Elliptic-curve diffie-hellman

As explained in 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.

Elliptic-curve Diffie-Hellman (ECDH) lets two parties create the same shared secret across an insecure network without transmitting that secret. Each party keeps a private key, exchanges a public key, and combines the other party’s public key with its own private key. The shared result can become an AES key in a hybrid-encryption design. section 7.1.2

Figure 7.3 The DH algorithm computes the same result from the (payment private key, warehouse public key) and (warehouse private key, payment public key) key combinations.

The key-combination diagram shows why both parties independently compute the same shared result. section 7.1.2

Practical security guidance:

• Use approved curves such as Curve25519 rather than choosing arbitrary elliptic curves; some curves have weaknesses. section 7.4
• Prefer configuring ECDH through protocols such as TLS or SSH instead of reimplementing its mathematics. section 7.4
• Compared with original DH, ECDH uses elliptic curves, shorter keys, and faster performance for comparable security. section 7.4

How Software Security for Developers covers it

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 it assumes

Assumes familiarity with AES and introduces Diffie-Hellman as the foundation for understanding ECDH.

What you can do after

Configure ECDH through established secure protocols and select approved curves without implementing the underlying mathematics.

How it connects

Connects elliptic-curve cryptography with Diffie-Hellman, AES, TLS, SSH, and the elliptic-curve discrete-logarithm problem.

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Also explained in

• 

  liveBookmanning.com
  Real-World CryptographyElliptic Curve Diffie-Hellman is a public-key key exchange method based on elliptic-curve cryptography that lets parties derive a shared secret.
• 

  liveBookmanning.com
  Hacking CryptographyElliptic Curve Diffie–Hellman is a key-agreement protocol that performs Diffie–Hellman operations with elliptic-curve points instead of modular exponentiation.

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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.

This explainer was generated by Manning's knowledge graph from the text of Software Security for Developers. The section links point to the parts of the book it draws on.