# Indistinguishability versus Indifferentiability

What is the Indifferentiability of Feistel Network?

Why is the concept of Indifferentiability useful and how it is applicable in the real world?

How is Indifferentiability compared to Indistinguishability?

• define indifferentiability. not a standard term Commented Dec 6, 2021 at 4:52
• At least not in cryptography. For functions in general it is, meaning the function has no derivative (over a region of interest). The Weirstrass Function is an early example of a continuous function that's indifferentiable over its entire domain (nowhere differentiable): it has no derivative. Fractal curves are generally "nowhere differentiable". None of that applies to anything commonly used in cryptography, and it's entirely unrelated to indistinguishability. Feistel Network functions are discrete, but using a difference quotient they do have a discrete derivative and so are differentiable. Commented Dec 7, 2021 at 0:13
• Indifferentiability is quite a standard term. And it's been used in many contexts for analyzing security of schemes. Commented Dec 8, 2022 at 10:48

The definitions of "indistinguishability" and "indifferentiability" were introduced in paper "Indifferentiability, Impossibility Results on Reductions, and Applications to the Random Oracle Methodology". In my opinion, the concept of "indistinguishability" is related to distinguisher, like a differential or integral one. The definition of "indifferentiability" is shown in the image below.

I can not provide any insights since I haven't read the paper yet...

• Note that the concept of a "distinguisher" is still part of the definition of indifferentiability. Indifferentiability is a generalisation of indistinguishability, where the adversary has the same "information access" as legitimate parties. Commented Sep 14, 2023 at 15:54