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The X3DH key agreement protocol

For educational purpuses only.

Spec: https://www.signal.org/docs/specifications/x3dh/x3dh.pdf

Created using bernedogit/Amber (https://github.com/bernedogit/amber).

An implementation of the “X3DH” (or “Extended Triple Diffie-Hellman”) key agreement protocol.

X3DH establishes a shared secret key among two parties who mutually validate each other based on public keys.

X3DH provides cryptographic deniability and forward secrecy. The protocol is intended for asynchronous contexts where one user (“Bob”) is offline but has published some information to an untrusted server. Another user (“Alice”) wants to use that data to send encrypted data to Bob and establish a shared secret key for future communication.

The source for the protocol can be found in x3dh.cpp (https://github.com/PaulLaux/X3DH-Key-Exchange/blob/master/x3dh.cpp).

Notable changes from the spec:

  • scrypt_blake2b is used as the key derivation function.
  • qDSA is used for signatures instead of XEdDSA.

Both changes are for better compatibility with the cryptographic library (Amber).

Other primitives:

  • ChaCha20 for symetric encryption.
  • Curve25519 for public key cryptography.

The protocol

The following diagram shows the DH calculations between keys. Note that DH1 and DH2 provide mutual authentication, while DH3 and DH4 provide forward secrecy.

image

For more information: https://www.signal.org/docs/specifications/x3dh/x3dh.pdf

Usage

make && ./x3dh

Tested on

Ubuntu Linux 20.04

GNU Make 4.2.1

g++ 9.3.0