On Decoding and Applications of Interleaved Goppa Codes

Lukas Holzbaur; Hedongliang Liu; Sven Puchinger; Antonia Wachter-Zeh

doi:10.1109/ISIT.2019.8849600

On Decoding and Applications of Interleaved Goppa Codes

Lukas Holzbaur, Hedongliang Liu, Sven Puchinger, Antonia Wachter-Zeh

Technical University of Munich

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

10 Scopus citations

Abstract

Goppa Codes are a well-known class of codes with, among others, applications in code-based cryptography. In this paper, we present a collaborative decoding algorithm for interleaved Goppa codes (IGC). Collaborative decoding increases the decoding radius beyond half of the designed minimum distance. We consider wild Goppa codes and show that we can collaboratively correct more errors for binary Goppa codes than the Patterson decoder. We propose a modified version of the McEliece cryptosystem using wild IGC based on a recently proposed system by Elleuch et al., analyze attacks on the system and present some parameters with the corresponding key sizes.

Original language	English
Title of host publication	2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	1887-1891
Number of pages	5
ISBN (Electronic)	9781538692912
DOIs	https://doi.org/10.1109/ISIT.2019.8849600
State	Published - Jul 2019
Event	2019 IEEE International Symposium on Information Theory, ISIT 2019 - Paris, France Duration: 7 Jul 2019 → 12 Jul 2019

Publication series

Name	IEEE International Symposium on Information Theory - Proceedings
Volume	2019-July
ISSN (Print)	2157-8095

Conference

Conference	2019 IEEE International Symposium on Information Theory, ISIT 2019
Country/Territory	France
City	Paris
Period	7/07/19 → 12/07/19

Keywords

Interleaved Goppa codes
McEliece system
code-based cryptography
decoding
public-key cryptosystem

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10.1109/ISIT.2019.8849600

Cite this

Holzbaur, L., Liu, H., Puchinger, S., & Wachter-Zeh, A. (2019). On Decoding and Applications of Interleaved Goppa Codes. In 2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings (pp. 1887-1891). Article 8849600 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2019-July). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT.2019.8849600

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title = "On Decoding and Applications of Interleaved Goppa Codes",

abstract = "Goppa Codes are a well-known class of codes with, among others, applications in code-based cryptography. In this paper, we present a collaborative decoding algorithm for interleaved Goppa codes (IGC). Collaborative decoding increases the decoding radius beyond half of the designed minimum distance. We consider wild Goppa codes and show that we can collaboratively correct more errors for binary Goppa codes than the Patterson decoder. We propose a modified version of the McEliece cryptosystem using wild IGC based on a recently proposed system by Elleuch et al., analyze attacks on the system and present some parameters with the corresponding key sizes.",

keywords = "Interleaved Goppa codes, McEliece system, code-based cryptography, decoding, public-key cryptosystem",

author = "Lukas Holzbaur and Hedongliang Liu and Sven Puchinger and Antonia Wachter-Zeh",

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doi = "10.1109/ISIT.2019.8849600",

language = "English",

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Holzbaur, L, Liu, H, Puchinger, S & Wachter-Zeh, A 2019, On Decoding and Applications of Interleaved Goppa Codes. in 2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings., 8849600, IEEE International Symposium on Information Theory - Proceedings, vol. 2019-July, Institute of Electrical and Electronics Engineers Inc., pp. 1887-1891, 2019 IEEE International Symposium on Information Theory, ISIT 2019, Paris, France, 7/07/19. https://doi.org/10.1109/ISIT.2019.8849600

On Decoding and Applications of Interleaved Goppa Codes. / Holzbaur, Lukas; Liu, Hedongliang; Puchinger, Sven et al.
2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2019. p. 1887-1891 8849600 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2019-July).

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

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AB - Goppa Codes are a well-known class of codes with, among others, applications in code-based cryptography. In this paper, we present a collaborative decoding algorithm for interleaved Goppa codes (IGC). Collaborative decoding increases the decoding radius beyond half of the designed minimum distance. We consider wild Goppa codes and show that we can collaboratively correct more errors for binary Goppa codes than the Patterson decoder. We propose a modified version of the McEliece cryptosystem using wild IGC based on a recently proposed system by Elleuch et al., analyze attacks on the system and present some parameters with the corresponding key sizes.

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Holzbaur L, Liu H, Puchinger S , Wachter-Zeh A. On Decoding and Applications of Interleaved Goppa Codes. In 2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings. Institute of Electrical and Electronics Engineers Inc. 2019. p. 1887-1891. 8849600. (IEEE International Symposium on Information Theory - Proceedings). doi: 10.1109/ISIT.2019.8849600

On Decoding and Applications of Interleaved Goppa Codes

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