Cryptanalysis of public-key cryptosystems that use subcodes of algebraic geometry codes

G.R. Pellikaan; I. Marquez-Corbella; A. Couvreur

doi:10.1007/978-3-319-17296-5_13

Cryptanalysis of public-key cryptosystems that use subcodes of algebraic geometry codes

G.R. Pellikaan, I. Marquez-Corbella, A. Couvreur

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/Congresprocedure › Conferentiebijdrage › Academic › peer review

Samenvatting

We give a polynomial time attack on the McEliece public key cryptosystem based on subcodes of algebraic geometry (AG) codes. The proposed attack reposes on the distinguishability of such codes from random codes using the Schur product. Wieschebrink treated the genus zero case a few years ago but his approach cannot be extent straightforwardly to other genera. We address this problem by introducing and using a new notion, which we call the t-closure of a code.

Originele taal-2	Engels
Titel	Coding Theory and Applications
Subtitel	4th International Castle Meeting, Palmela Castle, Portugal, September 15-18, 2014
Redacteuren	R. Pinto, P.R. Malonek, P. Vetton
Plaats van productie	Dordrecht
Uitgeverij	Springer
Pagina's	133-140
Aantal pagina's	8
ISBN van elektronische versie	978-3-319-17296-5
ISBN van geprinte versie	978-3-319-17295-8
DOI's	https://doi.org/10.1007/978-3-319-17296-5_13
Status	Gepubliceerd - 2015
Evenement	4th International Castle Meeting Coding Theory and Applications (4ICMCTA) - Palmela, Portugal Duur: 15 sep. 2014 → 18 sep. 2014 Congresnummer: 4 http://icmcta.web.ua.pt/

Publicatie series

Naam	CIM Series in Mathematical Sciences
Volume	3

Congres

Congres	4th International Castle Meeting Coding Theory and Applications (4ICMCTA)
Verkorte titel	ICMCTA
Land/Regio	Portugal
Stad	Palmela
Periode	15/09/14 → 18/09/14
Internet adres	http://icmcta.web.ua.pt/

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10.1007/978-3-319-17296-5_13

Citeer dit

Pellikaan, G. R., Marquez-Corbella, I., & Couvreur, A. (2015). Cryptanalysis of public-key cryptosystems that use subcodes of algebraic geometry codes. In R. Pinto, P. R. Malonek, & P. Vetton (editors), Coding Theory and Applications: 4th International Castle Meeting, Palmela Castle, Portugal, September 15-18, 2014 (blz. 133-140). (CIM Series in Mathematical Sciences ; Vol. 3). Springer. https://doi.org/10.1007/978-3-319-17296-5_13

Pellikaan, G.R. ; Marquez-Corbella, I. ; Couvreur, A. / Cryptanalysis of public-key cryptosystems that use subcodes of algebraic geometry codes. Coding Theory and Applications: 4th International Castle Meeting, Palmela Castle, Portugal, September 15-18, 2014. redacteur / R. Pinto ; P.R. Malonek ; P. Vetton. Dordrecht : Springer, 2015. blz. 133-140 (CIM Series in Mathematical Sciences ).

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title = "Cryptanalysis of public-key cryptosystems that use subcodes of algebraic geometry codes",

abstract = "We give a polynomial time attack on the McEliece public key cryptosystem based on subcodes of algebraic geometry (AG) codes. The proposed attack reposes on the distinguishability of such codes from random codes using the Schur product. Wieschebrink treated the genus zero case a few years ago but his approach cannot be extent straightforwardly to other genera. We address this problem by introducing and using a new notion, which we call the t-closure of a code.",

keywords = "Algebraic geometry codes; Code-based cryptography; Schur products of codes; Distinguishers ",

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booktitle = "Coding Theory and Applications",

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Pellikaan, GR, Marquez-Corbella, I & Couvreur, A 2015, Cryptanalysis of public-key cryptosystems that use subcodes of algebraic geometry codes. in R Pinto, PR Malonek & P Vetton (uitgave), Coding Theory and Applications: 4th International Castle Meeting, Palmela Castle, Portugal, September 15-18, 2014. CIM Series in Mathematical Sciences , vol. 3, Springer, Dordrecht, blz. 133-140, 4th International Castle Meeting Coding Theory and Applications (4ICMCTA) , Palmela, Portugal, 15/09/14. https://doi.org/10.1007/978-3-319-17296-5_13

Cryptanalysis of public-key cryptosystems that use subcodes of algebraic geometry codes. / Pellikaan, G.R.; Marquez-Corbella, I.; Couvreur, A.
Coding Theory and Applications: 4th International Castle Meeting, Palmela Castle, Portugal, September 15-18, 2014. uitgave / R. Pinto; P.R. Malonek; P. Vetton. Dordrecht: Springer, 2015. blz. 133-140 (CIM Series in Mathematical Sciences ; Vol. 3).

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/Congresprocedure › Conferentiebijdrage › Academic › peer review

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T1 - Cryptanalysis of public-key cryptosystems that use subcodes of algebraic geometry codes

AU - Pellikaan, G.R.

AU - Marquez-Corbella, I.

AU - Couvreur, A.

N1 - Conference code: 4

PY - 2015

Y1 - 2015

N2 - We give a polynomial time attack on the McEliece public key cryptosystem based on subcodes of algebraic geometry (AG) codes. The proposed attack reposes on the distinguishability of such codes from random codes using the Schur product. Wieschebrink treated the genus zero case a few years ago but his approach cannot be extent straightforwardly to other genera. We address this problem by introducing and using a new notion, which we call the t-closure of a code.

AB - We give a polynomial time attack on the McEliece public key cryptosystem based on subcodes of algebraic geometry (AG) codes. The proposed attack reposes on the distinguishability of such codes from random codes using the Schur product. Wieschebrink treated the genus zero case a few years ago but his approach cannot be extent straightforwardly to other genera. We address this problem by introducing and using a new notion, which we call the t-closure of a code.

KW - Algebraic geometry codes; Code-based cryptography; Schur products of codes; Distinguishers

U2 - 10.1007/978-3-319-17296-5_13

DO - 10.1007/978-3-319-17296-5_13

M3 - Conference contribution

SN - 978-3-319-17295-8

T3 - CIM Series in Mathematical Sciences

SP - 133

EP - 140

BT - Coding Theory and Applications

A2 - Pinto, R.

A2 - Malonek, P.R.

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PB - Springer

CY - Dordrecht

T2 - 4th International Castle Meeting Coding Theory and Applications (4ICMCTA)

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ER -

Pellikaan GR, Marquez-Corbella I, Couvreur A. Cryptanalysis of public-key cryptosystems that use subcodes of algebraic geometry codes. In Pinto R, Malonek PR, Vetton P, redacteurs, Coding Theory and Applications: 4th International Castle Meeting, Palmela Castle, Portugal, September 15-18, 2014. Dordrecht: Springer. 2015. blz. 133-140. (CIM Series in Mathematical Sciences ). doi: 10.1007/978-3-319-17296-5_13

Cryptanalysis of public-key cryptosystems that use subcodes of algebraic geometry codes

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