I saw two papers that are "H.Lipmaa et al., On the Additive Differential Probability of Exclusive-or" and "V.Velichkov et al., The Additive Differential Probability of ARX"

In this two paper, Limaa et al. and Velichkov et al. compute the probability of additive differential of xor in similar way.

But there is one difference between them.

That is matrix $$A_i$$ is different.

For example $$A_{000}$$ in first paper is $$A_{000}=\begin{pmatrix} 4& 0& 0& 1& 0& 1& 1& 0 \\0& 0& 0& 1& 0& 1& 0& 0 \\ \vdots & & & \cdots & \cdots & & & \vdots \\ 0& 0& 0& 0& 0& 0& 0& 0 \end{pmatrix}$$

and $$A_{000}$$ in second paper is $$A_{000}=\begin{pmatrix} 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 \\0& 1& 0& 0& 0& 0& 0 & 0 \\ \vdots & & & \cdots & \cdots & & & \vdots \\ 0& 0& 0& 0& 0& 0& 0& 1 \end{pmatrix}$$

I hope someone can tell me why there exists a difference.

• I find the answer... See the table 2. in second paper.
– jyj
Mar 8 '19 at 8:15
• If you found the answer, please be kind enough to share it. Mar 8 '19 at 9:02
• In second paper(V.Velichkov et al., The Additive Differential Probability of ARX), the table 2's order is not same to orginal order. For example, S[i] =0 when (s1[i],s2[i],s3[i])=(0,0,-1). So, there exist a difference
– jyj
Mar 8 '19 at 11:44
For example, $$S[i] =0$$ when $$(s_1[i],s_2[i],s_3[i])=(0,0,-1)$$. So, there exists a difference.