Structural Properties of Twisted Reed-Solomon Codes with Applications to Cryptography

Peter  Beelen; Martin Bossert; Sven Puchinger; Johan Sebastian Heesemann Rosenkilde

doi:10.1109/ISIT.2018.8437923

Structural Properties of Twisted Reed-Solomon Codes with Applications to Cryptography

Peter Beelen
, Martin Bossert
, Sven Puchinger
, Johan Sebastian Heesemann Rosenkilde

Ulm University
Technical University of Munich

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

Abstract

We present a generalisation of Twisted Reed-Solomon codes containing a new large class of MDS codes. We prove that the code class contains a large subfamily that is closed under duality. Furthermore, we study the Schur squares of the new codes and show that their dimension is often large. Using these structural properties, we single out a subfamily of the new codes which could be considered for code-based cryptography: These codes resist some existing structural attacks for Reed-Solomon-like codes, i.e. methods for retrieving the code parameters from an obfuscated generator matrix.

Original language	English
Title of host publication	Proceedings of 2018 IEEE International Symposium on Information Theory
Publisher	IEEE
Publication date	2018
Pages	946-950
ISBN (Print)	9781538647813
DOIs	https://doi.org/10.1109/ISIT.2018.8437923
Publication status	Published - 2018
Event	2018 IEEE International Symposium on Information Theory - Talisa Hotel, Vail, United States Duration: 17 Jun 2018 → 22 Jun 2018

Conference

Conference	2018 IEEE International Symposium on Information Theory
Location	Talisa Hotel
Country/Territory	United States
City	Vail
Period	17/06/2018 → 22/06/2018

Keywords

MDS Codes
Reed-Solomon Codes
McEliece Cryptosystem
Structural Attacks

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10.1109/ISIT.2018.8437923

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@inproceedings{be1768d2306249e5b540598272d57a53,

title = "Structural Properties of Twisted Reed-Solomon Codes with Applications to Cryptography",

abstract = "We present a generalisation of Twisted Reed-Solomon codes containing a new large class of MDS codes. We prove that the code class contains a large subfamily that is closed under duality. Furthermore, we study the Schur squares of the new codes and show that their dimension is often large. Using these structural properties, we single out a subfamily of the new codes which could be considered for code-based cryptography: These codes resist some existing structural attacks for Reed-Solomon-like codes, i.e. methods for retrieving the code parameters from an obfuscated generator matrix.",

keywords = "MDS Codes, Reed-Solomon Codes, McEliece Cryptosystem, Structural Attacks",

author = "Peter Beelen and Martin Bossert and Sven Puchinger and Rosenkilde, \{Johan Sebastian Heesemann\}",

year = "2018",

doi = "10.1109/ISIT.2018.8437923",

language = "English",

isbn = "9781538647813",

pages = "946--950",

booktitle = "Proceedings of 2018 IEEE International Symposium on Information Theory",

publisher = "IEEE",

address = "United States",

note = "2018 IEEE International Symposium on Information Theory, ISIT 2018 ; Conference date: 17-06-2018 Through 22-06-2018",

}

Beelen, P, Bossert, M, Puchinger, S & Rosenkilde, JSH 2018, Structural Properties of Twisted Reed-Solomon Codes with Applications to Cryptography. in Proceedings of 2018 IEEE International Symposium on Information Theory. IEEE, pp. 946-950, 2018 IEEE International Symposium on Information Theory, Vail, Colorado, United States, 17/06/2018. https://doi.org/10.1109/ISIT.2018.8437923

TY - GEN

T1 - Structural Properties of Twisted Reed-Solomon Codes with Applications to Cryptography

AU - Beelen, Peter

AU - Bossert, Martin

AU - Puchinger, Sven

AU - Rosenkilde, Johan Sebastian Heesemann

PY - 2018

Y1 - 2018

N2 - We present a generalisation of Twisted Reed-Solomon codes containing a new large class of MDS codes. We prove that the code class contains a large subfamily that is closed under duality. Furthermore, we study the Schur squares of the new codes and show that their dimension is often large. Using these structural properties, we single out a subfamily of the new codes which could be considered for code-based cryptography: These codes resist some existing structural attacks for Reed-Solomon-like codes, i.e. methods for retrieving the code parameters from an obfuscated generator matrix.

AB - We present a generalisation of Twisted Reed-Solomon codes containing a new large class of MDS codes. We prove that the code class contains a large subfamily that is closed under duality. Furthermore, we study the Schur squares of the new codes and show that their dimension is often large. Using these structural properties, we single out a subfamily of the new codes which could be considered for code-based cryptography: These codes resist some existing structural attacks for Reed-Solomon-like codes, i.e. methods for retrieving the code parameters from an obfuscated generator matrix.

KW - MDS Codes

KW - Reed-Solomon Codes

KW - McEliece Cryptosystem

KW - Structural Attacks

U2 - 10.1109/ISIT.2018.8437923

DO - 10.1109/ISIT.2018.8437923

M3 - Article in proceedings

SN - 9781538647813

SP - 946

EP - 950

BT - Proceedings of 2018 IEEE International Symposium on Information Theory

PB - IEEE

T2 - 2018 IEEE International Symposium on Information Theory

Y2 - 17 June 2018 through 22 June 2018

ER -

Structural Properties of Twisted Reed-Solomon Codes with Applications to Cryptography

Abstract

Conference

Keywords

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