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

A construction method of an isomorphic map between quadratic extension fields applicable for SIDH

Yuki NANJO, Masaaki SHIRASE, Takuya KUSAKA, Yasuyuki NOGAMI

Research output: Contribution to journal › Article › peer-review

Abstract

A quadratic extension field (QEF) defined by F1 = Fp[α]=(α2 +1) is typically used for a supersingular isogeny Diffe-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 F1 → Fi.

Original language	English
Pages (from-to)	1403-1406
Number of pages	4
Journal	IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Volume	E103A
Issue number	12
DOIs	https://doi.org/10.1587/transfun.2020TAL0002
Publication status	Published - Dec 2020

Keywords

Post-quantum cryptography
Quadratic extension field
SIDH

ASJC Scopus subject areas

Signal Processing
Computer Graphics and Computer-Aided Design
Electrical and Electronic Engineering
Applied Mathematics

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10.1587/transfun.2020TAL0002

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title = "A construction method of an isomorphic map between quadratic extension fields applicable for SIDH",

abstract = "A quadratic extension field (QEF) defined by F1 = Fp[α]=(α2 +1) is typically used for a supersingular isogeny Diffe-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 F1 → Fi.",

keywords = "Post-quantum cryptography, Quadratic extension field, SIDH",

author = "Yuki NANJO and Masaaki SHIRASE and Takuya KUSAKA and Yasuyuki NOGAMI",

note = "Funding Information: This research was supported by JSPS KAKENHI Grant Numbers 19J2108611 and 19K11966.",

year = "2020",

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AU - SHIRASE, Masaaki

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AU - NOGAMI, Yasuyuki

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