Privacy Coins & Confidential Transactions

Privacy coins are cryptocurrencies designed to protect user privacy by concealing:

• The sender and receiver identities,
• The transaction amount, and/or
• The transaction graph (the links between transactions).

Their goal is to achieve fungibility (each coin is indistinguishable) and financial privacy, similar to cash.

Examples: Monero (XMR), Zcash (ZEC), Firo (FIRO), Beam, Grin, MobileCoin, etc.

Privacy Matters in Cryptocurrency

Bitcoin and Ethereum transactions are public and traceable — anyone can see:

• The amount sent
• Sender and recipient addresses
• The transaction history of any address

Blockchain analysis companies can often deanonymize users.
Privacy coins aim to break this traceability while maintaining decentralized consensus.

3. Core Privacy Concepts

4. Cryptographic Techniques in Detail

4.1 Ring Signatures (Sender Anonymity)

• A ring signature allows one signer to sign a message on behalf of a group without revealing who actually did it.
• Each transaction input is signed with a ring of possible outputs, so it’s indistinguishable which output is being spent.

Used in: Monero.

Mathematical idea:

• Given public keys P1,P2,…,PnP_1, P_2, …, P_nP1​,P2​,…,Pn​, and one private key xix_ixi​,
• The signer produces a signature that proves “one of these public keys signed this,” without revealing which.

4.2 Stealth Addresses (Receiver Privacy)

• The sender generates a unique, one-time public address for each payment using the receiver’s public view key and public spend key.
• Only the receiver, with their private view key, can detect incoming funds.

Used in: Monero, Particl, Firo.

Effect: On the blockchain, no two transactions to the same user appear related.

4.3 Confidential Transactions (Amount Privacy)

Introduced by Greg Maxwell (2015) for Bitcoin, later adopted by Monero, Grin, Beam, etc.

Problem:

Without amount privacy, anyone can sum inputs/outputs and see how much is sent.

Solution: Pedersen Commitments

A Pedersen commitment hides the amount but allows arithmetic verification.

Formula: C=vG+rHC = vG + rHC=vG+rH

where

• vvv = value (amount),
• rrr = blinding factor (random number),
• G,HG, HG,H = independent elliptic curve generators.

Properties:

• Hiding: CCC hides vvv.
• Binding: You can’t change vvv later without knowing rrr.
• Additive: Commitments can be added/subtracted, enabling balance proofs.

Thus, nodes can verify: ∑Cinputs=∑Coutputs\sum C_{\text{inputs}} = \sum C_{\text{outputs}}∑Cinputs​=∑Coutputs​

without seeing the actual amounts.

4.4 Range Proofs (Proving Valid Amounts)

Since Pedersen commitments could hide negative values, range proofs ensure each vvv is in a valid range (e.g., 0–2⁶⁴).

• Borromean range proofs: Early Monero.
• Bulletproofs: Introduced 2018, shorter and faster; used in Monero, Grin.
• Bulletproof+ / Halo2: Further optimizations for smaller, faster proofs.

4.5 zk-SNARKs and zk-STARKs (Full Zero-Knowledge Proofs)

zk-SNARK = Zero-Knowledge Succinct Non-Interactive Argument of Knowledge

They allow proving that a transaction is valid (inputs exist and sums balance) without revealing any details.

Used in: Zcash, Mina, Aleo.

Properties:

• Zero-Knowledge: No sensitive info revealed.
• Succinct: Small proof size.
• Non-interactive: Doesn’t require back-and-forth communication.
• Trusted setup (in SNARKs): Requires initial secret parameters (a potential risk).

zk-STARKs:
More scalable, post-quantum secure, no trusted setup — but larger proofs.

4.6 CoinJoin and Mixers

• CoinJoin aggregates multiple users’ transactions into one big transaction with multiple inputs and outputs, breaking the link between senders and recipients.
• Implemented in Wasabi, Samourai Whirlpool, and partially in MimbleWimble chains.

Downsides:
Still somewhat linkable by timing analysis or imperfect mixing patterns.

Real-World Implementations

6. Wimbledon Protocol

A minimalist blockchain protocol that:

• Uses Confidential Transactions and cut-through (removes spent outputs),
• Doesn’t reveal addresses or amounts,
• Merges transactions, removing unnecessary data.

Advantages:
Compact, scalable, strong privacy.

Used in: Grin, Beam, and Litecoin’s MimbleWimble extension blocks.

7. Network-Level Privacy

Even if on-chain privacy is perfect, metadata leaks via network activity.

Techniques:

• Dandelion++: Obfuscates transaction propagation paths.
• Tor / I2P integration: Hides IP addresses.
• Mixnets / relays: Breaks timing correlations.

8. Trade-Offs

9. Future Directions

• zk-SNARK upgrades: Halo2 (recursive proofs, no trusted setup)
• Cross-chain privacy: Interoperability with bridges and wrapped tokens
• Layer-2 privacy: Private channels, rollups
• Privacy-preserving DeFi: zk-DeFi, Aztec Network, Penumbra
• Quantum resistance: zk-STARKs, lattice-based commitments

10. Summary Table