Symmetric password-authenticated key exchange

As explained in Real-World Cryptography

A symmetric password-authenticated key exchange is a password-based key exchange in which both parties use symmetric password-derived information rather than a server-held asymmetric password verifier.

A symmetric password-authenticated key exchange lets two parties that share a password authenticate each other and establish a session key. Unlike an asymmetric or augmented PAKE, both sides know the password or password-derived information. This makes short passwords practical when manually importing a long public key is inconvenient, such as pairing nearby devices. section 11.3 section 11.2.2

A simplified CPace exchange proceeds in phases:

• Both devices derive a generator for a predetermined cyclic group from their common password. section 11.3.2
• They use that generator as the base for an ephemeral Diffie–Hellman key exchange. section 11.3.2
• They derive the session key from the exchange output, ephemeral public keys, and a unique session identifier. section 11.3.2
• A careful implementation handles elliptic-curve group checks, hash-to-curve processing, and contextual metadata such as peer addresses. section 11.3.2

Connecting a device to home WiFi

Entering the same password on two devices illustrates the tradeoff: the user avoids importing a long public key, while the devices use a symmetric PAKE such as CPace to establish an authenticated connection. section 11.4 section 11.3

Figure 11.14 The CPace PAKE works by having the two devices create a generator based on a password and then use it to perform as a base for the usual ephemeral DH key exchange.

Shows the core CPace idea: derive a generator from the password, then use it for an ephemeral Diffie–Hellman exchange. section 11.3.2

How Real-World Cryptography covers it

How deep it goes

Explains CPace’s password-derived generator, ephemeral Diffie–Hellman exchange, key derivation, and elliptic-curve safeguards without implementation detail.

Examples

Uses two-device pairing, CPace, and home WiFi as concrete examples of shared-password authentication.

What it assumes

Assumes familiarity with passwords and device connections while introducing PAKE terminology and the role of ephemeral Diffie–Hellman.

What you can do after

Evaluate when a shared-password exchange is more practical than transferring asymmetric keys for authenticating connected devices.

How it connects

Connects passwords, ephemeral Diffie–Hellman, elliptic-curve cryptography, asymmetric PAKEs, and short authenticated strings.

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Related concepts

• CPaceincludes · 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.
• mutually authenticated key exchangekind of · A mutually authenticated key exchange is an authenticated key exchange in which both participants authenticate each other while establishing a shared secret.
• asymmetric password-authenticated key exchangecontrasts with · An asymmetric password-authenticated key exchange is a password-authenticated key exchange in which the server does not learn the user's password and typically stores a verifier derived from it.

This explainer was generated by Manning's knowledge graph from the text of Real-World Cryptography. The section links point to the parts of the book it draws on.