Decoding Square-Free Goppa Codes Over \BBF

We propose a new, efficient nondeterministic decoding algorithm for square-free Goppa codes over F p for any prime p. If the code in question has degree t and the average distance to the closest codeword is at least (4/p)t + 1, the proposed decoder can uniquely correct up to (2/p)t errors with high...

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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 59; no. 10; pp. 6851 - 6858
Main Authors: Barreto, Paulo S. L. M., Misoczki, Rafael, Lindner, Richard
Format: Journal Article
Language:English
Published: New York IEEE 01.10.2013
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Coding theory
Cryptography
Decoding
error correction
Goppa codes
Information theory
Lattices
Polynomials
Probability
Proposals
Vectors
ISSN:0018-9448, 1557-9654
Online Access:Get full text
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Summary:We propose a new, efficient nondeterministic decoding algorithm for square-free Goppa codes over F p for any prime p. If the code in question has degree t and the average distance to the closest codeword is at least (4/p)t + 1, the proposed decoder can uniquely correct up to (2/p)t errors with high probability. The correction capability is higher if the distribution of error magnitudes is not uniform, approaching or reaching t errors when any particular error value occurs much more often than others or exclusively. This makes the method interesting for (semantically secure) cryptosystems based on the decoding problem for permuted and punctured Goppa codes.
Bibliography:SourceType-Scholarly Journals-1
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ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2013.2270272