Feistel's construction makes it possible to build invertible functions from other functions that are themselves not invertible.

Note: Saying that an operator is reversible is not the same as saying that it is an invertible function on the set of states.

Furthermore, the probability must be a differentiable and invertible function of .

Due to a block cipher's characteristic as an invertible function, its output becomes distinguishable from a truly random output string over time due to the birthday problem.

If the nonlinearity is a fixed invertible function, then the LNP model is a generalized linear model.

Formally, the discrete cosine transform is a linear, invertible function (where denotes the set of real numbers), or equivalently an invertible N x N square matrix.

The implicit function theorem is closely related to the inverse function theorem, which states when a function looks like graphs of invertible functions pasted together.

It is an invertible function that maps one differentiable manifold to another, such that both the function and its inverse are smooth.

Let be the category of finite sets and bijections (the collection of all finite sets, and invertible functions between them).

The straightforward XORing with the keystream, or the use of any invertible function known to the attacker, such as mod 26 addition, creates a potential vulnerability in message integrity.