Monero

Related:

Breaking Monero

Monero Part 1: Key Concepts

Monero Part 2: How It Works

Monero relies on three cryptographic mechanisms.

• One-time keys generated for each transaction hide the actual recipient of a transaction.

• Ring signatures mix the spender’s input among other people’s inputs (which are hidden,

see below). The spender can spend (sign) the amount spent but it is not possible for

an external party to link different transactions. A special adaptation of this mechanism

detects double spending.

• Ring confidential transactions hide the transferred amount.

The Monero Building Blocks series is the result of a personal interest in the mathematical underpinnings of Monero.

Range Proof

Monero Becomes Bulletproof

Evaluation of Bulletproof Implementation

Before introducing bullet proof: Borromean-style range proofs in the CT

bulletproofs would significantly

reduce the size of the blockchain, as well as bring down transaction fees on the platform by an

estimated 70-80%.

Stealth Address

Ring Signatures

Monero Ring Signatures

A ring signature is essentially a signature that proves that the signer has a private key corresponding to one of a specific set of public keys, without revealing which one.

全ての検証鍵を知っていればz=vであることを検証できるが、そのうちのいずれか１つの署名鍵を知らないとz=vに調整することができない。

https://gyazo.com/f73d559054629f8ca4b487553e1e82ae

linkable ring signatureによりprivate keyの二重使用を探知可能。

tx outputはone-time addressに保持される

one-time addressからのspendingは多くのone-time addressを使ったring signatureで行われる。

spenderはblockchainからone-time addressesをランダムにピックアップ

one-time address private keyでring sigを生成

double spendingを防ぐために2つのlinkable ring sigsが生成

Linkable Spontaneous Anonymous Group Signatures

Inputs/Outputs structure

https://youtu.be/-zJpvsj1rWE

Anonimityに考慮して2inputs/2outputsに強制。

1inputで十分な場合でもdummy inputを加える