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As is well known, a sigma protocol can be transformed into a NIZK protocol through a Fiat-Shamir transform.

But can the Sigma protocol be transformed into a signature of knowledge in a similar manner?

Intuitively, it seems possible, but which research studies have directly proven this issue?

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  • $\begingroup$ You will receive better answers if you phrase your question more precisely with definitions. $\endgroup$
    – lamontap
    Nov 9, 2023 at 16:38

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I am a little unsure exactly what you mean.

If I am correct; you are stating that an interactive identification scheme can be turned into a non-interactive signature scheme using the Fiat-Shamir Transformation? If that is the case: I agree.

Further you ask if a sigma protocol be transformed into a signature of knowledge. I am not sure what you ask for here. However, if you have successfully turned an interactive ID-scheme into a non-interactive signature scheme using the Fiat-Shamir transformation, you can obtain a non-interactive proof of knowledge.

I would encourage you to read more about the Fiat-Shamir Transformation and maybe check out the Feige–Fiat–Shamir ID scheme as well as the Fiat-Shamir with Aborts Transformation.

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