Szczegóły

Tytuł artykułu

Arithmetic Using Compression on Elliptic Curves in Huff’s Form and Its Applications

Tytuł czasopisma

International Journal of Electronics and Telecommunications

Rocznik

2021

Wolumin

vol. 67

Numer

No 2

Autorzy

Afiliacje

Dryło, Robert : Institute of Mathematics and Cryptology, Faculty of Cybernetics, Military University of Technology, Warsaw, Poland ; Kijko, Tomasz : Institute of Mathematics and Cryptology, Faculty of Cybernetics, Military University of Technology, Warsaw, Poland ; Wroński, Michał : Institute of Mathematics and Cryptology, Faculty of Cybernetics, Military University of Technology, Warsaw, Poland

Słowa kluczowe

Huff’s curves ; Isogeny-based cryptography ; Compression functions on elliptic curves

Wydział PAN

Nauki Techniczne

Zakres

193-200

Wydawca

Polish Academy of Sciences Committee of Electronics and Telecommunications

Bibliografia

[1] D. J. Bernstein and T. Lange, “Montgomery curves and the montgomery ladder.” IACR Cryptol. ePrint Arch., vol. 2017, p. 293, 2017.
[2] C. Costello and B. Smith, “Montgomery curves and their arithmetic,” Journal of Cryptographic Engineering, vol. 8, no. 3, pp. 227–240, 2018.
[3] P. L. Montgomery, “Speeding the pollard and elliptic curve methods of factorization,” Mathematics of Computation, vol. 48, pp. 243–264, 1987.
[4] E. Brier and M. Joye, “Weierstraß elliptic curves and side-channel attacks,” in International workshop on public key cryptography. Springer, 2002, pp. 335–345.
[5] R. R. Farashahi and S. G. Hosseini, “Differential addition on twisted edwards curves,” in Australasian Conference on Information Security and Privacy. Springer, 2017, pp. 366–378.
[6] B. Justus and D. Loebenberger, “Differential addition in generalized edwards coordinates,” in International Workshop on Security. Springer, 2010, pp. 316–325.
[7] R. R. Farashahi and M. Joye, “Efficient arithmetic on hessian curves,” in International Workshop on Public Key Cryptography. Springer, 2010, pp. 243–260.
[8] W. Castryck and F. Vercauteren, “Toric forms of elliptic curves and their arithmetic,” Journal of Symbolic Computation, vol. 46, no. 8, pp. 943–966, 2011.
[9] R. Dryło, T. Kijko, and M. Wro´nski, “Determining formulas related to point compression on alternative models of elliptic curves,” Fundamenta Informaticae, vol. 169, no. 4, pp. 285–294, 2019.
[10] K. Okeya and K. Sakurai, “Efficient elliptic curve cryptosystems from a scalar multiplication algorithm with recovery of the y-coordinate on a montgomery-form elliptic curve,” in International Workshop on Cryptographic Hardware and Embedded Systems. Springer, 2001, pp. 126–141.
[11] M. Joye, M. Tibouchi, and D. Vergnaud, “Huff’s model for elliptic curves,” in International Algorithmic Number Theory Symposium. Springer, 2010, pp. 234–250.
[12] H. Wu and R. Feng, “Elliptic curves in huff’s model,” Wuhan University Journal of Natural Sciences, vol. 17, no. 6, pp. 473–480, 2012.
[13] T. Oliveira, J. L´opez, H. Hıs¸ıl, A. Faz-Hern´andez, and F. Rodr´ıguez- Henr´ıquez, “How to (pre-) compute a ladder,” in International Conference on Selected Areas in Cryptography. Springer, 2017, pp. 172–191.
[14] R. R. Farashahi and S. G. Hosseini, “Differential addition on binary elliptic curves,” in International Workshop on the Arithmetic of Finite Fields. Springer, 2016, pp. 21–35.
[15] D. Moody and D. Shumow, “Analogues of v´elu’s formulas for isogenies on alternate models of elliptic curves,” Mathematics of Computation, vol. 85, no. 300, pp. 1929–1951, 2016.
[16] C. Costello and H. Hisil, “A simple and compact algorithm for sidh with arbitrary degree isogenies,” in International Conference on the Theory and Application of Cryptology and Information Security. Springer, 2017, pp. 303–329.
[17] D. Jao, R. Azarderakhsh, M. Campagna, C. Costello, L. Feo, B. Hess, A. Jalali, B. Koziel, B. LaMacchia, P. Longa, M. Naehrig, G. Pereira, J. Renes, V. Soukharev, and D. Urbanik, “Supersingular isogeny key encapsulation,” 04 2019.
[18] D. Jeon, C. H. Kim, and Y. Lee, “Families of elliptic curves over quartic number fields with prescribed torsion subgroups,” Mathematics of Computation, vol. 80, no. 276, pp. 2395–2410, 2011.

Data

2021.05.25

Typ

Article

Identyfikator

DOI: 10.24425/ijet.2021.135964 ; eISSN 2300-1933 (since 2013) ; ISSN 2081-8491 (until 2012)

Źródło

International Journal of Electronics and Telecommunications; 2021; vol. 67; No 2; 193-200
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