Ph.D. position in Information Theory / Coding Theory - Lattice hash functions for secret key generation

Lattice hash functions for secret key generation

Future fifth-generation (5G) wireless networks will see the rise of direct device-to-device communications, leading to the Internet of Things, a unified network of smart connected objects. The new generation of networks poses great challenges for system design, and security is a major concern. In traditional communication systems, reliability is guaranteed by channel coding at the physical layer, while security is entrusted to encryption protocols at the network and data link layers. This architecture is ill-suited to mobile, decentralized networks since it requires the centralized distribution of secret keys through a trusted link. On the other hand, asymmetric encryption methods rely on the assumption that certain “trapdoor” functions are hard to invert. As the computational power of attackers increases due to advances such as quantum computing, these techniques become insecure.

Physical layer security aims at harnessing the randomness inherent in wireless propagation, such as fading and noise, in order to secure information. The works by Maurer, Ahlswede and Csiszár in information theory have shown that two legitimate users can exploit correlated observations of noisy channels to generate a shared secret key, even in the presence of an adversary who has access to a third sequence of observations and can intercept all the messages exchanged by the users over a public channel. Computational secrecy is replaced by information-theoretic secrecy, which is measured in terms of statistical independence between the eavesdropper’s observations and the secret key. This means that even an attacker with unlimited computational resources cannot extract any information from the signal.

The proposed Ph.D. thesis will develop novel techniques to generate secret keys for realistic wireless channel models, such as fading and multiple-antenna (MIMO) channels. This research will leverage our preliminary results on secret-key agreement from Gaussian sources using a new extractor based on lattice codes [1], and will provide a proof of concept of the feasibility of secret key generation at the physical layer. The applications of randomness extraction from continuous sources are not limited to physical channels, but include biometrics from fingerprints or retina scans, which can be used for authentication.

The objectives of the project are three-fold: studying the fundamental information-theoretic limits of secret key generation from wireless channel observations, developing low-complexity key agreement protocols based on lattice extractors, and experimental testing.


[1] C. Ling, L. Luzzi, M. Bloch, “Secret key generation from Gaussian sources using lattice hashing”, Proc. of Int. Symp. Inf. Theory (ISIT), Istanbul (Turkey), July 7-12, 2013


The candidate should have completed a master’s degree (or equivalent) in applied mathematics, electrical engineering, computer science, or related fields.

Good ability in mathematical reasoning is very important. Knowledge of information theory and coding theory is desirable but not mandatory.


Laura Luzzi (laura.luzzi@ensea.fr)

Laboratoire ETIS (UMR 8051) - Equipe Information, Communication et Imagerie (ICI)
6, avenue du Ponceau, 95014 Cergy-Pontoise
Phone: +33 (0)1 30 73 62 96

Webpage: http://perso-etis.ensea.fr/luzzi/index.html