Falcone, Giovanni; Figula, Agota; Hannusch, Carolin On the generating matrices of Goppa codes over hyperelliptic curves. (English) Zbl 1498.14071 J. Ramanujan Math. Soc. 37, No. 3, 273-279 (2022). Reviewer: Marco Timpanella (Perugia) MSC: 14G50 94B27 PDFBibTeX XMLCite \textit{G. Falcone} et al., J. Ramanujan Math. Soc. 37, No. 3, 273--279 (2022; Zbl 1498.14071) Full Text: Link
Sutherland, Andrew Fast Jacobian arithmetic for hyperelliptic curves of genus 3. (English) Zbl 1516.14061 Scheidler, Renate (ed.) et al., ANTS XIII. Proceedings of the thirteenth algorithmic number theory symposium, University of Wisconsin-Madison, WI, USA, July 16–20, 2018. Berkeley, CA: Mathematical Sciences Publishers (MSP). Open Book Ser. 2, 425-442 (2019). MSC: 14H40 11G10 11G40 14H25 14K15 PDFBibTeX XMLCite \textit{A. Sutherland}, Open Book Ser. 2, 425--442 (2019; Zbl 1516.14061) Full Text: DOI arXiv
Hutter, Michael; Wenger, Erich Fast multi-precision multiplication for public-key cryptography on embedded microprocessors. (English) Zbl 1442.94039 J. Cryptology 31, No. 4, 1164-1182 (2018). MSC: 94A60 14G50 PDFBibTeX XMLCite \textit{M. Hutter} and \textit{E. Wenger}, J. Cryptology 31, No. 4, 1164--1182 (2018; Zbl 1442.94039) Full Text: DOI
Gallin, Gabriel; Celik, Turku Ozlum; Tisserand, Arnaud Architecture level optimizations for Kummer based HECC on FPGAs. (English) Zbl 1429.94058 Patra, Arpita (ed.) et al., Progress in cryptology – INDOCRYPT 2017. 18th international conference on cryptology in India, Chennai, India, December 10–13, 2017. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 10698, 44-64 (2017). MSC: 94A60 14G50 PDFBibTeX XMLCite \textit{G. Gallin} et al., Lect. Notes Comput. Sci. 10698, 44--64 (2017; Zbl 1429.94058) Full Text: DOI HAL
You, Lin; Han, Guangguo; Zeng, Jiwen; Sang, Yongxuan Computing the characteristic polynomials of a class of hyperelliptic curves for cryptographic applications. (English) Zbl 1213.94144 Math. Probl. Eng. 2011, Article ID 437541, 25 p. (2011). MSC: 94A60 14G50 PDFBibTeX XMLCite \textit{L. You} et al., Math. Probl. Eng. 2011, Article ID 437541, 25 p. (2011; Zbl 1213.94144) Full Text: DOI EuDML
Sutherland, Andrew V. A generic approach to searching for Jacobians. (English) Zbl 1208.14020 Math. Comput. 78, No. 265, 485-507 (2009). Reviewer: Dimitros Poulakis (Thessaloniki) MSC: 14G50 11Y16 11G20 11M38 PDFBibTeX XMLCite \textit{A. V. Sutherland}, Math. Comput. 78, No. 265, 485--507 (2009; Zbl 1208.14020) Full Text: DOI arXiv
Avanzi, R.; Thériault, N.; Wang, Z. Rethinking low genus hyperelliptic Jacobian arithmetic over binary fields: Interplay of field arithmetic and explicit formulæ. (English) Zbl 1146.14032 J. Math. Cryptol. 2, No. 3, 227-255 (2008). MSC: 14Q05 11G20 14H45 PDFBibTeX XMLCite \textit{R. Avanzi} et al., J. Math. Cryptol. 2, No. 3, 227--255 (2008; Zbl 1146.14032) Full Text: DOI
Jacobson, M. J.; Scheidler, R.; Stein, A. Cryptographic protocols on real hyperelliptic curves. (English) Zbl 1207.94056 Adv. Math. Commun. 1, No. 2, 197-221 (2007). MSC: 94A60 14H45 14Q05 PDFBibTeX XMLCite \textit{M. J. Jacobson} et al., Adv. Math. Commun. 1, No. 2, 197--221 (2007; Zbl 1207.94056) Full Text: DOI
Gaudry, P.; Thomé, E.; Thériault, N.; Diem, C. A double large prime variation for small genus hyperelliptic index calculus. (English) Zbl 1179.94062 Math. Comput. 76, No. 257, 475-492 (2007). MSC: 94A60 14G50 11Y16 11T71 PDFBibTeX XMLCite \textit{P. Gaudry} et al., Math. Comput. 76, No. 257, 475--492 (2007; Zbl 1179.94062) Full Text: DOI
Frey, Gerhard; Lange, Tanja Fast bilinear maps from the Tate-Lichtenbaum pairing on hyperelliptic curves. (English) Zbl 1143.94345 Hess, Florian (ed.) et al., Algorithmic number theory. 7th international symposium, ANTS-VII, Berlin, Germany, July 23–28, 2006. Proceedings. Berlin: Springer (ISBN 3-540-36075-1/pbk). Lecture Notes in Computer Science 4076, 466-479 (2006). MSC: 94A60 11T71 14G50 PDFBibTeX XMLCite \textit{G. Frey} and \textit{T. Lange}, Lect. Notes Comput. Sci. 4076, 466--479 (2006; Zbl 1143.94345) Full Text: DOI
Espinosa García, J.; Hernández Encinas, L.; Muñoz Masqué, J. A review on the isomorphism classes of hyperelliptic curves of genus 2 over finite fields admitting a Weierstrass point. (English) Zbl 1113.11036 Acta Appl. Math. 93, No. 1-3, 299-318 (2006). Reviewer: Fernando Torres (Campinas) MSC: 11G20 14H10 14G50 14H45 14H50 94A60 PDFBibTeX XMLCite \textit{J. Espinosa García} et al., Acta Appl. Math. 93, No. 1--3, 299--318 (2006; Zbl 1113.11036) Full Text: DOI
Kitamura, Izuru; Katagi, Masanobu; Takagi, Tsuyoshi A complete divisor class halving algorithm for hyperelliptic curve cryptosystems of genus two. (English) Zbl 1127.94347 Boyd, Colin (ed.) et al., Information security and privacy. 10th Australasian conference, ACISP 2005, Brisbane, Australia, July 4–6, 2005. Proceedings. Berlin: Springer (ISBN 3-540-26547-3/pbk). Lecture Notes in Computer Science 3574, 146-157 (2005). MSC: 94A60 14G50 PDFBibTeX XMLCite \textit{I. Kitamura} et al., Lect. Notes Comput. Sci. 3574, 146--157 (2005; Zbl 1127.94347) Full Text: DOI
Galbraith, Steven; Menezes, Alfred Algebraic curves and cryptography. (English) Zbl 1079.94014 Finite Fields Appl. 11, No. 3, 544-577 (2005). Reviewer: Richard A. Mollin (Calgary) MSC: 94A60 11T71 14G50 94-02 PDFBibTeX XMLCite \textit{S. Galbraith} and \textit{A. Menezes}, Finite Fields Appl. 11, No. 3, 544--577 (2005; Zbl 1079.94014) Full Text: DOI
Lange, Tanja Formulae for arithmetic on genus 2 hyperelliptic curves. (English) Zbl 1068.14065 Appl. Algebra Eng. Commun. Comput. 15, No. 5, 295-328 (2005). Reviewer: Juan Tena Ayuso (Valladolid) MSC: 14Q05 14G50 94A60 14H45 PDFBibTeX XMLCite \textit{T. Lange}, Appl. Algebra Eng. Commun. Comput. 15, No. 5, 295--328 (2005; Zbl 1068.14065) Full Text: DOI
Pelzl, Jan; Wollinger, Thomas; Paar, Christof Low cost security: explicit formulae for genus-4 hyperelliptic curves. (English) Zbl 1081.94033 Matsui, Mitsuru (ed.) et al., Selected areas in cryptography. 10th annual international workshop, SAC 2003, Ottawa, Canada, August 14–15, 2003. Revised papers. Berlin: Springer (ISBN 3-540-21370-8/pbk). Lecture Notes in Computer Science 3006, 1-16 (2004). MSC: 94A60 14G50 PDFBibTeX XMLCite \textit{J. Pelzl} et al., Lect. Notes Comput. Sci. 3006, 1--16 (2004; Zbl 1081.94033) Full Text: DOI
Choie, YoungJu; Jeong, Eunkyung Isomorphism classes of elliptic and hyperelliptic curves over finite fields \(\mathbb F_{(2g+1)^n}\). (English) Zbl 1082.11040 Finite Fields Appl. 10, No. 4, 583-614 (2004). Reviewer: Robert F. Lax (Baton Rouge) MSC: 11G20 14H25 14H45 11T71 14G15 94A60 PDFBibTeX XMLCite \textit{Y. Choie} and \textit{E. Jeong}, Finite Fields Appl. 10, No. 4, 583--614 (2004; Zbl 1082.11040) Full Text: DOI
Basiri, Abdolali; Enge, Andreas; Faugère, Jean-Charles; Gürel, Nicolas Implementing the arithmetic of \(C_{3,4}\) curves. (English) Zbl 1148.14304 Buell, Duncan (ed.), Algorithmic number theory. 6th international symposium, ANTS-VI, Burlington, VT, USA, June 13–18, 2004. Proceedings. Berlin: Springer (ISBN 3-540-22156-5/pbk). Lecture Notes in Computer Science 3076, 87-101 (2004). MSC: 14Q05 11G20 11Y16 13C20 PDFBibTeX XMLCite \textit{A. Basiri} et al., Lect. Notes Comput. Sci. 3076, 87--101 (2004; Zbl 1148.14304) Full Text: DOI