Polynomial Time Attack on Wild McEliece Over Quadratic Extensions

We present a polynomial-time structural attack against the McEliece system based on Wild Goppa codes defined over a quadratic finite field extension. We show that such codes can be efficiently distinguished from random codes. The attack uses this property to compute a filtration, that is to say, a f...

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Bibliographic Details
Published inIEEE transactions on information theory Vol. 63; no. 1; pp. 404 - 427
Main Authors Couvreur, Alain, Otmani, Ayoub, Tillich, Jean-Pierre
Format Journal Article
LanguageEnglish
Published New York IEEE 01.01.2017
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Institute of Electrical and Electronics Engineers
Subjects
Algebra
Complexity theory
Computer Science
cryptanalysis
Cryptography and Security
Decoding
Encryption
Fields (mathematics)
Goppa code distinguishing problem
Goppa codes
Information Theory
McEliece cryptosystem
Polynomials
Public key cryptography
Wild Goppa code
Wild Goppa code
McEliece cryptosystem
cryptanalysis
Index Terms—McEliece cryptosystem
Goppa Code Distinguishing problem
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Summary:We present a polynomial-time structural attack against the McEliece system based on Wild Goppa codes defined over a quadratic finite field extension. We show that such codes can be efficiently distinguished from random codes. The attack uses this property to compute a filtration, that is to say, a family of nested subcodes which will reveal their secret algebraic description.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2016.2574841