An algorithm to select a secure twisted elliptic curve in cryptography
DOI:
https://doi.org/10.54654/isj.v1i15.832Keywords:
fault attacks, twist curve, Montgomery ladder, elliptic curve cryptosystemTóm tắt
Abstract—Fault attack is a powerful adjacency
channel attack technique to break cryptographic
schemes. On elliptic curve cryptography (ECC),
fault attacks can be divided into three types: safeerror attacks, weak-curve-based attacks, and
differential fault attacks. In the paper [1], the
author has presented the fault attack on the elliptic
curve cryptosystem based on the quadratic twist
curve and Proposed criteria to resist elliptic fault
attack on the elliptic curve. In this paper, we
propose an algorithm to choose a twist secure
elliptic curve and evaluate the paths published in
cryptographic standards around the world.
Tóm tắt— Tấn công gây lỗi là một kỹ thuật tấn
công kênh kề mạnh nhằm phá vỡ các lược đồ mật
mã. Tấn công gây lỗi lên mật mã đường cong
elliptic (ECC) có thể được chia thành ba loại: tấn
công safe-error, tấn công dựa trên đường cong yếu
và tấn công gây lỗi vi sai. Trong bài báo [1], nhóm
tác giả đã làm tường minh tấn công gây lỗi lên
ECC dựa vào đường cong xoắn và đề xuất tiêu chí
để chống lại tấn công gây lỗi trên ECC. Bài báo
này nhóm tác giả đề xuất thuật toán lựa chọn
đường elliptic an toàn xoắn và đánh giá an toàn
xoắn cho các đường cong elliptic đã công bố trong
một số chuẩn mật mã.
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References
Dinh Quoc Tien, Do Dai Chi, “Về tấn công gây
lỗi trên hệ mật đường cong elliptic dựa vào đường
cong xoắn", Journal Journal of Science and
Technology on Information security, No 2. 2016.
Accredited Standards Committee X9. "American
National Standard X9.62-2005, Public key
cryptography for the financial services industry:
the elliptic curve digital signature algorithm
(ECDSA)." 2005
B. Black, J. Bos, C. Costello, P. Longa, M.
Naehrig, “Elliptic Curve Cryptography (ECC)
Nothing Up My Sleeve (NUMS) Curves and
Curve Generation”,
https://datatracker.ietf.org/doc/html/draft-blacknumscurves-02
Certicom Research. " SEC 1: Elliptic Curve
Cryptography, Version 2.0." May 21, 2009.
Certicom Research, “SEC 2: Recommended
Elliptic Curve Domain Parameters”, 2010.
Daniel J. Bernstein, Tanja Lange, And Peter
Schwabe, “On the correct use of the negation map
in the Pollard rho method” ,
https://eprint.iacr.org/2011/003.pdf
Diego F. Aranha, Paulo S. L. M. Barreto,
Geovandro C. C. F. Pereira, And Jefferson E.
Ricardini, “A note on high-security generalpurpose elliptic curves”, 2013,
https://eprint.iacr.org/2013/647.pdf
ECC Brainpool, “ECC Brainpool Standard
Curves and Curve Generation”, 2010.
Hoheisel, G., Primzahlprobleme in der Analysis.
Sitz. Preuss. Akad. Wiss. 33 (1930), 580—588.
P.-A. Fouque, R. Lercier, D. Réal and F. Valette,
“Fault attack on elliptic curve Montgomery ladder
implementation, Fault Diagnosis and Tolerance in
Cryptography”, 2008. FDTC'08. 5th Workshop
on, IEEE,, 2008.
RFC 7836, “Guidelines on the Cryptographic
Algorithms to Accompany the Usage of
Standards GOST R 34.10-2012 and GOST R
11-2012”,
https://datatracker.ietf.org/doc/rfc7836/
Roberto M. Avanzi, Henri Cohen, Christophe
Doche, Gerhard Frey, Tanja Lange, Kim Nguyen,
Frederik Vercauteren, “Handbook of Elliptic and
Hyperelliptic Curve Cryptography”, 2005.
U.S. Department of Commerce/National Institute
of Standards and Technology,
“Recommendations for Discrete LogarithmBased Cryptography: Elliptic Curve Domain
Parameters”, FIPS-186-6 (draft) 2019.
Miracl, Miracl Cryptographic SDK,
https://github.com/miracl/MIRACL, Accessed on
/9/2020
B. Buhrow. (2010) yafu. Available:
http://sourceforge.net/projects/yafu/
Edlyn Teske (2000), “On Random Walks for
Pollard’s Rho Method”, Mathematichs of
Computation, Vol. 70, No. 234, pp. 809-825.
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