What are Monero Bulletproofs?

Bulletproofs are a type of zero-knowledge proof that Monero uses to hide transaction amounts. They prove that a transaction amount is positive (no negative/overflow values that would create XMR from nothing) without revealing what the actual amount is. Introduced in October 2018, Bulletproofs replaced the older Borromean range proofs, reducing transaction sizes by ~80% and fees by ~96%.

What is the difference between Bulletproofs and Bulletproofs+?

Bulletproofs+ (introduced August 2022 in the Fluorine Fermi upgrade) is an improved version that reduces transaction sizes by an additional ~5-7% and verification time by ~5-8% compared to original Bulletproofs. Same security, smaller and faster. The mathematical improvement is in the inner-product argument structure.

How do Bulletproofs hide the amount?

Bulletproofs use Pedersen commitments to encode the amount. A Pedersen commitment hides the value while preserving addition: commitment(a) + commitment(b) = commitment(a+b). This means miners can verify that inputs equal outputs (no inflation) without knowing the actual amounts. The Bulletproof then proves that each committed value is in a valid range (0 to 2^64) — preventing overflow attacks.

Did Bulletproofs reduce Monero transaction fees?

Dramatically. Before Bulletproofs (pre-October 2018): typical transaction ~13 KB, fee ~$0.60. After Bulletproofs: ~1.5 KB, fee ~$0.02. After Bulletproofs+ (2022): ~1.4 KB, fee ~$0.001. That's a 96%+ reduction in fees. This made Monero practical for small payments and everyday use.

What comes after Bulletproofs+?

FCMP++ (Full-Chain Membership Proofs) is the next major privacy upgrade for Monero. It replaces ring signatures with a proof that your output exists somewhere in the entire blockchain — without revealing which one. This eliminates the ring size limit and makes Monero's anonymity set the entire UTXO set. Bulletproofs+ will continue handling amount hiding.

Monero Bulletproofs (2026)

How zero-knowledge proofs hide transaction amounts

TL;DR: Bulletproofs (2018) and Bulletproofs+ (2022) are cryptographic proofs that hide how much XMR you're sending while proving no inflation. They reduced transaction sizes by ~80% and fees by ~96% (from $0.60 to $0.001). Part of Monero's four-layer privacy: ring signatures (hide sender), stealth addresses (hide receiver), RingCT + Bulletproofs (hide amount), Dandelion++ (hide IP).

Evolution of Amount Hiding

Technology	Period	Tx Size	Fee	Improvement
Borromean range proofs	Jan 2017 – Oct 2018	~13 KB	~$0.60	First confidential amounts
Bulletproofs	Oct 2018 – Aug 2022	~1.5 KB	~$0.02	80% smaller, 96% cheaper
Bulletproofs+	Aug 2022 – present	~1.4 KB	~$0.001	Additional 5-7% smaller

How It Works (Simplified)

The problem: Monero needs to hide how much you're sending, but miners still need to verify that you're not creating XMR from nothing (inflation). How do you prove inputs = outputs without revealing the numbers?

Step 1 — Pedersen commitments: Instead of writing "5 XMR" on the blockchain, Monero writes a mathematical commitment — a number that encodes 5 XMR but looks random. The magic: commitments preserve addition. Commitment(3) + Commitment(2) = Commitment(5). Miners verify inputs = outputs by checking commitments add up, without knowing the actual values.

Step 2 — Range proof (Bulletproofs): Pedersen commitments have a vulnerability: you could commit to a negative number, creating XMR from nothing. Bulletproofs prove that each committed value is between 0 and 2⁶⁴ — a valid positive number — without revealing what it is. This is the "zero-knowledge" part: the proof reveals nothing except "this number is valid."

Privacy Layer Stack

Layer	Technology	What It Hides
Sender	Ring Signatures	Who sent the transaction
Receiver	Stealth Addresses	Who received the transaction
Amount	RingCT + Bulletproofs+	How much was sent
Network	Dandelion++	Origin IP address
Future	FCMP++	Full-chain anonymity set

Why This Matters

On Bitcoin, everyone can see: "Address A sent 2.5 BTC to Address B." On Monero: "Someone sent something to someone." That's it. Bulletproofs ensure the "something" is a valid amount without revealing what it is.

This matters for business privacy (competitors can't see your revenue), personal privacy (nobody knows your balance), and fungibility (no XMR can be "tainted" because amounts are invisible).

Summary

Bulletproofs+ are the current state-of-the-art for hiding transaction amounts in Monero.

They reduced fees by 96% (to $0.001) and transaction sizes by 80%+ since their original introduction.

Combined with ring signatures, stealth addresses, and Dandelion++, they make Monero the most private cryptocurrency in existence.

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