Details
Title
Arithmetic Using Compression on Elliptic Curves in Huff’s Form and Its ApplicationsJournal title
International Journal of Electronics and TelecommunicationsYearbook
2021Volume
vol. 67Issue
No 2Authors
Affiliation
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, PolandKeywords
Huff’s curves ; Isogeny-based cryptography ; Compression functions on elliptic curvesDivisions of PAS
Nauki TechniczneCoverage
193-200Publisher
Polish Academy of Sciences Committee of Electronics and TelecommunicationsBibliography
[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.