TY - GEN
T1 - Direct construction of recursive MDS diffusion layers using shortened BCH codes
AU - Augot, Daniel
AU - Finiasz, Matthieu
N1 - Publisher Copyright:
© International Association for Cryptologic Research 2015.
PY - 2015/1/1
Y1 - 2015/1/1
N2 - MDS matrices allow to build optimal linear diffusion layers in block ciphers. However, MDS matrices cannot be sparse and usually have a large description, inducing costly software/hardware implementations. Recursive MDS matrices allow to solve this problem by focusing on MDS matrices that can be computed as a power of a simple companion matrix, thus having a compact description suitable even for constrained environments. However, up to now, finding recursive MDS matrices required to perform an exhaustive search on families of companion matrices, thus limiting the size of MDS matrices one could look for. In this article we propose a new direct construction based on shortened BCH codes, allowing to efficiently construct such matrices for whatever parameters. Unfortunately, not all recursive MDS matrices can be obtained from BCH codes, and our algorithm is not always guaranteed to find the best matrices for a given set of parameters.
AB - MDS matrices allow to build optimal linear diffusion layers in block ciphers. However, MDS matrices cannot be sparse and usually have a large description, inducing costly software/hardware implementations. Recursive MDS matrices allow to solve this problem by focusing on MDS matrices that can be computed as a power of a simple companion matrix, thus having a compact description suitable even for constrained environments. However, up to now, finding recursive MDS matrices required to perform an exhaustive search on families of companion matrices, thus limiting the size of MDS matrices one could look for. In this article we propose a new direct construction based on shortened BCH codes, allowing to efficiently construct such matrices for whatever parameters. Unfortunately, not all recursive MDS matrices can be obtained from BCH codes, and our algorithm is not always guaranteed to find the best matrices for a given set of parameters.
KW - BCH codes
KW - Linear diffusion
KW - Recursive MDS matrices
U2 - 10.1007/978-3-662-46706-0_1
DO - 10.1007/978-3-662-46706-0_1
M3 - Conference contribution
AN - SCOPUS:84942543850
SN - 9783662467053
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 3
EP - 17
BT - Fast Software Encryption - 21st International Workshop, FSE 2014, Revised Selected Papers
A2 - Cid, Carlos
A2 - Rechberger, Christian
PB - Springer Verlag
T2 - 21st International Workshop on Fast Software Encryption, FSE 2014
Y2 - 3 March 2014 through 5 March 2014
ER -