Add public.json && Update README

README.md

@@ -1,39 +1,86 @@
 # AK-381: A SNARK verification library using bls12-381
 
-This Aiken library implements utilities to verificate Zero-Knowledge proof following the Groth16 protocol. The main feature is a Zero-Knowledge verification function. The library is tailored to use with the Circom language and/or the SnarkJs modules. 
+This Aiken library implements utilities to verificate Zero-Knowledge proof
+following the Groth16 protocol. The main feature is a Zero-Knowledge
+verification function. The library is tailored to use with the Circom language
+and the SnarkJs module.
 
+### The 3 prime factorization example
+
+In order to make this library ilustrative, we use a circuit that proofs that we
+know the multiplication of three big prime numbers to a verifier. Although in
+this example we use small prime numbers, to deduce the prime factors from the
+result is usually an hard and challenging computation problem. In this case for
+a given number we show just one factor and we proof that we know the other two
+without revealing them.
 
 ### Requisites
 
-In order to use this library you must have circom and Snarkjs. You can get both installed following this part of the [circom documentation](https://docs.circom.io/getting-started/installation/)
+In order to use this library you must have circom and Snarkjs. You can get both
+installed following this part of the
+[circom documentation](https://docs.circom.io/getting-started/installation/)
 
 ### Structure folder
 
-* Circuits: The folder where you put your circom circuits.
-* 3_fac: The output of the circuit that we use as example.
-
+- Circuits: The folder where you put your circom circuits.
+- 3_fac: The output of the circuit that we use as example.
+- conversion: The javascript module where you can convert the proof and
+  verification-key given by circom into the serialization that Plutus need.
 
 ### Start Grot16 process
 
-Once you circom file is set in your circuits folder, you can start the Groth16 protocol from setup, to proof and verification using: 
+Once you circom file is set in your circuits folder, you can start the Groth16
+protocol from setup, to proof and verification using:
 
 ```bash
 ./groth16
 ```
 
-And it's going to ask you about the circuit that you want to use. It is going to create you a folder with the name of the circuit which will storage all the outputs of the process.
+This script it's going to ask you about the circuit that you want to use. It is
+going to create you a folder with the name of the circuit which will storage all
+the outputs of the process.
 
 ### Use it with SnarkJs
 
-Todo
+Once you have completed the setup and created the `<circuit>_final.zkey`you can
+create new proof and verify them.
 
-### The 3 factorization example
+**Creating the witness**
 
-Todo
+We create set the inputs of our proof in the `input.json` file. In this case we
+define the 3 factors (x1,x2 and x3) with these:
 
-### Verify the proof
+```JSON
+{ "x1": 3, "x2": 11, "x3": 17 }
+```
 
-Todo
+Then we take the wasm compilation of the circuit and the input and output the
+result in `witness.wtns`
+
+```bash
+snarkjs wc 3_fac_js/3_fac.wasm input.json witness.wtns
+```
+
+**Creating the proof**
+
+With the witness ready we can compute the proof.
 
+```bash
+narkjs g16p 3_fac_final.zkey witness.wtns proof.json public.json
+```
+
+**Verifying the proof**
+
+```bash
+snarkjs g16v verification_key.json public3.json proof3.json
+```
 
+And should output the following:
 
+```bash
+[INFO]  snarkJS: OK!
+```
+
+### The conversion
+
+Todo

conversion/public.json

@@ -0,0 +1,4 @@
+[
+ "561",
+ "3"
+]