A method of establishing a quantum key between a first quantum network node ( QNode X ) and a second quantum network node ( QNode Y ), the first and second nodes sharing respective authentication keys with a third network node ( QNode W ) and the method comprising a key agreement step followed by an authentication step, and characterised in that in the authentication step: (i) each of the first ( QNode X ) and second ( QNode Y ) nodes generates a respective cryptographic hash ([ MXY ] AI , [ MYX ] AJ ) of a message ( MXY , MYX ) it generated and sent to the other node ( QNode Y , QNode X ) in the key agreement step, each respective cryptographic hash ([ MXY ] AI , [ MYX ] AJ ) being generated using the respective authentication key ( AI,AJ ) shared with the third node ( QNode W ), then each of the first and second nodes exchange the respective cryptographic hashes ([ MXY ] AI ,[ MYX ] AJ ) and pass the exchanged hashes to the third node; (ii) at the third node ( QNode W ), the cryptographic hash ([ MXY ] AI ) generated by the first node and passed to the third node by the second node is de-crypted, re-encrypted ([ MXY ] AJ ) using the authentication key ( AJ ) shared by the second and third nodes and passed to the second node ( QNode Y ); (iii) at the third node ( QNode W ), the cryptographic hash ([ MYX ] AJ ) generated by the second node and passed to the third node by the first node is de-crypted, re-encrypted ([ MYX ] AI ) using the authentication key ( AI ) shared by the first and third nodes and passed to the first node; and (iv) at the first and second nodes, the re-encrypted cryptographic hashes ([ MXY ] AJ , [ MYX ] AI ) generated by the third node are decrypted to reproduce the messages ( MXY,MYX ) generated by the first and second nodes in the key agreement step. (i) each of the first ( QNode X ) and second ( QNode Y ) nodes generates a respective cryptographic hash ([ MXY ] AI , [ MYX ] AJ ) of a message ( MXY , MYX ) it generated and sent to the other node ( QNode Y , QNode X ) in the key agreement step, each respective cryptographic hash ([ MXY ] AI , [ MYX ] AJ ) being generated using the respective authentication key ( AI,AJ ) shared with the third node ( QNode W ), then each of the first and second nodes exchange the respective cryptographic hashes ([ MXY ] AI ,[ MYX ] AJ ) and pass the exchanged hashes to the third node; (ii) at the third node ( QNode W ), the cryptographic hash ([ MXY ] AI ) generated by the first node and passed to the third node by the second node is de-crypted, re-encrypted ([ MXY ] AJ ) using the authentication key ( AJ ) shared by the second and third nodes and passed to the second node ( QNode Y ); (iii) at the third node ( QNode W ), the cryptographic hash ([ MYX ] AJ ) generated by the second node and passed to the third node by the first node is de-crypted, re-encrypted ([ MYX ] AI ) using the authentication key ( AI ) shared by the first and third nodes and passed to the first node; and (iv) at the first and second nodes, the re-encrypted cryptographic hashes ([ MXY ] AJ , [ MYX ] AI ) generated by the third node are decrypted to reproduce the messages ( MXY,MYX ) generated by the first and second nodes in the key agreement step. <EOS>