FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W4250572011> ?p ?o ?g. }

• W4250572011 endingPage "256" @default.
• W4250572011 startingPage "231" @default.
• W4250572011 abstract "MDS matrices are used in the design of diffusion layers in many block ciphers and hash functions due to their optimal branch number. But MDS matrices, in general, have costly implementations. So in search for efficiently implementable MDS matrices, there have been many proposals. In particular, circulant, Hadamard, and recursive MDS matrices from companion matrices have been widely studied. In a recent work, recursive MDS matrices from sparse DSI matrices are studied, which are of interest due to their low fixed cost in hardware implementation. In this paper, we present results on the exhaustive search for (recursive) MDS matrices over GL(4, F2). Specifically, circulant MDS matrices of order 4, 5, 6, 7, 8; Hadamard MDS matrices of order 4, 8; recursive MDS matrices from companion matrices of order 4; recursive MDS matrices from sparse DSI matrices of order 4, 5, 6, 7, 8 are considered. It is to be noted that the exhaustive search is impractical with a naive approach. We first use some linear algebra tools to restrict the search to a smaller domain and then apply some space-time trade-off techniques to get the solutions. From the set of solutions in the restricted domain, one can easily generate all the solutions in the full domain. From the experimental results, we can see the (non) existence of (involutory) MDS matrices for the choices mentioned above. In particular, over GL(4, F2), we provide companion matrices of order 4 that yield involutory MDS matrices, circulant MDS matrices of order 8, and establish the nonexistence of involutory circulant MDS matrices of order 6, 8, circulant MDS matrices of order 7, sparse DSI matrices of order 4 that yield involutory MDS matrices, and sparse DSI matrices of order 5, 6, 7, 8 that yield MDS matrices. To the best of our knowledge, these results were not known before. For the choices mentioned above, if such MDS matrices exist, we provide base sets of MDS matrices, from which all the MDS matrices with the least cost (with respect to d-XOR and s-XOR counts) can be obtained. We also take this opportunity to present some results on the search for sparse DSI matrices over finite fields that yield MDS matrices. We establish that there is no sparse DSI matrix S of order 8 over F28 such that S8 is MDS." @default.
• W4250572011 created "2022-05-12" @default.
• W4250572011 creator A5013219977 @default.
• W4250572011 creator A5047180976 @default.
• W4250572011 creator A5058432784 @default.
• W4250572011 date "2019-09-20" @default.
• W4250572011 modified "2023-09-26" @default.
• W4250572011 title "Exhaustive Search for Various Types of MDS Matrices" @default.
• W4250572011 doi "https://doi.org/10.46586/tosc.v2019.i3.231-256" @default.
• W4250572011 hasPublicationYear "2019" @default.
• W4250572011 type Work @default.
• W4250572011 citedByCount "3" @default.
• W4250572011 countsByYear W42505720112021 @default.
• W4250572011 countsByYear W42505720112022 @default.
• W4250572011 crossrefType "journal-article" @default.
• W4250572011 hasAuthorship W4250572011A5013219977 @default.
• W4250572011 hasAuthorship W4250572011A5047180976 @default.
• W4250572011 hasAuthorship W4250572011A5058432784 @default.
• W4250572011 hasBestOaLocation W42505720111 @default.
• W4250572011 hasConcept C10138342 @default.
• W4250572011 hasConcept C114614502 @default.
• W4250572011 hasConcept C115973184 @default.
• W4250572011 hasConcept C118615104 @default.
• W4250572011 hasConcept C134306372 @default.
• W4250572011 hasConcept C162324750 @default.
• W4250572011 hasConcept C177264268 @default.
• W4250572011 hasConcept C182306322 @default.
• W4250572011 hasConcept C199360897 @default.
• W4250572011 hasConcept C30463267 @default.
• W4250572011 hasConcept C33923547 @default.
• W4250572011 hasConcept C36503486 @default.
• W4250572011 hasConcept C41008148 @default.
• W4250572011 hasConcept C60292330 @default.
• W4250572011 hasConcept C6497535 @default.
• W4250572011 hasConceptScore W4250572011C10138342 @default.
• W4250572011 hasConceptScore W4250572011C114614502 @default.
• W4250572011 hasConceptScore W4250572011C115973184 @default.
• W4250572011 hasConceptScore W4250572011C118615104 @default.
• W4250572011 hasConceptScore W4250572011C134306372 @default.
• W4250572011 hasConceptScore W4250572011C162324750 @default.
• W4250572011 hasConceptScore W4250572011C177264268 @default.
• W4250572011 hasConceptScore W4250572011C182306322 @default.
• W4250572011 hasConceptScore W4250572011C199360897 @default.
• W4250572011 hasConceptScore W4250572011C30463267 @default.
• W4250572011 hasConceptScore W4250572011C33923547 @default.
• W4250572011 hasConceptScore W4250572011C36503486 @default.
• W4250572011 hasConceptScore W4250572011C41008148 @default.
• W4250572011 hasConceptScore W4250572011C60292330 @default.
• W4250572011 hasConceptScore W4250572011C6497535 @default.
• W4250572011 hasLocation W42505720111 @default.
• W4250572011 hasOpenAccess W4250572011 @default.
• W4250572011 hasPrimaryLocation W42505720111 @default.
• W4250572011 hasRelatedWork W1565892411 @default.
• W4250572011 hasRelatedWork W2057091980 @default.
• W4250572011 hasRelatedWork W2237294945 @default.
• W4250572011 hasRelatedWork W2811073802 @default.
• W4250572011 hasRelatedWork W2950772023 @default.
• W4250572011 hasRelatedWork W3124308887 @default.
• W4250572011 hasRelatedWork W3154819821 @default.
• W4250572011 hasRelatedWork W4293714547 @default.
• W4250572011 hasRelatedWork W4304172779 @default.
• W4250572011 hasRelatedWork W55162897 @default.
• W4250572011 isParatext "false" @default.
• W4250572011 isRetracted "false" @default.
• W4250572011 workType "article" @default.