warmannet123 / mugraph

A standard for instant, untraceable, easy to use payments on the Cardano Blockchain.

Instant, untraceable payments for Cardano.

Mugraph (pronounced "mew-graph") is a Layer 2 Network for the Cardano blockchain for untraceable payments with instant finality.

By untraceable, we mean that, inside a given group $A$ of users:

• All transactions between users inside $A$ are untraceable, meaning senders and receivers are not bound in any way.
• All transactions to users outside $A$ come from a single, shared identity for all group participants.

This shared identity comes from Delegates, similar to Payment Networks in the traditional banking system, like Paypal, Venmo or CashApp, but with some crucial distinctions:

• Delegates hold funds in a fully auditable Smart Contract Vault, held in the Layer 1.
• Delegates can not spend user funds without their authorization.
• Delegates are blind, meaning they don't know who is transacting.
• Delegates provide group concealing for their users, signing transactions on behalf of them.

An user can, and usually will, hold balance in multiple Delegates at once, and they do not need to have balance in a Delegate to receive payments there.

Motivation

Why are people not using cryptocurrencies for payments?

This is the question I wanted to address when Mugraph started. Bitcoin was created to address this specific problem, yet The Lightning Network is not widely supported even in countries that adopted Bitcoin as legal tender.

Even if Cardano has much more advanced technology than Bitcoin does (like eUTXO or Smart Contracts), buying groceries with USDM remains nighly impossible.

ZeroHedge explains this phenomenon in their article "What Happened to Bitcoin?":

At the same time, new technologies were becoming available that vastly improved the efficiency and availability of exchange in fiat dollars. They included Venmo, Zelle, CashApp, FB payments, and many others besides, in addition to smartphone attachments and iPads that enabled any merchant of any size to process credit cards. These technologies were completely different from Bitcoin because they were permission-based and mediated by financial companies. But to users, they seemed great and their presence in the marketplace crowded out the use case of Bitcoin at the very time that my beloved technology had become an unrecognizable version of itself.

Excluding volatility (already being taken seriously by Stablecoins), we identified three main problems that prevent the average person from considering cryptocurrencies as a payment option:

1. Scalability: Cryptocurrency transactions are slow compared to centralized solutions. For example, credit cards have a practical confirmation limit of 2 seconds.

2. Privacy: Users do not want to reveal their identity for every purchase. Financial privacy is a human right, and in the age of big data analysis and AI, pseudonymity does not provide sufficient privacy.

3. Ease of Use: Users prefer not to deal with complex protocols, multiple wallets, or extensive security considerations.

I think that Mugraph has a real shot of solving those problems, and that's why I'm building it.

Overview

Note

This overview describes a variant of the blind signatures protocol proposed by David Wagner here2. For all practical terms, they are equivalent.

In 1983, David Chaum conceived ECash, arguably the first form of cryptographically secure digital money, in his paper Blind Signatures for Untraceable Payments. In it, David Chaum describes a bank (called a Mint) that emit Bearer Tokens.

They are called "bearer" tokens because, like physical cash, possession of the token itself confers the right to redeem its value, and are created through a process called Blind Signature.

Blind Signatures

A Blind Signature is a signature in which the signer is able to verify attribution (that they in fact signed it at some point), while not revealing what signed message created that input. Following the usual conventions for cryptographic examples, we have Alice (the user) and Bob (the Mint). Given that:

• $G$ is a publicly available generator point on the Ristreto25519 curve,
• Bob has a public/private keypair $k, K$, and $K$ is publicly available.
• Alice has a secret $x$, representing her deposit on Bob.

Then:

1. Alice computes $Y = H(x)$, where $H$ is a function that maps the secret to a point on the elliptic curve (hash to curve).
2. Alice generats a random blinding factor $r$.
3. Alice the blinded point $B' = Y + r \cdot G$:
4. Alice sends $B'$ to Bob.
5. Bob receives $B'$ and computes the blinded signature $C' = k \cdot B'$.
6. Bob sends $C'$ back to Alice.
7. Alice unblinds the signature by subtracting $r \cdot K$ from $C'$:

$$ \begin{align} C = C' - r \cdot K \\ = k \cdot B' - r \cdot K \\ = k \cdot (Y + r \cdot G) - r \cdot (k \cdot G) \\ = k \cdot Y + k \cdot r \cdot G - r \cdot k \cdot G \\ = k \cdot Y \end{align} $$

To verify the signature, Alice (or any verifier) can check if $C = k \cdot H(x)$. If this equality holds, it proves that $C$ originated from Bob's private key $k$, without Bob knowing the original message $x$.

This protocol has been implemented multiple times before, notably in the Protocol, running on top of the Lightning Network. It is very cryptographically solid, even 40+ years after it was created, but it also has some very known flaws:

1. Mints are in total control of issuing tokens, and the only thing barring them from practicing fractional reserves is the risk of a Bank Run.
2. Mints don't know which deposit they are redeeming, but they know what asset is being transacted and the amounts. Those increase risk of deanonimization with data and pattern analysis.

Protocol

Mugraph differentiates itself from ECash because we use Zero-Knowledge Proofs, specifically ZK-SNARKS, to move the state forward. This means:

1. Instead of Mints, we have Delegates. They don't emit tokens or control the funds at all, instead they only verify and apply proofs.
2. Users do all operations inside the system, delegates only protect against double-spend.
3. Notes themselves can have programs, allowing for arbitrary conditions on spending.

Delegates

The equivalent to Mints in Mugraph are Delegates.

1. Verifying operation proofs and signing Blinded Notes.
2. Signing external transctions on behalf of the user.
3. Emitting Notes in response to user deposits.

Default Programs

$F$: Fission

Splits a note into two blinded notes. It is defined as:

$$ F(n, i) \mapsto { n'_o, n'_c } $$

Where:

• $n$ is the input note to be slit in two
• $i$ is the output amount requested by the operation
• $n'_o$ is a blinded note for the amount $i$
• $n'_c$ is another blinded note for the amount $n_i - i$, where $n_i$ is the note amount.

$F'$: Fusion

Joins two notes with the same Asset ID and server keys into a single one. It is defined as:

$F'(n_0, n_1) \mapsto n'$

Where:

• $n_0$ and $n_1$ are the input notes to be fused
• $n'$ is a blinded node for the amount $n_0i + n_1i$

Mugraph (pronounced "mew-graph") is a Layer 2 Network for the Cardano blockchain for untraceable payments with instant finality. It is very simplified in both operations and architecture, meant to be easy to integrate anywhere.

Glossary

Symbol	Description
$G$	A generator point in the Ristreto25519 curve.
$n$	A Note, blindly signed by the Delegate and ready to be used.
$n'$	A Note with a blinded nullifier to be sent to the Delegate for signing.

Further Reading

1. Roadmap
2. Licensing