16. – 21. Dezember 2018, Dagstuhl-Seminar 18511

Algebraic Coding Theory for Networks, Storage, and Security


Martin Bossert (Universität Ulm, DE)
Eimear Byrne (University College Dublin, IE)
Antonia Wachter-Zeh (TU München, DE)

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Algebraic Coding Theory for Networks, Storage, and Security was the fourth in a series of seminars exploring applications of coding theory in modern communications theory (see also Dagstuhl Seminars 16321 (2016), 13351 (2013) and 11461 (2011)). The seminar brought together 50 mathematicians, engineers and computer scientists with expertise in coding theory, network coding, storage coding, cryptography and code-based security to participate in dissemination and collaboration within the seminar themes.

The main focus of this workshop was to explore novel results in coding theory for application in data storage management, cryptography and privacy. The impact of novel coding techniques across these domains was discussed and explored. Particular emphasis was placed on new applications of coding theory in public key cryptography, coding techniques for privacy in distributed storage and on practical schemes using coding theory for content delivery. These novel coding applications continue to have a significant impact on changing focus and broadening of coding theory fundamentals.

Overview talks were given by Philippe Gaborit (Recent Results for Cryptography Based on Rank Metric), Emina Soljanin, (Service Rates of Codes), Eitan Yaakobi, (Private Proximity Retrieval), Sacha Kurz, (Multisets of Subspaces and Divisible Codes), Heide Gluesing-Luerssen (On Ferrers Diagram Codes) and Salim El Rouayheb (GASP Codes for Secure Distributed Matrix Multiplication). In addition, several short talks were given by other participants based on current research interests with a view to stimulating collaboration. Presentations on system cybersecurity, private information retrieval, locally recoverable codes, adversarial channels and various aspects of rank metric codes were given. The remaining seminar time was allocated to discussion groups, including those in code-based cryptography, private computation, service rates of codes, algebraic geometry codes and adversarial channels. Aside from the working group discussions, particpants took the opportunity to engage in specific collaborations with co-authors.

We summarize some of the content of the working group discussions below. It has been well documented that redundancy is a basic requirement for stability of distributed data storage systems. Algebraic codes have been identified as having applications in providing efficiency in this domain far exceeding replication. Coding theory methods allow information retrieval minimizing disc access, storage size, local recoverability, data repair and data retrieval. Consequently, the area of storage coding has seen an exponential growth. An important aspect of user access in distributed storage is privacy of information retrieval so that users who are remotely accessing files can do so without storage servers knowing what they have accessed. Attempts to efficiently solve this problem come from coding theory.

An important application of secret sharing schemes is distributed storage of private data, where each party is a storage node and all parties wish to store a secret securely and reliably. Secret sharing is a fundamental cryptographic primitive and is used as a building block in numerous secure protocols. In our discussions we focussed on secret sharing schemes for the threshold access structure and on secret sharing with errors/attacks in a broader context. Fuzzy vaults and secret sharing over networks were discussed. A motivation for this area is for example biometric authentication in the presence of adversaries.

Another aspect of distributed storage is the service rate of codes. Emerging applications, such as distributed learning and fog computing, add yet another use for coding. In these applications, the goal is to maximize the number of users that can be simultaneously served by the system. One such service is simultaneous download of different jointly coded data blocks by many users competing for the system's resources. Here, coding affects the rates at which users can be served. The achievable service rate region is the set of request rates for each file that can be supported by the system. A variety of approaches to open problems about service rate were discussed. In particular, we addressed the question of code constructions that serve all requests for fixed rate constraints on file and the problem of how to determine the achievable service rate region for certain families of codes.

Privacy and security present formidable challenges in our modern connected world. Public-key cryptography is the foundation of multi-party communication as well as for key exchange of symmetric cryptosystems. With the increasing likelihood of a capable quantum computer, post-quantum secure systems have recently turned into the research focus, especially for devices that are hard to update and have very long life cycles. Code-based cryptography provides post-quantum secure public-key systems.

The working group on code-based-cryptography discussed the importance of security reduction arguments and went through several examples of these in relation to coding theory in cryptography. This discussion was a great benefit to the participants, many of whom have expertise in coding theory and keen to broaden their understanding of cryptography. The group also focussed on McEliece-like systems based on quasi-cyclic moderate density parity-check (QC-MDPC) codes and on low-rank parity-check (LRPC) codes. Distinguisher attacks were discussed, as well as possible modifications to the broken Gabidulin based cryptosystem.

Reliable communication across a channel in the presence of an adversary is a very general channel model that arises in many applications. Coding strategies for data transmission and authentication across the arbitrarily varying channel (where an adversary may alter the channel statistics) and for covert communication were discussed. A framework for linear systems under attack, such as the scenario where a restricted number of sensor measurements is vulnerable to adversarial attacks, was introduced and coding theoretic arguments used for attack detection and correction strategies.

There were about 20 PhD and postdoctoral researchers in attendance, who reported a very positive experience and satisfaction at being give the opportunity to explore new collaborations with more senior researchers and to get exposure to new problems in coding theory. All participants welcomed the time made available to them to take part in discussion groups and in more focussed collaborations. All were very pleased with the quality of the facilities and administrative support offered by staff at Schloss Dagstuhl, which made for a very productive meeting. Andreas Lenz and Rawad Bitar organised an afternoon excursion to Trier for the group. Giuseppe Cotardo collected and compiled data for the final published report.

Summary text license
  Creative Commons BY 3.0 Unported license
  Martin Bossert, Eimear Byrne, and Antonia Wachter-Zeh

Dagstuhl-Seminar Series


  • Data Structures / Algorithms / Complexity
  • Networks
  • Security / Cryptology


  • Distributed storage
  • Network coding
  • Coding theory
  • Cryptography
  • Privacy


In der Reihe Dagstuhl Reports werden alle Dagstuhl-Seminare und Dagstuhl-Perspektiven-Workshops dokumentiert. Die Organisatoren stellen zusammen mit dem Collector des Seminars einen Bericht zusammen, der die Beiträge der Autoren zusammenfasst und um eine Zusammenfassung ergänzt.


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