Elliptic-curve diffie-hellman
Elliptic-curve Diffie-Hellman is a public-key key-agreement method in which parties derive a shared secret through elliptic-curve point operations.
Real-World Cryptography
Elliptic Curve Diffie-Hellman is a public-key key exchange method based on elliptic-curve cryptography that lets parties derive a shared secret.
- How it is used
- Provides a compact public-key mechanism for deriving shared secrets in key exchanges and hybrid encryption.
- How deep it goes
- Explains parameter agreement, key generation, scalar operations, shared-secret equality, security assumptions, and key validation.
- Examples
- Uses Alice and Bob, base point G, P-256, Curve25519, and visual comparisons between ordinary DH and elliptic-curve groups.
- What you can do after
- Apply ECDH by selecting standardized curves, deriving matching shared secrets, validating public keys, and adding authentication where required.
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Software Security for Developers
Elliptic-curve Diffie-Hellman is a Diffie-Hellman key-agreement algorithm based on the discrete-logarithm problem for points on elliptic curves.
- How it is used
- Generates shared symmetric keys for encrypted communication over insecure networks, including modern TLS deployments.
- How deep it goes
- Explains key exchange, security assumptions, curve selection, and deployment guidance but stops short of mathematical derivation.
- Examples
- Uses a payment service and warehouse service, public-key combinations, AES encryption, and approved curves such as Curve25519.
- What you can do after
- Configure ECDH through established secure protocols and select approved curves without implementing the underlying mathematics.
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Hacking Cryptography
Elliptic Curve Diffie–Hellman is a key-agreement protocol that performs Diffie–Hellman operations with elliptic-curve points instead of modular exponentiation.
- How it is used
- Uses elliptic-curve arithmetic to establish shared keys, especially as the primary key-exchange method in TLS 1.3.
- How deep it goes
- Defines the arithmetic substitution and protocol role, but defers ephemeral ECDH and perfect-forward-secrecy details.
- Examples
- Contrasts elliptic-curve point addition with modular exponentiation and situates ECDH in TLS 1.3.
- What you can do after
- Evaluate/understand how elliptic-curve arithmetic adapts Diffie–Hellman key agreement for TLS 1.3.
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Related concepts
- cryptographic keyproduces · A cryptographic key is a value supplied to a cryptographic algorithm to control operations such as encryption, decryption, signing, authentication, or verification.
- Diffie–Hellman key exchangekind of · Diffie–Hellman key exchange is a public-key key-agreement protocol that enables parties to derive a shared secret over an insecure channel without transmitting it.
- key exchangekind of · Key exchange is a cryptographic protocol by which communicating parties establish a shared secret over a communication channel without directly transmitting that secret.
- elliptic curve point multiplicationuses · Elliptic-curve point multiplication multiplies a point by an integer scalar through repeated point addition and doubling.
- API keyproduces · An API key is a credential used to identify or authorize a client accessing an application programming interface.
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