Lightweight MDS Serial-Type Matrices with Minimal Fixed XOR Count

  • Dylan Toh
  • Jacob Teo
  • Khoongming Khoo
  • Siang Meng Sim
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10831)


Many block ciphers and hash functions require the diffusion property of Maximum Distance Separable (MDS) matrices. Serial matrices with the MDS property obtain a trade-off between area requirement and clock cycle performance to meet the needs of lightweight cryptography. In this paper, we propose a new class of serial-type matrices called Diagonal-Serial Invertible (DSI) matrices with the sparse property. These matrices have a fixed XOR count (contributed by the connecting XORs) which is half that of existing matrices. We prove that for matrices of order 4, our construction gives the matrix with the lowest possible fixed XOR cost. We also introduce the Reversible Implementation (RI) property, which allows the inverse matrix to be implemented using the similar hardware resource as the forward matrix, even when the two matrices have different finite field entries. This allows us to search for serial-type matrices which are lightweight in both directions by just focusing on the forward direction. We obtain MDS matrices which outperform existing lightweight (involutory) matrices.


MDS matrix Serial matrix Lightweight cryptography XOR count 


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Dylan Toh
    • 1
  • Jacob Teo
    • 1
  • Khoongming Khoo
    • 2
  • Siang Meng Sim
    • 2
    • 3
  1. 1.NUS High School of Math and ScienceSingaporeSingapore
  2. 2.DSO National LaboratoriesSingaporeSingapore
  3. 3.Nanyang Technological UniversitySingaporeSingapore

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