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

Yuki NANJO; Masaaki SHIRASE; Takuya KUSAKA; Yasuyuki NOGAMI

doi:10.1587/transfun.2020TAL0002

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

Yuki NANJO, Masaaki SHIRASE, Takuya KUSAKA, Yasuyuki NOGAMI

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Summary :

A quadratic extension field (QEF) defined by F₁ = F_p[α]/(α²+1) is typically used for a supersingular isogeny Diffie-Hellman (SIDH). However, there exist other attractive QEFs F_i 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 F_i by using an isomorphic map F₁ → F_i.

Publication: IEICE TRANSACTIONS on Fundamentals 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

Authors

Yuki NANJO
  Okayama University
Masaaki SHIRASE
  Future University Hakodate
Takuya KUSAKA
  Okayama University
Yasuyuki NOGAMI
  Okayama University

Keyword

post-quantum cryptography, SIDH, quadratic extension field

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Yuki NANJO, Masaaki SHIRASE, Takuya KUSAKA, Yasuyuki NOGAMI, "A Construction Method of an Isomorphic Map between Quadratic Extension Fields Applicable for SIDH" in IEICE TRANSACTIONS on Fundamentals, vol. E103-A, no. 12, pp. 1403-1406, December 2020, doi: 10.1587/transfun.2020TAL0002.
Abstract: A quadratic extension field (QEF) defined by F₁ = F_p[α]/(α²+1) is typically used for a supersingular isogeny Diffie-Hellman (SIDH). However, there exist other attractive QEFs F_i 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 F_i by using an isomorphic map F₁ → F_i.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2020TAL0002/_p

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@ARTICLE{e103-a_12_1403,
author={Yuki NANJO, Masaaki SHIRASE, Takuya KUSAKA, Yasuyuki NOGAMI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A Construction Method of an Isomorphic Map between Quadratic Extension Fields Applicable for SIDH},
year={2020},
volume={E103-A},
number={12},
pages={1403-1406},
abstract={A quadratic extension field (QEF) defined by F₁ = F_p[α]/(α²+1) is typically used for a supersingular isogeny Diffie-Hellman (SIDH). However, there exist other attractive QEFs F_i 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 F_i by using an isomorphic map F₁ → F_i.},
keywords={},
doi={10.1587/transfun.2020TAL0002},
ISSN={1745-1337},
month={December},}

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TY - JOUR
TI - A Construction Method of an Isomorphic Map between Quadratic Extension Fields Applicable for SIDH
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1403
EP - 1406
AU - Yuki NANJO
AU - Masaaki SHIRASE
AU - Takuya KUSAKA
AU - Yasuyuki NOGAMI
PY - 2020
DO - 10.1587/transfun.2020TAL0002
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E103-A
IS - 12
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - December 2020
AB - A quadratic extension field (QEF) defined by F₁ = F_p[α]/(α²+1) is typically used for a supersingular isogeny Diffie-Hellman (SIDH). However, there exist other attractive QEFs F_i 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 F_i by using an isomorphic map F₁ → F_i.
ER -