Applications of Codes and Lattices in Cryptography and Wireless Communications

Amin Sakzad, Khoa Nguyen

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Modern digital communication is widely used today in all kinds of online e-communications, including secure WWW communications, credit-card and EFTPOS transactions, Internet banking, smartphone and wireless networking, satellite communication, and many others.

Random and structured codes and lattices form effective building blocks for various cryptographic and wireless communications designs and analyses. For example, Euclidean lattice reduction techniques, such as the celebrated LLL and BKZ algorithms, have been used to evaluate the best known attacks on lattice-based cryptographic primitives and set concrete parameters for such constructions. The abovementioned lattice reduction tools have also been used to design, analyze, and efficiently implement transmitting and receiving communication schemes in multiple-input multiple-output (MIMO) channels and physical layer network coding.

Hard lattice-based and code-based problems, e.g., finding (within some approximation factor) the shortest nonzero lattice vector (approximate shortest vector problem (Approx-SVP)) or a lattice vector close to a given target vector (approximate bounded distance decoding (Approx-BDD)), are now considered the most likely candidates to thwart the threat presented to Internet security from the rise of quantum computers. For example, the US National Institute of Standards and Technology (NIST) initiated a 5–10 year standardization process at the end of 2017 for quantum-resistant cryptographic algorithms to be evaluated for selecting the new public-key cryptography standards. Beyond that, lattices and codes have been the main building block of the efficient and secure traditional and advanced cryptographic primitives.

Wireless communication engineers and particularly coding and information theorists are interested in employing Euclidean lattices for quantization and modulation and lattice reduction techniques for receiver designs. The goodness of lattices for these problems scales with the lattice dimension.

This Special Issue aims to be a forum for the presentation of novel techniques and application of codes and lattices in wireless communications and cryptography. In particular, the design, analysis, and implementation of real-world wireless communication and cryptographic problems with the help of algebraic number theory tools based on algebraic codes and (structured) Euclidean lattices fall within the scope of this Special Issue.
Original languageEnglish
Number of pages6
Publication statusAccepted/In press - 2021

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