# The security effect caused by an MDS matrix in word-oriented designs

Considering a design where the MixColumns operation of AES is replaced by a lighter MDS matrix where by the term lighter we mean the number of required XOR to implement an MDS matrix.

As you know the most relevant property of an MDS matrix in an AES-like design beyond its branch number is the so-called related differential.

My question: Is there any security escalation or degeneration due to the differences of the bit-level representations of the MDS matrices? (For more details please see Remark section of [1]).

• Do you have any reason about your claim that there is a relation between the implementation of lightweight MDS matrices and zero XOR-sum subject. I think you misunderstood about the structure of binary MDS matrices over $\mathbb{F}_2$. For example the binary matrix in this post that you mentioned in your answer, is not a $32\times 32$ binary matrix. – user0410 Feb 1 at 10:40
• In fact, that binary matrix is a $4\times 4$ MDS block-matrix over 8-bit words that each coefficients of this matrix is a $8 \times 8$ binary matrix. In other words, the coefficients of binary MDS matrices over $\mathbb{F}_2$ for $m$-bit words are $m \times m$ binary matrices and not a zero or one value. – user0410 Feb 1 at 10:40