Elliptic Curve Cryptography - Cryptography | The Secret

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Elliptic Curve Cryptography

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.

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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!

Why can elliptic curves use such small keys?

Select an answer to continue!