Master the mathematics behind Bitcoin, TLS, and modern cryptography. Learn how elliptic curves enable secure key exchange and digital signatures with dramatically smaller keys than RSA.
🎯 Hook
💡 Intuition
📚 Theory
🎮 Playground
💻 Code
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✏️ Practice
How Does Bitcoin Sign Transactions with Just 256 Bits?
RSA needs 3072+ bits for security. Bitcoin uses only 256.
Every Bitcoin transaction is signed with a key that's 12 times smaller than traditional RSA - yet it's just as secure. What makes this possible?
The Key Size Mystery
For decades, RSA was the gold standard of public-key cryptography. But modern systems like Bitcoin, Signal, and TLS 1.3 all use elliptic curve cryptography with dramatically smaller keys. Why?
Key Size Comparison (for equivalent security)
RSA-2048
2048
bits (112-bit security)
RSA-3072
3072
bits (128-bit security)
ECC-256
256
bits (128-bit security)
ECC-384
384
bits (192-bit security)
Relative Key Size (for 128-bit security):
RSA-3072:
3072 bits
ECC-256:
256 bits
ECC achieves the same security with ~12x smaller keys!
