Quantum-safe cryptography: crossroads of coding theory and cryptography

We present an overview of quantum-safe cryptography (QSC) with a focus on post-quantum cryptography (PQC) and information-theoretic security. From a cryptographic point of view, lattice and code-based schemes are among the most promising PQC solutions. Both approaches are based on the hardness of decoding problems of linear codes with different metrics. From an information-theoretic point of view, lattices and linear codes can be constructed to achieve certain secrecy quantities for wiretap channels as is intrinsically classical- and quantum-safe. Historically, coding theory and cryptography are intimately connected since Shannon’s pioneering studies but have somehow diverged later. QSC offers an opportunity to rebuild the synergy of the two areas, hopefully leading to further development beyond the NIST PQC standardization process. In this paper, we provide a survey of lattice and code designs that are believed to be quantum-safe in the area of cryptography or coding theory. The interplay and similarities between the two areas are discussed. We also conclude our understandings and prospects of future research after NIST PQC standardisation.

Transmission rate conditions for distributed filtering in sensor networks against eavesdropper

This paper studies the distributed secure estimation problem of sensor networks (SNs) in the presence of eavesdroppers. In an SN, sensors communicate with each other through digital communication channels, and the eavesdropper overhears the messages transmitted by the sensors over fading wiretap channels. The increasing transmission rate plays a positive role in the detectability of the network while playing a negative role in the secrecy. Two types of SNs under two cooperative filtering algorithms are considered. For networks with collectively observable nodes and the Kalman filtering algorithm, by studying the topological entropy of sensing measurements, a sufficient condition of distributed detectability and secrecy, under which there exists a code–decode strategy such that the sensors’ estimation errors are bounded while the eavesdropper’s error grows unbounded, is given. For collectively observable SNs under the consensus Kalman filtering algorithm, by studying the topological entropy of the sensors’ covariance matrices, a necessary condition of distributed detectability and secrecy is provided. A simulation example is given to illustrate the results.