Is the practice of providing simple examples in research papers recommended?

Question

This question is restricted to the domain of Cryptography.

While reading research papers from the Cryptography domain, I came across papers that provide examples for the schemes or algorithms they proposed.

I feel that there is no use in providing simple examples except pedagogical. And the examples do not provide any extra information or insights regarding the scheme or algorithm. Some authors use a separate section to provide an example of their proposed scheme or algorithm.

Is it a recommended act to provide a simple example for the scheme proposed in research papers (especially SCI-rated) journals?

I am using the word simple because some readers may think that authors are using some large or special numbers in their example. But it is not the case. The numbers are small and with easy properties that can be done by even a beginner or intermediate in the domain.

Answer 1

As mentioned by lighthouse keeper in the comments, the culture of including examples will depend on your discipline. But within your discipline, you should ask yourself: why am I including this example?

When writing a paper, I try to keep this general idea in mind:

Only include information that will be helpful to someone.

Examples can be great expositional tools in a paper. Did you just introduce a definition that seems technical, but the underlying idea is easy to understand? A well-executed example illustrating the underlying idea would be very helpful!

On the other hand, there are examples that will help no one. They may be too simple, too convoluted, or something else entirely. I have seen examples that are simultaneously too simple and too complicated: the example is overly basic for expert readers, and non-expert readers will not have enough exposure to the material to get anything out of the example.

It is something of an art to balance writing a paper that is enlightening to experts and also readable to new researchers. I certainly have not mastered this art, but this skill is what makes papers by certain authors (like John Milnor in math) an absolute delight to read.

Answer 2

If you include an example inline in a paper, it can obscure the flow of the argument (by putting extraneous material within it), and it increases the length (which may add to intimidation, or may push you up against venue page limits).

Whereas, a good example shows what your argument actually means in practice, which can help bring lofty ideas down to the real world and readers check their understanding^[1]. This can help make your work more accessible—not just to newbies in the field, but to experienced veterans who are too proud to admit incomprehension!

One way to get some benefits of both approaches is to pull the examples out into an appendix. This keeps the main body of the paper short, but gives people the opportunity to follow up on concepts that might have eluded them in the main text.

In the end, you're overthinking this; it's just a writing choice. It usually won't be particularly standard or nonstandard^[2]. Unless your venue has a specific guideline, it's down to a choice of the author(s). I personally recommend short examples, which I find interweave nicely with the actual expository text in the first place. This is because I infinitely prefer a slightly longer, but clear, paper, versus a terse and confusing one. However, that would be an opinion only.

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^{[1] Caveat: I have gotten burned multiple times in paper reviews for making the work too accessible. Once people understand something clearly, they tend to mistake it as being obvious.
[2] I guess in Programming Languages research, examples are highly recommended in certain classes of paper. I could see this being the case for Cryptography, too. However, the point remains as stated: this is a choice—at best a tendency, not a requirement.}