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#Elliptic Curves

3 articles with this tag.

Modern Asymmetric Algorithms Advanced

Elliptic Curve Diffie-Hellman (ECDH)

ECDH lets two parties agree on a shared secret using points on an elliptic curve. Learn how P-256, P-384, and secp256k1 define the group, how public keys are encoded and validated, why the secret is only an x coordinate, and how an invalid-curve attack works.

23 min read

Modern Asymmetric Algorithms Advanced

ECDSA: Elliptic Curve Digital Signature Algorithm

ECDSA is the elliptic curve version of DSA, used to sign TLS handshakes and Bitcoin transactions. Learn how signing and verifying work, why a repeated nonce reveals the private key, how RFC 6979 removes that risk, and how a signature is encoded.

23 min read

Modern Asymmetric Algorithms Advanced

X25519 and Curve25519

X25519 is the Diffie-Hellman function on Curve25519, defined in RFC 7748. Learn how a 32-byte private key is clamped, how the Montgomery ladder multiplies a point using only its u coordinate, why the curve was chosen, and what the all-zero check protects against.

18 min read

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