Differential equations of addition

In cryptography, differential equations of addition (DEA) are one of the most basic equations related to differential cryptanalysis that mix additions over two different groups (e.g. addition modulo 2³² and addition over GF(2)) and where input and output differences are expressed as XORs.

Differential equations of addition (DEA) are of the following form:

${\displaystyle (x+y)\oplus ((x\oplus a)+(y\oplus b))=c}$

where ${\displaystyle x}$ and ${\displaystyle y}$ are ${\displaystyle n}$-bit unknown variables and ${\displaystyle a}$, ${\displaystyle b}$ and ${\displaystyle c}$ are known variables. The symbols ${\displaystyle +}$ and ${\displaystyle \oplus }$ denote addition modulo ${\displaystyle 2^{n}}$ and bitwise exclusive-or respectively. The above equation is denoted by ${\displaystyle (a,b,c)}$.

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