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Group-based cryptography
Group-based cryptography is a use of (nonabelian) groups to construct cryptographic primitives.

Magyarik, Wagner
The idea of using complexity of infinite nonabelian groups in cryptography goes back to Magyarik and Wagner [ref] who in 1985 devised a public key protocol based the unsolvability of the Word Problem for finitely presented groups (or so they thought)

Commutator Key Exchange Protocol
Commutator Key Exchange is a cryptographic protocol that allows two parties that have no prior knowledge of each other to jointly establish a shared secret key over an insecure communications channel. This key can then be used to encrypt subsequent communications using a symmetric key cipher. Also known as Anshel-Anshel-Goldfeld (AAG) protocol. CKE is an anonymous (non-authenticated) key-agreement protocol.

First published in 1999.

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