A Construction Method of an Isomorphic Map between Quadratic Extension Fields Applicable for SIDH

Yuki NANJO  Masaaki SHIRASE  Takuya KUSAKA  Yasuyuki NOGAMI  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E103-A    No.12    pp.1403-1406
Publication Date: 2020/12/01
Publicized: 2020/07/06
Online ISSN: 1745-1337
DOI: 10.1587/transfun.2020TAL0002
Type of Manuscript: Special Section LETTER (Special Section on Information Theory and Its Applications)
Category: Cryptography and Information Security
post-quantum cryptography,  SIDH,  quadratic extension field,  

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A quadratic extension field (QEF) defined by F1 = Fp[α]/(α2+1) is typically used for a supersingular isogeny Diffie-Hellman (SIDH). However, there exist other attractive QEFs Fi that result in a competitive or rather efficient performing the SIDH comparing with that of F1. To exploit these QEFs without a time-consuming computation of the initial setting, the authors propose to convert existing parameter sets defined over F1 to Fi by using an isomorphic map F1Fi.