, If g = 3r + 4 and (f, f ) is such that 2r ? f ? g
Monodromy of the p-rank strata of the moduli space of curves, International Mathematics Research Notices. IMRN, p.53, 2008. ,
The p-rank strata of the moduli space of hyperelliptic curves, Advances in Mathematics, vol.227, issue.5, pp.1846-1872, 2011. ,
Fast and flexible hardware support for ECC over multiple standard prime fields, IEEE Transactions on Very Large Scale Integration (VLSI) Systems, vol.22, pp.2661-2674, 2014. ,
Geometry of Algebraic Curves, vol.1, 1985. ,
Flexible hardware architectures for curve-based cryptography, IEEE International Symposium on Circuits and Systems (ISCAS 2006), pp.4839-4842, 2006. ,
Prym varieties: a survey, Theta functions, vol.49, pp.607-620, 1987. ,
Cohomology of arrangements and moduli spaces, 2016. ,
Explicit-formulas database ,
Hyper-and-elliptic-curve cryptography, LMS Journal of Computation and Mathematics, vol.17, pp.181-202, 2014. ,
The partial differential equations for the hyperelliptic ?-and ?-functions, American Journal of Mathematics, vol.21, issue.2, pp.107-125, 1899. ,
Fast cryptography in genus 2, Journal of Cryptology, vol.29, issue.1, pp.28-60, 2016. ,
The Magma algebra system I: The user language, Computational algebra and number theory, vol.24, pp.235-265, 1993. ,
The p-rank of ramified covers of curves, Compositio Mathematica, vol.126, issue.3, pp.295-322, 2001. ,
The arithmetic of Prym varieties in genus 3, Compositio Mathematica, vol.144, issue.2, pp.317-338, 2008. ,
Computing in the Jacobian of a hyperelliptic curve, Mathematics of Computation, vol.48, issue.177, pp.95-101, 1987. ,
Characterizing curves by their odd Theta-characteristics, Journal für die reine und angewandte Mathematik, pp.101-135, 2002. ,
Recovering plane curves from their bitangents, Journal of Algebraic Geometry, vol.12, issue.2, pp.225-244, 2003. ,
Prolegomena to a Middlebrow Arithmetic of Curves of Genus 2, London Mathematical Society Lecture Note Series, vol.230, 1996. ,
Non-ordinary curves with a Prym variety of low p-rank, Women in Numbers Europe II, pp.117-158, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01579544
Tritangents and their space sextics ,
, Syzygies of torsion bundles and the geometry of the level modular variety over M g. Inventiones Mathematicae, vol.194, pp.73-118, 2013.
Sequences of numbers generated by addition in formal groups and new primality and factorization tests, Advances in Applied Mathematics, vol.7, issue.4, pp.385-434, 1986. ,
Fast, uniform scalar multiplication for genus 2 Jacobians with fast Kummers, Selected Areas in Cryptography-SAC 2016, pp.465-481, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01353480
Algebraic Geometry and Theta Functions, 1961. ,
Handbook of Elliptic and Hyperelliptic Curve Cryptography, 2006. ,
Applications des fonctions thêta à la cryptographie sur courbes hyperelliptiques, 2011. ,
Lines on del Pezzo surfaces with in characteristic = 2, Communications in Algebra, vol.27, issue.3, pp.1197-1206, 1999. ,
Plane quartics: the universal matrix of bitangents, Israel Journal of Mathematics, vol.217, pp.111-138, 2017. ,
Surfaces de del Pezzo, Séminaire sur les Singularités des Surfaces, pp.23-69, 1980. ,
DOI : 10.1007/bfb0085875
, The Sage Developers. SageMath, the Sage Mathematics Software System, 2017.
New directions in cryptography, IEEE Transactions on Information Theory, vol.22, issue.6, pp.644-654, 2006. ,
Classical Algebraic Geometry: A Modern View, 2012. ,
Montgomery scalar multiplication for genus 2 curves, 6th International Symposium, ANTS-VI, vol.3076, pp.153-168, 2004. ,
URL : https://hal.archives-ouvertes.fr/hal-00457826
An elementary proof of Thomae's formulae, Online Journal of Analytic Combinatorics, vol.3, 2008. ,
On efficient implementation of FPGA-based hyperelliptic curve cryptosystems, Computers and Electrical Engineering, vol.33, issue.5, pp.349-366, 2007. ,
Thomae type formulae for singular Z N curves, Letters in Mathematical Physics, vol.76, issue.2, pp.187-214, 2006. ,
Complete subvarieties of moduli spaces and the Prym map, Journal für die reine und angewandte Mathematik, vol.573, pp.117-137, 2004. ,
HECC goes embedded: An area-efficient implementation of HECC, Selected Areas in Cryptography, pp.387-400, 2009. ,
An explicit solution to the weak Schottky problem, 2017. ,
On the Riemann-Jacobi Formula. 2]: [Nachrichten der Akademie der Wissenschaften in Göttingen, 1979. ,
Über die Form der Argumente der Thetafunction und über die Bestimmung von ?(0, 0...0) als Function der Klassenmoduln, Journal für die reine und angewandte Mathematik, vol.73, pp.305-324, 1871. ,
Architecture level optimizations for Kummer based HECC on FPGAs, of International Conference in Cryptology in India : Progress in Cryptology-INDOCRYPT 2017, vol.10698, pp.44-64, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01614063
Algorithmique des courbes hyperelliptiques et applications à la cryptologie, 2000. ,
URL : https://hal.archives-ouvertes.fr/tel-00514848
Fast genus 2 arithmetic based on Theta functions, Journal of Mathematical Cryptology, vol.1, issue.3, pp.243-265, 2007. ,
URL : https://hal.archives-ouvertes.fr/inria-00000625
Principles of Algebraic Geometry, 1978. ,
Gradients of odd theta functions, Journal für die reine und angewandte Mathematik, issue.573, pp.45-59, 2004. ,
Theta functions of arbitrary order and their derivatives, Journal für die reine und angewandte Mathematik, issue.590, pp.31-43, 2006. ,
On the Torelli problem and Jacobian Nullwerte in genus three, The Michigan Mathematical Journal, vol.60, issue.1, pp.51-65, 2011. ,
Ultra high performance ECC over NIST primes on commercial FPGAs, Cryptographic Hardware and Embedded Systems-CHES 2008, pp.62-78, 2008. ,
On some geometric constructions related to theta characteristics, Contributions to Automorphic Forms, Geometry, and Number, 2004. ,
Theta-characteristics on algebraic curves, Transactions of the American Mathematical Society, vol.271, issue.2, pp.611-638, 1982. ,
Algebraic Geometry, 1977. ,
Supersingular curves of genus two and class numbers, Compositio Mathematica, vol.57, issue.2, pp.127-152, 1986. ,
Arithmetic variety of moduli for genus two, Annals of Mathematics, Second Series, vol.72, pp.612-649, 1960. ,
Hyperelliptic curve coprocessors on a FPGA, Information Security Applications, pp.360-374, 2005. ,
Hyperelliptic cryptosystems, Journal of Cryptology, vol.1, issue.3, pp.139-150, 1989. ,
Remarks on Takase's paper "a generalization of Rosenhain's normal form with an application, Proceedings of the Japan Academy, Series A, Mathematical Sciences, vol.73, issue.1, pp.12-13, 1997. ,
Rational Curves on Algebraic Varieties, vol.32, 1996. ,
Superspecial curves of genus 4 in small characteristic, Finite Fields and Their Applications, vol.45, pp.131-169, 2017. ,
Real space sextics and their tritangents, 2017. ,
DOI : 10.1145/3208976.3208977
URL : http://dl.acm.org/ft_gateway.cfm?id=3208977&type=pdf
Speeding the pollard and elliptic curve methods of factorization, Mathematics of Computation, vol.48, pp.243-243, 1987. ,
DOI : 10.2307/2007888
URL : http://www.ams.org/mcom/1987-48-177/S0025-5718-1987-0866113-7/S0025-5718-1987-0866113-7.pdf
Hardware and arithmetic for hyperelliptic curves cryptography ,
High-performance architecture for elliptic curve cryptography over prime fields on FPGAs, Interdisciplinary Information Sciences, vol.18, issue.2, pp.167-173, 2012. ,
Montgomery addition for genus two curves, Algorithmic Number Theory, vol.3076, pp.309-317, 2004. ,
DOI : 10.1007/978-3-540-24847-7_23
Formulae for arithmetic on genus 2 hyperelliptic curves, vol.15, pp.295-328, 2005. ,
DOI : 10.1007/s00200-004-0154-8
URL : http://www.hyperelliptic.org/tanja/preprints/expl.pdf
Any smooth plane quartic can be reconstructed from its bitangents, Israel Journal of Mathematics, vol.146, issue.1, pp.371-379, 2005. ,
DOI : 10.1007/bf02773542
Effective reconstruction of generic genus 4 curves from their theta hyperplanes, International Mathematics Research Notices, issue.19, pp.9472-9485, 2015. ,
DOI : 10.1093/imrn/rnu235
URL : http://arxiv.org/pdf/1001.1237
Fast multiplication on elliptic curves over GF(2m) without precomputation, Cryptographic Hardware and Embedded Systems, pp.316-327, 1999. ,
, Arithmetic on abelian and Kummer varieties. Finite Fields and Their Applications, vol.39, pp.130-158, 2016.
DOI : 10.1016/j.ffa.2016.01.009
URL : https://hal.archives-ouvertes.fr/hal-01057467
A high-speed elliptic curve cryptographic processor for generic curves over GF(p), Revised Selected Papers on Selected Areas in Cryptography-SAC 2013, vol.8282, pp.421-437, 2014. ,
DOI : 10.1007/978-3-662-43414-7_21
URL : https://link.springer.com/content/pdf/10.1007%2F978-3-662-43414-7_21.pdf
Cubic forms ,
, , 1989.
An elementary introduction to hyperelliptic curves, Algebraic Aspects of Cryptography, 1998. ,
On the equations defining abelian varieties. I. Inventiones mathematicae, vol.1, pp.287-354, 1966. ,
Tata Lectures on Theta I, Birkhäuser Basel, vol.28, 1983. ,
, Tata Lectures on Theta II. Birkhäuser Basel, 2007.
, Tata Lectures on Theta II. Modern Birkhäuser Classics, 2007.
A new proof of a Thomae-like formula for non hyperelliptic genus 3 curves, Arithmetic, geometry, cryptography and coding theory, vol.686, pp.137-155, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01128237
Efficient elliptic curve cryptosystems from a scalar multiplication algorithm with recovery of the y-coordinate on a Montgomery-form elliptic curve, Cryptographic Hardware and Embedded Systems-CHES 2001, pp.126-141, 2001. ,
On the existence of ordinary and almost ordinary Prym varieties, 2017. ,
Theta functions with applications to Riemann surfaces, 1974. ,
µKummer: efficient hyperelliptic signatures and key exchange on microcontrollers, Cryptographic Hardware and Embedded Systems-CHES 2016, volume 9813 of Cryptographic Hardware and Embedded Systems-CHES 2016, 2016. ,
Theorie der Abel'schen Functionen, Journal für die reine und angewandte Mathematik, vol.54, pp.101-155, 1857. ,
Über das Verschwinden der ?-Functionen, Journal für die reine und angewandte Mathematik, vol.65, pp.161-172, 1866. ,
DOI : 10.1515/crll.1866.65.161
URL : https://zenodo.org/record/1575902/files/article.pdf
Point counting on genus 3 non hyperelliptic curves, Algorithmic Number Theory Symposium (ANTS), 2004. ,
URL : https://hal.archives-ouvertes.fr/hal-01099875
Claudio Rocchini's Home Page ,
Abhandlung über die Functionen zweier Variabler mit vier Perioden. Ostwald's Klassiker der Exacten Wissenschaften, vol.65, p.1895 ,
Superscalar coprocessor for high-speed curve-based cryptography, Cryptographic Hardware and Embedded Systems-CHES 2006, pp.415-429, 2006. ,
Modular varieties with level 2 theta structure, American Journal of Mathematics, vol.116, issue.6, pp.1489-1511, 1994. ,
Sur la topologie des variétés algébriques en caractéristique p, Symposium internacional de topología algebraica, pp.24-53, 1958. ,
Flexible hardware implementation of hyperelliptic curves cryptosystem, International Journal of Computer Science and Information Security, vol.14, issue.4, p.1, 2016. ,
Thomae's formulae for non-hyperelliptic curves and spinorial square roots of theta-constants on the moduli space of curves, 2008. ,
A formula for the Cartier operator on plane algebraic curves, Journal für die reine und angewandte Mathematik, vol.377, pp.49-64, 1987. ,
A generalization of Rosenhain's normal form for hyperelliptic curves with an application, Proceedings of the Japan Academy, Series A, Mathematical Sciences, vol.72, issue.7, pp.162-165, 1996. ,
0) durch die Klassenmoduln algebraischer Funktionen, Journal für die reine und angewandte Mathematik, vol.71, pp.201-222, 1870. ,
DOI : 10.1515/crll.1870.71.201
The fibre of the Prym map in genus three, Mathematische Annalen, vol.276, issue.3, pp.433-448, 1987. ,
Theorie der Abel'schen Funktionen vom Geschlecht 3, 1876. ,
Constructing hyperelliptic curves of genus 2 suitable for cryptography, Mathematics of Computation, vol.72, pp.435-458, 2003. ,
, Untersuchungen über Thetafunctionen. B. G. Teubner, p.1895
Software and hardware implementation of hyperelliptic curve cryptosystems, 2004. ,
On the Jacobian varieties of hyperelliptic curves over fields of characteristic p > 2, Journal of Algebra, vol.52, issue.2, pp.378-410, 1978. ,
Del Pezzo surfaces of degree 1 and Jacobians, Mathematische Annalen, vol.340, issue.2, pp.407-435, 2008. ,
On hyperelliptic ?-functions with rational characteristics, American Journal of Mathematics, vol.50, issue.3, pp.315-344, 1928. ,