellite channel. From our analysis we discuss the potential of keyless information theoretic physical layer security for satellite channels based on wiretap coding. We also identify system design implications for enabling simultaneous operation with additional information theoretic security protocols

Polynomial-Time, Semantically-Secure Encryption Achieving the Secrecy Capacity

In the wiretap channel setting, one aims to get information-theoretic privacy of communicated data based only on the assumption that the channel from sender to receiver is noisier than the one from sender to adversary. The secrecy capacity is the optimal (highest possible) rate of a secure scheme, and the existence of schemes achieving it has been shown. For thirty years the ultimate and unreached goal has been to achieve this optimal rate with a scheme that is polynomial-time. (This means both encryption and decryption are proven polynomial time algorithms.) This paper finally delivers such a scheme. In fact it does more. Our scheme not only meets the classical notion of security from the wiretap literature, called MIS-R (mutual information security for random messages) but achieves the strictly stronger notion of semantic security, thus delivering more in terms of security without loss of rate

Algorithm-Based Secure and Fault Tolerant Outsourcing of Matrix Computations

page number : 7 , Extended abstractWe study interactive algorithmic schemes for outsourcing matrix computations on untrusted global computing infrastructures such as clouds or volunteer peer-to-peer platforms. In these schemes the client outsources part of the computation with guaranties on both the inputs' secrecy and output's integrity. For the sake of efficiency, thanks to interaction, the number of operations performed by the client is almost linear in the input/output size, while the number of outsourced operations is of the order of matrix multiplication. Our scheme is based on efficient linear codes (especially evaluation/interpolation version of Reed-Solomon codes). Confidentiality is ensured by encoding the inputs using a secret generator matrix, while fault tolerance is ensured together by using fast probabilistic verification and high correction capability of the code. The scheme can tolerate multiple malicious errors and hence provides an efficient solution beyond resilience against soft errors. These schemes also allow to securely compute multiplication of a secret matrix with a known public matrix. Under reasonable hypotheses, we further prove the non-existence of such unconditionally secure schemes for general matrices

Cryptographic error correction

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.Includes bibliographical references (leaves 67-71).It has been said that "cryptography is about concealing information, and coding theory is about revealing it." Despite these apparently conflicting goals, the two fields have common origins and many interesting relationships. In this thesis, we establish new connections between cryptography and coding theory in two ways: first, by applying cryptographic tools to solve classical problems from the theory of error correction; and second, by studying special kinds of codes that are motivated by cryptographic applications. In the first part of this thesis, we consider a model of error correction in which the source of errors is adversarial, but limited to feasible computation. In this model, we construct appealingly simple, general, and efficient cryptographic coding schemes which can recover from much larger error rates than schemes for classical models of adversarial noise. In the second part, we study collusion-secure fingerprinting codes, which are of fundamental importance in cryptographic applications like data watermarking and traitor tracing. We demonstrate tight lower bounds on the lengths of such codes by devising and analyzing a general collusive attack that works for any code.by Christopher Jason Peikert.Ph.D