Is the ring of octonions "commonly" used in Cryptography? I've recently read "Fully Homomorphic Encryption on Octonion Ring" by Yagisawa, which is based on octonion rings over finite fields.

Personally I've never encountered octonion rings in cryptography before. Is there any example of them being used in previous work?

Please don't mention the mentioned previous version of this scheme.
I can’t remember having stumbled upon them in RealLife™ cryptography either, but I am well aware of a somewhat older, related patent by the same author. (Which might or might not violate your “Please don't mention the mentioned previous version of this scheme.” depending on what you’ve previously been reading. The patent is titled “Schemes for signcryption” and dates back to 2012. The paper published before the one you’ve mentioned was “Fully Homomorphic Encryption without bootstrapping”, published in 2015.)

Anyway…

From what I’ve seen, “patents” related to cryptography are a good way to ensure that no one feels the urge to use your “invention” anytime soon – which might explain the (lack of) popularity of the term.


  Publication number: US20140169556 A1
  Publication type: Application
  Application number: US 13/995,312
  PCT number: PCT/US2012/070369
  Publication date: Jun 19, 2014
  Filing date: Dec 18, 2012
  Priority date: Dec 18, 2012
  Also published as WO2014098807A1
  Inventors: Masahiro Yagisawa
  Original Assignee: Empire Technology Development Llc
  Export Citation: BiBTeX, EndNote, RefMan
  Classifications (10), Legal Events (2)
  External Links: USPTO, USPTO Assignment, Espacenet
  
  Schemes for signcryption
  
  US 20140169556 A1 
  
  Abstract
  
  Technologies are generally described for providing a signcryption scheme. In some examples, a method performed under control of a sender device may include calculating a public key of the sender device based on a system parameter, calculating a temporary public key of the sender device based on the system parameter, calculating a temporary common key of the sender device based on a temporary secret key of the sender device and a public key of a receiver device, calculating a ciphertext from a message based on the temporary common key and generating a signature of the sender device based on an intermediate parameter, the system parameter and the secret key of the sender device. The temporary secret key of the sender device, intermediate parameter and secret key of the sender device are engaged in a non-associative octonion ring.
  
  In some examples, a method performed under control of a receiver device may include calculating a public key of the receiver device based on a system parameter, calculating a temporary common key of the receiver device based on a temporary public key of the sender device and a secret key of a receiver device, deciphering the ciphertext based on the temporary common keys of receiver device, determining whether the digital signature received is generated by sender device. A temporary public key of the sender device, the secret key of the receiver device and the temporary common keys of the receiver device are engaged in a non-associative octonion ring.