Public Parameters
Free group
, a freely reduced word 
in F and an automorphism 
of infinite order.
Alice
Bob
Key Creation
Choose private key
.
Compute
(
denotes the set of all freely reduced words with letters in
.)
Publish c.
Encryption
Choose plaintext
.
Choose random ephemeral key
.
Compute
Send ciphertext 
to Alice.
Decryption
Compute
which is the message from Bob.