A1 Refereed original research article in a scientific journal
Bounds for the multicovering radii of Reed-Muller codes with applications to stream ciphers
Authors: Honkala I, Klapper A
Publisher: KLUWER ACADEMIC PUBL
Publication year: 2001
Journal: Designs, Codes and Cryptography
Journal name in source: DESIGNS CODES AND CRYPTOGRAPHY
Journal acronym: DESIGN CODE CRYPTOGR
Volume: 23
Issue: 2
First page : 131
Last page: 145
Number of pages: 15
ISSN: 0925-1022
DOI: https://doi.org/10.1023/A:1011291913974(external)
Abstract
The multicovering radii of a code are recent generalizations of the covering radius of a code. For positive m, the m-covering radius of C is the least radius t such that every m-tuple of vectors is contained in at least one ball of radius t centered at some codeword. In this paper upper bounds are found for the multicovering radii of first order Reed-Muller codes. These bounds generalize the well-known Norse bounds for the classical covering radii of first order Reed-Muller codes. They are exact in some cases. These bounds are then used to prove the existence of secure families of keystreams against a general class of cryptanalytic attacks. This solves the open question that gave rise to the study of multicovering radii of codes.
The multicovering radii of a code are recent generalizations of the covering radius of a code. For positive m, the m-covering radius of C is the least radius t such that every m-tuple of vectors is contained in at least one ball of radius t centered at some codeword. In this paper upper bounds are found for the multicovering radii of first order Reed-Muller codes. These bounds generalize the well-known Norse bounds for the classical covering radii of first order Reed-Muller codes. They are exact in some cases. These bounds are then used to prove the existence of secure families of keystreams against a general class of cryptanalytic attacks. This solves the open question that gave rise to the study of multicovering radii of codes.
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