# MD5 Algorithm is nonlinear?

https://iopscience.iop.org/article/10.1088/1742-6596/978/1/012116/pdf

Each operation performs a nonlinear function on three of a, b, c,and d.

F(X,Y,Z) = XY v not(X) Z
G(X,Y,Z) = XZ v Y not(Z)
H(X,Y,Z) = X xor Y xor Z
I(X,Y,Z) = Y xor (X v not(Z))

So MD5 Algorithm is nonlinear?

• Welcome to Cryptography.SE. Do you know what is linear and non-linear? What operations can be linear? And, do you know what will happen a linear cryptographic algorithm? – kelalaka Apr 19 at 13:23
• I think y=x is linear and y = x^2 is non-linear,a linear cryptographc algorithm can not be hash algorithm,I don't know what operations can be linear. – cuthead Apr 19 at 13:29
• Usually a function $f$ is linear if $f(a+b) = f(a) + f(b)$. This is not a desirable property of any cryptographic hash function. – bmm6o Apr 19 at 15:59
• if a hash function was linear, would it be useful? – user253751 Apr 19 at 16:35
• A linear hash function could have an easy collision and pre-images. – kelalaka Apr 19 at 16:50