Diffie–Hellman key exchange

As explained in Elliptic Curve Cryptography for Developers

A public-key key-agreement protocol that lets parties establish a shared secret over an insecure network using private values and exchanged public values.

Diffie–Hellman key exchange lets two parties derive the same secret without transmitting it directly. In elliptic-curve use, each party combines a private scalar with the other party’s public point; both obtain the same shared point and use its x value as a symmetric-encryption key. section 4.0 section 4.5

The elliptic-curve exchange proceeds as follows:

• Choose a curve, finite-field parameters, and a base point. section 4.3
• Create each private key as a large integer; a hash of a pass phrase can generate one without storing the phrase. section 4.0 section 4.5
• Derive and exchange public points. section 4.1
• Multiply each private key by the other party’s public point, then use the resulting point’s x value as the shared secret. section 4.1 section 4.5

Figure 4.1 Creating a shared secret key by exchanging public keys

Use the diagram to trace the two public-key transmissions and the converging calculations that produce one shared secret. section 4.1

Testing both sides

A test program computes myshare from one private key and the other public key, then computes theirshare using the reverse pairing. Comparing the two multiprecision results should print “Keys match.” The test verifies the mathematics but does not transmit keys over a network. section 4.3.2

How Elliptic Curve Cryptography for Developers covers it

How deep it goes

Explains the exchange flow and test implementation, but defers detailed curve and prime selection.

Examples

Demonstrates reciprocal multiprecision calculations with pass-phrase and random private-key inputs, producing matching hexadecimal shares.

What it assumes

Assumes elliptic-curve mathematics routines for point addition and multiplication, while introducing their cryptographic use.

What you can do after

Build a testable elliptic-curve exchange and verify that both parties compute identical shared key material.

How it connects

Connects elliptic-curve point multiplication, public-key cryptography, symmetric encryption, AES, hashing, and MQV.

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Also explained in

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  Real-World CryptographyDiffie-Hellman key exchange is a public-key protocol that lets parties establish a shared secret over an insecure channel.
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  Hacking CryptographyDiffie–Hellman key exchange is a key-agreement protocol in which participants derive a shared secret from exchanged public values and retained private exponents.
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  Software Security for DevelopersDiffie-Hellman is a public-key key-agreement algorithm based on the computational difficulty of the discrete logarithm problem.

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Related concepts

• X3DHused by · X3DH is a non-interactive key-exchange protocol that combines multiple Diffie-Hellman exchanges to establish shared keying material for asynchronous messaging.
• API keyproduces · An API key is a credential used to identify or authorize a client accessing an application programming interface.
• 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 diffie-hellmanincludes · Elliptic-curve Diffie-Hellman is a public-key key-agreement method in which parties derive a shared secret through elliptic-curve point operations.
• CPaceused by · CPace is a symmetric password-authenticated key-exchange algorithm in which parties derive a group generator from a shared password and use it for ephemeral Diffie-Hellman key exchange.

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