[WIP] Module/Week 1

[adrianmcli]

1️⃣ Week 1 - Cryptographic Basics

Practical

• [x] Getting Started with Circom (syntax + zkrepl)
• [x] Write a circuit to prove input to hash
• [ ] Write a circuit to prove private key to public key
• [x] Write a circuit to prove inclusion in Merkle tree
• [ ] Write a circuit to prove set membership

Study

• [x] Symmetric vs Asymmetric Encryption (AES, RSA)
• [x] Hash Functions, Merkle Trees
• [ ] Digital Signatures (Schnorr)
• [x] DLP-based Public-Key Cryptography (DLP, DH, Elgamal)
• [x] Cryptographic Commitments
• [ ] Intro to Elliptic Curve Cryptography
• [ ] BLS Signatures (keep this simple and black-boxed)
• [ ] Pairing-Based Cryptography (keep this simple and black-boxed)

[adrianmcli]

@NOOMA-42 has stated he will fill in the Practical (Circom) section of this Module. I will review and make my edits afterwards.

[adrianmcli]

The answer for writing a circuit to check output of hash:

pragma circom 2.1.6;

include "circomlib/poseidon.circom";

template HashProof() {
    signal input preimage;
    signal input hash;
    signal output hashOutput;

    component hasher = Poseidon(1);
    hasher.inputs[0] <== preimage;

    hashOutput <== hasher.out;

    // Enforce that the hash matches the given hash
    hash === hashOutput;
}

component main = HashProof();

/* INPUT = {
    "preimage": "12345",
    "hash": "4267533774488295900887461483015112262021273608761099826938271132511348470966"
} */

Instead of showing the above, we should break it down so that we force the student to come up with the above. We can give it to them in parts. Please see the latest commit for an example.

[NOOMA-42]

1. I removed set membership section because a very simple set membership is Merkle tree inclusion. We just go over in the previous section.
2. I change private key to public key to elliptic curve addition. The code is easier to understand and also involved with cryptography

[adrianmcli]

@NOOMA-42 do you think it is sufficiently simple and black-boxed?

I will just merge it now, we can always improve this later.