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WCC 2011 - Workshop on coding and cryptography, Paris : France (2011)

The non-gap sequence of a subcode of a generalized Reed-Solomon code

Irene Marquez-Corbella 1, Edgar Martinez-Moro 2, Ruud Pellikaan 3

(2011-04)

This paper addresses the question of how often the square code of an arbitrary l-dimensional subcode of the code GRSk(a; b) is exactly the code GRS2k-1(a; b * b). To answer this question we rst introduce the notion of gaps of a code which allows us to characterize such subcodes easily. This property was rst stated and used in [10] where Wieschebrink applied the Sidelnikov-Shestakov attack [8] to brake the Berger-Loidreau cryptostystem [1].

1:	Department of Algebra, Geometry and Topology, University of Valladolid
	Department of Algebra, Geometry and Topology, Un
2:	Department of Applied Mathematics, University of Valladolid,
	Department of Applied Mathematics, University of Valladolid,
3:	Department of Mathematics and Computer Science
	Eindhoven University of Technology – Technishe Universiteit Eihdhoven

Domain

:

Computer Science/Cryptography and Security Computer Science/Discrete Mathematics Computer Science/Information Theory and Coding Mathematics/Information Theory

Keywords: Berger-Loidreau cryptosystem – square code – GRS codes – gaps of a code.

inria-00608102, version 1

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From: Assia Saadi <>

Submitted on: Tuesday, 12 July 2011 11:08:05

Updated on: Tuesday, 12 July 2011 14:08:12