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Yongge Wang claimed to have designed efficient fully homomorphic encryption schemes using octonion algebras.

Reference: Yongge Wang. Algebra and Noise-Free Fully Homomorphic Encryption (FHE) Schemes, IACR ePrint, https://eprint.iacr.org/2016/068.pdf Octonion ^{dead link}

The paper of Wang is now withdrawn. As there is not clear why this happened, maybe the chapter on crypto applications should be more cautious. Isbromberg ( talk) 19:34, 15 April 2016 (UTC) reply

The section was removed from the article. Use in encryption may be described and documented and returned to the article. — Rgdboer ( talk) 00:47, 20 July 2016 (UTC) reply

2nd formula on page... (q+Qe)(r+Re) = (qr+yR*Q)+(Rq+qr*)e

...should be... (q+Qe)(r+Re) = (qr+yR*Q)+(Rq+Qr*)e

meaning : last q should be Q

no changes made. Peawormsworth ( talk) 01:49, 8 June 2020 (UTC) reply

I think this comment is missleading: the algebra devised by Furey is that of complex quaternions (a quaternion with complex components) which is eigth dimensional, of course, but it is not the same as Cayley - Dickson algebra with eight dimensions. Complex quaternions have nilpotents, idempotents ^[1] and many other zero divisors, while Cayley - Dickson octonions are a division algebra. — Preceding unsigned comment added by Crodrigue1 ( talk • contribs) 02:06, 30 January 2021 (UTC) reply