docs: add initial docs of Introduction PODs section, with some diagrams (#285)

book/src/SUMMARY.md

@@ -22,6 +22,7 @@
 - [POD types](./podtypes.md)
   - [SignedPOD](./signedpod.md)
   - [MainPOD](./mainpod.md)
+- [Introduction PODs](./introductionpods.md)
 - [Examples](./examples.md)
 
 # Architecture

book/src/introductionpods.md

@@ -0,0 +1,63 @@
+# Introduction PODs
+
+Introduction PODs are a kind of POD used to introduce any cryptographic data
+structure into the POD system. This allows the POD system to reason about
+cryptographic data and cryptographic primitives that are not part of the POD
+system itself.
+
+An example of an IntroductionPod are the `Ed25519Pod` and the `EcdsaPod`, both
+of them allowing to incorporate their respective kind of signature schemes that
+are not supported in the core of the POD system.
+This allows to the POD system to incorporate data validated by those
+Introduction PODs, and recursively use it in future proofs combining them with
+any logical reasoning together with other PODs.
+
+For example, we could have an scenario where we use 3 different Introduction
+PODs (Ed25519Pod, RSAPod, EcdsaPod), to prove that a user controls an Ethereum
+wallet *AND* a GitHub account. To do so, the user would produce a new `MainPod`
+which proves that the user has signed a certain message with the given ECDSA key
+(Ethereum wallet) *AND* with either the given Ed25519 key *OR* the RSA key (from
+a GitHub account).
+
+<img src="img/introductionpod-mainpod.png" style="max-width:80%;" />
+
+### Interface
+The interface of a `IntroductionPod` is just the one of the
+[RecursivePod](https://github.com/0xPARC/pod2/tree/3ea0d5be71ce98971305076b220079a1b2b7a8d0/src/middleware/mod.rs#L823)
+trait, together with matching the expected `vds_root` of the used `VDSet` in the
+`MainPod`, and using the same circuit configuration for the proof verification.
+
+This means that as long as we fit into the `RecursivePod` interface, the
+`IntroductionPod` will fit into the recursive verification chain of the
+`MainPods`.
+
+### Different configurations
+There are some cases, where the operations needed for the `IntroductionPod`
+require a different circuit configuration than the standard recursive circuit
+configuration that is used for the `MainPods`.
+
+In those cases, we do a previous recursive step, where we verify the logic of
+the intended `IntroductionPod`, and then the proof of this circuit is the one
+verified in the real `IntroductionPod`.
+
+This is done in order to be able to *converge* the different circuit
+configuration shape (and thus different `common_data`) into a new proof that can
+be verified with the standard configuration (used for the MainPods).
+
+<img src="img/introductionpod-2-steps.png" style="max-width:80%;" />
+
+Notice that this is not a requirement for implementing a new `IntroductionPod`,
+and if the IntroductionPod logic can be directly verified with the standard
+recursion configuration, we don't need this previous recursive step.
+
+As examples of the two-recursive steps approach, we have the `EcdsaPod` and the
+`Ed25519Pod`. Both of them, require different circuit configurations that would
+not match the one used for the standard recursion with `MainPods`. Therefore we
+first generate a circuit proof of correct signature verification, and then this
+proof is the one actually verified in the `EcdsaPod`/`Ed25519Pod` respectively,
+not the original signature itself.
+
+<img src="img/introductionpod-2-steps-ecdsa-example.png" style="max-width:80%;" />
+
+> Examples of `IntroductionPods` can be found at the git repository
+> [github.com/0xPARC/introduction-pods](https://github.com/0xPARC/introduction-pods/).