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I spent all day trying to figure ring signature schemes out but apparently I wasted time.
I read the original ring signature paper (Rivest's How to leak a secret).
I'm having numerous problems. Let's just say that a nice and simple example would make everything clear.

I'm talking about something like this example for RSA.

The problem is that no one provides this. I read 12 papers and… nothing. I would like to have an example with small numbers. Is this even possible? Could you provide such a “toy” example?

If I can be more specific: my problem with the original paper is step 4:

solve for…

I have no idea how to solve an equation where on the left side I have the encryption (known key) of an unknown value and a value on the right side.

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Here is an explanation of step 4.
Look at Figure 2 of the paper.
Lets say $y_s$ is $y_3$ at 6 o'clock.
Start at 12 o'clock and calculate going clockwise until you arrive at 6 o'clock. Denote the result by $r$.
Start again at 12 o'clock and calculate going counter-clockwise until you arrive at 6 o'clock. Denote the result by $l$.
Now $l =r \oplus y_s$, which gives the solution $y_s =r \oplus l$.

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