✍️ ECDSA: How Bitcoin Signs Transactions
Understand the Elliptic Curve Digital Signature Algorithm powering crypto
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ECDSA (Elliptic Curve Digital Signature Algorithm) proves you authorized a transaction without revealing your private key!
🎯 What Are Digital Signatures?
Think of a digital signature like a handwritten signature, but mathematically provable:
- •Can be forged with practice
- •Same signature every time
- •Can be copied to other documents
- •Mathematically impossible to forge
- •Different for every message
- •Tied to specific message (can't copy)
🎮 Interactive: Sign a Message
In real life, this is a 256-bit number kept secret!
🔍 Signature Verification
Anyone can verify your signature using only your public key (no access to private key needed):
Modular inverse of s
Two scalar values from message hash and signature
Where Q is your public key
If x-coordinate matches r, signature is valid!
Verification works because of the mathematical relationship between your private key (d), public key (Q = dG), and the signature (r, s). Only someone with private key d could have created a valid signature!
⚠️ Critical Security Rules
If you use the same k for two different messages, attackers can calculate your private key! This is how PlayStation 3 was hacked in 2010.
Predictable k values can leak your private key. Use cryptographically secure random number generators!
Your private key is like your password. If someone gets it, they can sign transactions as you!
📚 ECDSA Summary
- • Requires: Private key (d)
- • Inputs: Message + Random k
- • Output: Signature (r, s)
- • Purpose: Prove authorization
- • Requires: Public key (Q)
- • Inputs: Message + Signature (r, s)
- • Output: Valid or Invalid
- • Purpose: Confirm authenticity