IgniteCaptcha is a library for creating captcha for .Net Core 2.0 projects quickly and simply.

For you can use the library, you have to create a folder on your file system, and map it as example in the box below in method Configure at Startup.cs file.

app.UseStaticFiles(new StaticFileOptions(){
	FileProvider = new PhysicalFileProvider(
		Path.Combine(Directory.GetCurrentDirectory(), @"output")),
		RequestPath = new PathString("/captcha")
	});

Next step is source example for generate the captcha, that example use the session for save the captcha value for compare the value, but there are different ways for this. I recommends you read the oficcial documents about session and application state in ASP.NET Core and chosse the best way for your application.

Should you write in your controller a source code with the same look you can see box below.

public ActionResult Index(){
	string cptvalue = null;
	ViewData["captcha"] = IgniteCaptcha.GenCaptcha(
		Path.Combine(Directory.GetCurrentDirectory(), @"output"), 300, 150, out cptvalue);
	HttpContext.Session.SetString("CaptchaValue", cptvalue);
	return View();
}

In your view file, you can write a HTML as the box below to can see the image captcha.

		<img src="~/captcha/@ViewData["captcha"]" />

The project IgniteCaptchaSample is a simple example how you can use that library.

References:

Introduction to session and application state in ASP.NET Core.

https://docs.microsoft.com/en-us/aspnet/core/fundamentals/app-state?tabs=aspnetcore2x