In this paper, we propose some Diffie-Hellman type key exchange protocols using isogenies of elliptic curves. The first method which uses the endomorphism ring of an ordinary elliptic curve $ E $, is a straightforward generalization of elliptic curve Diffie-Hellman key exchange. The method uses commutativity of the endomorphism ring $ End(E) $. Then using dual isogenies, we propose a second method. This case uses the endomorphism ring of an elliptic curve $ E $, which can be ordinary or supersingular. We extend this method using isogenies between two elliptic curves $ E $ and $ E' $. Our methods have the security level of that of [D. Jao and L. De Feo, Towards quantum-resistant cryptosystems from supersingular elliptic curve isogenies, J. Math. Cryptol. 8 (2014), no. 3, 209--247], with the advantage of transmitting less information between two parties.
Daghigh, H., Khodakaramian Gilan, R., & Seifi Shahpar, F. (2017). Diffie-Hellman type key exchange protocols based on isogenies. Bulletin of the Iranian Mathematical Society, 43(Issue 4 (Special Issue)), 77-88.
MLA
Daghigh, H., Khodakaramian Gilan, R., & Seifi Shahpar, F. "Diffie-Hellman type key exchange protocols based on isogenies", Bulletin of the Iranian Mathematical Society, 43, Issue 4 (Special Issue), 2017, 77-88.
HARVARD
Daghigh H., Khodakaramian Gilan R., Seifi Shahpar F. (2017). 'Diffie-Hellman type key exchange protocols based on isogenies', Bulletin of the Iranian Mathematical Society, 43(Issue 4 (Special Issue)), pp. 77-88.
CHICAGO
H. Daghigh, R. Khodakaramian Gilan & F. Seifi Shahpar, "Diffie-Hellman type key exchange protocols based on isogenies," Bulletin of the Iranian Mathematical Society, 43 Issue 4 (Special Issue) (2017): 77-88,
VANCOUVER
Daghigh H., Khodakaramian Gilan R., Seifi Shahpar F. Diffie-Hellman type key exchange protocols based on isogenies. BIMS. 2017;43(Issue 4 (Special Issue)):77-88.
