Low-Rank Parity-Check Codes over the Ring of Integers Modulo a Prime Power

Julian Renner; Sven Puchinger; Antonia Wachter-Zeh; Camilla Hollanti; Ragnar Freij-Hollanti

doi:10.1109/ISIT44484.2020.9174384

Low-Rank Parity-Check Codes over the Ring of Integers Modulo a Prime Power

Julian Renner
, Sven Puchinger
, Antonia Wachter-Zeh
, Camilla Hollanti
, Ragnar Freij-Hollanti

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

10 Citations (Scopus)

Abstract

We define and analyze low-rank parity-check (LRPC) codes over extension rings of the finite chain ring {{\mathbb{Z}}-{{p^r}}}, where p is a prime and r is a positive integer. LRPC codes have originally been proposed by Gaborit et al. (2013) over finite fields for cryptographic applications. The adaption to finite rings is inspired by a recent paper by Kamche et al. (2019), which constructed Gabidulin codes over finite principle ideal rings with applications to space-time codes and network coding. We give a decoding algorithm based on simple linear-algebraic operations. Further, we derive an upper bound on the failure probability of the decoder. The upper bound is valid for errors whose rank is equal to the free rank.

Original language	English
Title of host publication	2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings
Publisher	IEEE
Pages	19-24
Number of pages	6
ISBN (Electronic)	9781728164328
DOIs	https://doi.org/10.1109/ISIT44484.2020.9174384
Publication status	Published - Jun 2020
MoE publication type	A4 Conference publication
Event	IEEE International Symposium on Information Theory - Los Angeles, United States Duration: 21 Jul 2020 → 26 Jul 2020

Publication series

Name	IEEE International Symposium on Information Theory - Proceedings
Publisher	IEEE
Volume	2020-June
ISSN (Print)	2157-8095

Conference

Conference	IEEE International Symposium on Information Theory
Abbreviated title	ISIT
Country/Territory	United States
City	Los Angeles
Period	21/07/2020 → 26/07/2020

Funding

S. Puchinger has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant J. Renner and A. Wachter-Zeh were supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 801434). C. Hollanti was supported by the Academy of Finland, under grants 303819 and 318937, and by the TU Munich – Institute for Advanced Study, funded by 97th8e-G1e-r7m2a8n1E-x6c4el3le2n-c8e/I2ni0ti/a$tiv3e1a.n0d0t h©e2E0U270th IFErEamEeworkProgrammeunder19 1NotethatonecanmapeveryelementofFptoanarbitraryelementISITof2020the grantagreementno.291763,viaaHansFischerFellowship. residueclassRq/m,wheremismaximalidealofRq.

Access to Document

10.1109/ISIT44484.2020.9174384

https://arxiv.org/abs/2001.04800

Cite this

Renner, J., Puchinger, S., Wachter-Zeh, A., Hollanti, C., & Freij-Hollanti, R. (2020). Low-Rank Parity-Check Codes over the Ring of Integers Modulo a Prime Power. In 2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings (pp. 19-24). Article 9174384 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2020-June). IEEE. https://doi.org/10.1109/ISIT44484.2020.9174384

@inproceedings{c5a279bbed2d4d27bf0f4cdd1d0040c4,

title = "Low-Rank Parity-Check Codes over the Ring of Integers Modulo a Prime Power",

abstract = "We define and analyze low-rank parity-check (LRPC) codes over extension rings of the finite chain ring \{\{\textbackslash{}mathbb\{Z\}\}-\{\{p\textasciicircum{}r\}\}\}, where p is a prime and r is a positive integer. LRPC codes have originally been proposed by Gaborit et al. (2013) over finite fields for cryptographic applications. The adaption to finite rings is inspired by a recent paper by Kamche et al. (2019), which constructed Gabidulin codes over finite principle ideal rings with applications to space-time codes and network coding. We give a decoding algorithm based on simple linear-algebraic operations. Further, we derive an upper bound on the failure probability of the decoder. The upper bound is valid for errors whose rank is equal to the free rank.",

author = "Julian Renner and Sven Puchinger and Antonia Wachter-Zeh and Camilla Hollanti and Ragnar Freij-Hollanti",

year = "2020",

month = jun,

doi = "10.1109/ISIT44484.2020.9174384",

language = "English",

series = "IEEE International Symposium on Information Theory - Proceedings",

publisher = "IEEE",

pages = "19--24",

booktitle = "2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings",

address = "United States",

note = "IEEE International Symposium on Information Theory, ISIT ; Conference date: 21-07-2020 Through 26-07-2020",

}

Renner, J, Puchinger, S, Wachter-Zeh, A, Hollanti, C & Freij-Hollanti, R 2020, Low-Rank Parity-Check Codes over the Ring of Integers Modulo a Prime Power. in 2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings., 9174384, IEEE International Symposium on Information Theory - Proceedings, vol. 2020-June, IEEE, pp. 19-24, IEEE International Symposium on Information Theory, Los Angeles, California, United States, 21/07/2020. https://doi.org/10.1109/ISIT44484.2020.9174384

Low-Rank Parity-Check Codes over the Ring of Integers Modulo a Prime Power. / Renner, Julian; Puchinger, Sven; Wachter-Zeh, Antonia et al.
2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings. IEEE, 2020. p. 19-24 9174384 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2020-June).

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

TY - GEN

T1 - Low-Rank Parity-Check Codes over the Ring of Integers Modulo a Prime Power

AU - Renner, Julian

AU - Puchinger, Sven

AU - Wachter-Zeh, Antonia

AU - Hollanti, Camilla

AU - Freij-Hollanti, Ragnar

PY - 2020/6

Y1 - 2020/6

N2 - We define and analyze low-rank parity-check (LRPC) codes over extension rings of the finite chain ring {{\mathbb{Z}}-{{p^r}}}, where p is a prime and r is a positive integer. LRPC codes have originally been proposed by Gaborit et al. (2013) over finite fields for cryptographic applications. The adaption to finite rings is inspired by a recent paper by Kamche et al. (2019), which constructed Gabidulin codes over finite principle ideal rings with applications to space-time codes and network coding. We give a decoding algorithm based on simple linear-algebraic operations. Further, we derive an upper bound on the failure probability of the decoder. The upper bound is valid for errors whose rank is equal to the free rank.

AB - We define and analyze low-rank parity-check (LRPC) codes over extension rings of the finite chain ring {{\mathbb{Z}}-{{p^r}}}, where p is a prime and r is a positive integer. LRPC codes have originally been proposed by Gaborit et al. (2013) over finite fields for cryptographic applications. The adaption to finite rings is inspired by a recent paper by Kamche et al. (2019), which constructed Gabidulin codes over finite principle ideal rings with applications to space-time codes and network coding. We give a decoding algorithm based on simple linear-algebraic operations. Further, we derive an upper bound on the failure probability of the decoder. The upper bound is valid for errors whose rank is equal to the free rank.

UR - https://www.scopus.com/pages/publications/85090420499

U2 - 10.1109/ISIT44484.2020.9174384

DO - 10.1109/ISIT44484.2020.9174384

M3 - Conference article in proceedings

AN - SCOPUS:85090420499

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 19

EP - 24

BT - 2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings

PB - IEEE

T2 - IEEE International Symposium on Information Theory

Y2 - 21 July 2020 through 26 July 2020

ER -

Low-Rank Parity-Check Codes over the Ring of Integers Modulo a Prime Power

Abstract

Publication series

Conference

Funding

Access to Document

Other files and links

Fingerprint

Number-theoretic and combinatorial tools for private and secure cloud services

Cite this

Low-Rank Parity-Check Codes over the Ring of Integers Modulo a Prime Power

Abstract

Publication series

Conference

Funding

Access to Document

Other files and links

Fingerprint

Projects

Number-theoretic and combinatorial tools for private and secure cloud services

Cite this