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SCIENCE CHINA Information Sciences, Volume 61, Issue 11: 119102(2018) https://doi.org/10.1007/s11432-017-9320-8

The lightest $4\times4$ MDS matrices over ${\rm~GL}(4,~{\mathbb~F}_2)$

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  • ReceivedMay 22, 2017
  • AcceptedNov 30, 2017
  • PublishedSep 12, 2018

Abstract

There is no abstract available for this article.


Acknowledgment

This work was supported by National Natural Science Foundation of China (Grant No. 11371356).


References

[1] Sarkar S, Syed H. Lightweight diffusion layer: importance of toeplitz matrices. IACR Trans Symmetric Cryptol, 2016, 2016: 95--113. Google Scholar

[2] Li Y Q, Wang M S. On the construction of lightweight circulant involutory MDS matrices. In: Proceedings of International Conference on Fast Software Encryption. Berlin: Springer, 2016. 121--139. Google Scholar

[3] Bai J, Li T, Sun Y, et al. The lightest 4$\times$4 MDS matrices over ${\rm~~GL}(4,~\F_2)$. Cryptology ePrint Archive, Report 2016/686 (2016). http://eprint.iacr.org/2016/686. Google Scholar

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    Algorithm 1 The $2~\times~2$ searching algorithm

    Output:The set of 2$\times$ 2 MDS matrices $L~\in~{\mathcal~M}(2,4)$.

    $L~\Leftarrow~\emptyset$;

    for all every matrix $A~\in~GL(4,{\mathbb~F}_2)$

    if $A$ is not in row-minimal form then

    go to Step 2;

    end if

    for all every matrix $B~\in~GL(4,{\mathbb~F}_2)$

    if $B$ is not in column-minimal form then

    go to Step 6;

    end if

    for all every matrix $C~\in~GL(4,{\mathbb~F}_2)$

    if $C$ is not in row-minimal form then

    go to Step 10;

    for all every matrix $D~\in~GL(4,{\mathbb~F}_2)$

    $D'~\Leftarrow~C\cdotp~A^{-1}\cdotp~B+D$;

    if $D'$ is invertible then

    $L~\Leftarrow~L~\cup~\{{\tiny(\begin{array}{cc} A&B\\ C&D\\ ~\end{array})}\}$;

    end if

    end for

    end if

    end for

    end for

    end for

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