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docs/benchmark.md

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+# 1. MPC Calculation
+
+## Preprocessing phase
+Groth16: 1.5s
+
+Marlin: 10s
+
+
+## Online phase
+
+run_online.zsh(Marlin): 7s
+
+Since proving and verifying time of ciruits are depends on the number of constrains, and the way it depends is roughly the same as in the previous study, Collaboative zk-SNARKs, only the number of constrains will be recorded here.
+
+For example, when the constraints $\approx 2^{10}$ and executing in Marlin, then the Proving time $\approx 2$s as follows.
+
+![image](./../images/constraints-times.png)
+cited from [Collaborative zk-SNARKs](https://eprint.iacr.org/2021/1530).
+
+
+## MPC (Bitwise Operations) components 
+| Calculation Name | Total Time | Content |
+| -------- | -------- | -------- |
+| BitDecomposition | 479ms ~ 652ms | Input: 1 field element. Output: bitwise share.|
+| LessThan |   1.092s ~ 1.178s | Input: 2 field elements. Output: comparison result value |
+
+
+# 2. Circuits Constraints
+
+Main Circuits are:
+| Circuit Name | Total Constrarints | Content |
+| -------- | -------- | -------- |
+| MySecretInputCircuit | 6574 | 1 secret & its Pedersen commitment & additional range constraints |
+| (PedersenComCircuit)     | 2544     | 1 secret & its Pedernsen commitment     |
+| MyCircuit | 5094 | 2 commited secrets & their multiplication | 
+
+Werewolf's circuits are:
+| Circuit Name | Total Constrarints | Content |
+| -------- | -------- | -------- |
+| KeyPublicizeCircuit (3 parties)     | 15266     | 3 commited secrets & their sum     |
+| DivinationCircuit (3 parties)     | 22249     | many commited secrets & ElGamal encryption   |
+
+
+## Main Circuits (MPC Bitwise Operations)
+Main circuits are:
+
+| Circuit Name | Total Constrarints | Proving Time | Content |
+| -------- | -------- | -------- | -------- |
+| BitDecompositionCircuit | 672 | 2.028s | 1 secret |
+| (SmallerEqThanCircuit) |   621~625   |   1.468s~1.483s   | 1 bitwise secret & 1 comparison |
+| (EqualityZeroCircuit) | 4 | 368.426ms | 1 secret | 
+| (PedersenComCircuit) | 2,543 | 6.572s | 1 secret & its Pedernsen commitment |
+| (SmallerThanCircuit) | 2,016 | 4.039s | 2 secrets and ordering |