Bounds for the multicovering radii of Reed-Muller codes with applications to stream ciphers



: Honkala I, Klapper A

Publisher: KLUWER ACADEMIC PUBL

: 2001

: Designs, Codes and Cryptography

: DESIGNS CODES AND CRYPTOGRAPHY

: DESIGN CODE CRYPTOGR

: 23

: 2

: 131

: 145

: 15

: 0925-1022

DOI: https://doi.org/10.1023/A:1011291913974


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.



Last updated on 2024-26-11 at 13:02