From 3eea8fdb55c3cc04491851de87e409e21538a91e Mon Sep 17 00:00:00 2001
From: derekpierre <derek.pierre@gmail.com>
Date: Tue, 18 Jul 2023 16:31:58 -0400
Subject: [PATCH] Preliminary prose about the different Ferveo decryption
 variants.

---
 book/src/SUMMARY.md  |  1 +
 book/src/variants.md | 45 ++++++++++++++++++++++++++++++++++++++++++++
 2 files changed, 46 insertions(+)
 create mode 100644 book/src/variants.md

diff --git a/book/src/SUMMARY.md b/book/src/SUMMARY.md
index ee5181af..4727acee 100644
--- a/book/src/SUMMARY.md
+++ b/book/src/SUMMARY.md
@@ -8,6 +8,7 @@
   - [Initialization](./dkginit.md)
   - [Publicly Verifiable Secret Sharing](./pvss.md)
 - [Threshold Encryption Scheme](./tpke.md)
+  - [Threshold Decryption Variants](./variants.md)
 
 
 # Appendix
diff --git a/book/src/variants.md b/book/src/variants.md
new file mode 100644
index 00000000..0ea66101
--- /dev/null
+++ b/book/src/variants.md
@@ -0,0 +1,45 @@
+# Threshold Decryption (Variants)
+
+Threshold decryption can be performed using one of two optional cryptographic strategies a.k.a *variants*:
+- Simple
+- Precomputed
+
+The chosen variant dictates the decryption shares returned by nodes and how those shares are combined. Either variant can be used 
+for decryption, and each has its advantages and disadvantages.
+
+
+## Simple
+
+When decrypting using the *Simple* variant, any arbitrary m-of-n set of nodes (where `m` is the threshold) will each return a *simple* decryption share, and *any*
+`m` set of decryption shares can be combined to successfully decrypt the encrypted data. Any arbitrary combination of the `m` *simple* decryption shares from the `n` nodes
+can be used to obtain the decrypted data.
+
+This is the case where you can concurrently contact `n` nodes and simply wait until any `m` nodes respond with decryption shares.
+
+### Advantages
+- Any (arbitrary) `m` decryption shares out of `n` can be requested, obtained, and combined
+- Any singular unresponsive node does not prevent the ability to combine returned *simple* decryption shares
+- Only one request round is needed if done concurrently i.e. send `n` request, and wait for `m` replies. A total of
+  `n - m + 1` nodes would have to not respond for the failure case.
+
+### Disadvantages
+- Since the `m` nodes are arbitrary, combining the decryption shares requires the requester to do a more computationally intensive operation.
+
+
+## Precomputed
+
+When decrypting using the *Precomputed* variant, you will first choose a specific sub-set of `m` nodes from `n` i.e pick an arbitrary `m-of-n` set of nodes (where `m` is the threshold),
+and those specific `m` nodes need to reply with precomputed decryption shares. If any of those specific `m` nodes does not respond, you will need fail over logic. This could entail:
+- using the *precomputed* variant again and choosing another group of `m` nodes, without any node(s) that didn't respond
+- switching to *simple* variant if the first round of *precomputed* fails
+- other combination of logic
+
+### Advantages
+In the happy path:
+- faster operation since the requester only contacts `m` nodes so there is no need for the other `n - m`
+- since the list of `m` nodes is known, the operation to combine the `m` *precomputed* decryption shares is less computationally intensive than *simple*, which can work well for a lightweight requester
+
+
+### Disadvantages
+- Underlying availability issue since if any of the specific `m` nodes is unresponsive it can cause the *precomputed* variant to fail
+- If the happy path does not happen, failover logic is required and it can end up being an overall slower operation than the *simple* variant