[. Lochter, M. Et, M. , and J. , Elliptic Curve Cryptography (ECC) Brainpool Standard Curves and Curve Generation Internet Engineering Task Force, mar, RFC, vol.5639, 2010.
DOI : 10.17487/rfc5639

URL : http://info.internet.isi.edu/in-notes/pdfrfc/rfc5639.txt.pdf

E. B. Barker, SP 800-57. Recommendation for Key Management, p.127, 2016.

[. Barker, E. B. Et, K. , and J. M. , SP 800-90A Rev.1. Recommendation for Random Number Generation Using Deterministic Random Bit Generators, Rapp. tech, vol.93, 2015.

T. Bibliothèques-logicielles-[-gmp-]-granlund, T. Et, . Gmp, . Team, . Gnu et al., The GNU Multiple Precision Arithmetic Library

. Magma, W. Bosma, J. Cannon, P. Et, and C. , « The Magma algebra system. I. The user language » Computational algebra and number theory, In : J. Symbolic Comput, vol.24, pp.3-4, 1993.

[. Gp, version 2.7.5. available from http://pari.math.u-bordeaux.fr/. The PARI Group, p.92

. Sage and T. S. Developers, Sage Mathematics Software (Version x.y.z)

[. Baignères, T. Delerablée, C. Finiasz, M. Goubin, L. Lepoint et al., « Trap Me If You Can -Million Dollar Curve, 2016.

[. Bosselaers, A. Govaerts, R. Et, V. , and J. , Comparison of three modular reduction functions, Advances in Cryptology?CRYPTO'93, pp.175-186, 1994.
DOI : 10.1007/3-540-48329-2_16

. Bj03a, O. Billet, J. Et, and M. , The Jacobi model of an elliptic curve and side-channel analysis Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, pp.34-42, 2003.

]. Bj03b, E. Brier, J. Et, M. De, F. et al., « Fast Point Multiplication on Elliptic Curves through Isogenies. » In : AAECC. Sous la dir, Lecture Notes in Computer Science, vol.54, pp.43-50, 2003.

. Bl, D. Bernstein, L. Et, and T. , Explicit-formulas database URL : http://www.hyperelliptic.org/EFD, p.36

. Bl07a, D. J. Bernstein, L. Et, and T. , Faster addition and doubling on elliptic curves, Advances in cryptology?ASIACRYPT 2007, pp.29-50, 2007.

]. Bl07b, D. J. Bernstein, L. Et, and T. , Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, pp.20-27, 2007.

[. Barreto, P. S. Lynn, B. Et, S. , and M. , Constructing Elliptic Curves with Prescribed Embedding Degrees, pp.257-267, 2003.
DOI : 10.1007/3-540-36413-7_19

[. Blum, T. Et, P. , and C. , High-radix Montgomery modular exponentiation on reconfigurable hardware, IEEE Transactions on Computers, vol.50, issue.7, pp.759-764, 2001.
DOI : 10.1109/12.936241

[. Baktir, S. Et, S. , and B. , Optimal tower fields, IEEE Transactions on Computers, vol.53, issue.10, pp.1231-1243, 2004.
DOI : 10.1109/TC.2004.83

[. Benger, N. Et, S. , M. «. Hasan, M. Et et al., Constructing Tower Extensions of Finite Fields for Implementation of Pairing-Based Cryptography Arithmetic of Finite Fields, Lecture Notes in Computer Science, vol.608776, pp.180-195, 2010.

[. , D. V. Et, C. , and G. , « Sequences of numbers generated by addition in formal groups and new primality and factorization tests, Advances in Applied Mathematics, vol.7425, pp.1986-87

[. , J. W. Et, F. , and E. , Prolegomena to a middlebrow arithmetic of curves of genus 2. T. 230, 1996.

H. Cohen, A. Miyaji, O. Et, and T. , Efficient Elliptic Curve Exponentiation Using Mixed Coordinates, Advances in Cryptology?ASIACRYPT'98, pp.51-65, 1998.
DOI : 10.1007/3-540-49649-1_6

]. Coh+12, H. Cohen, G. Frey, R. Avanzi, C. Doche et al., Handbook of Elliptic and Hyperelliptic Curve Cryptography, Second Edition, pp.20-66, 2012.

]. Cor99 and J. «. Coron, Resistance against differential power analysis for elliptic curve cryptosystems, Cryptographic Hardware and Embedded Systems, pp.292-302, 1999.

]. Cox89 and D. A. Cox, « Primes of the Form x 2 + ny 2, 1989.

J. Dhe98-]-dhem, Design of an efficient public-key cryptographic library for RISC-based smart cards, 1998.

S. Duq07-]-duquesne, Improving the arithmetic of elliptic curves in the Jacobi model, Information Processing Letters, vol.104, issue.3, pp.101-105, 2007.
DOI : 10.1016/j.ipl.2007.05.012

. Edw07 and H. Edwards, « A normal form for elliptic curves, In : Bulletin of the American Mathematical Society, vol.44337, pp.393-422, 2007.

[. Eldridge, S. E. Et, W. , and C. D. , Hardware implementation of Montgomery's modular multiplication algorithm, IEEE Transactions on Computers, vol.42, issue.6, pp.693-699, 1993.
DOI : 10.1109/12.277287

[. , T. Et, P. , C. Oswald, E. Et et al., « Ultra High Performance ECC over NIST Primes on Commercial FPGAs, Lecture Notes in Computer Science, vol.5154102, pp.62-78, 2008.

H. Hisil, G. Carter, D. Et, E. Srinathan, K. Rangan et al., New Formulae for Efficient Elliptic Curve Arithmetic, Progress in Cryptology ? INDOCRYPT, pp.138-151, 2007.
DOI : 10.1007/978-3-540-77026-8_11

[. , G. Et, Q. , and J. Montgomery, Exponentiation with no Final Subtractions : Improved Results, Lecture Notes in Computer Science, vol.106, pp.293-301, 1965.

H. Hwcd09b-]-hisil, K. K. Wong, G. Carter, D. Et, and E. , Faster group operations on elliptic curves, Proceedings of the Seventh Australasian Conference on Information Security, pp.7-20, 2009.

H. H?s10-]-hisil, Elliptic curves, group law, and efficient computation ». phd, 2010.

[. , D. Miller, S. D. Venkatesan, and R. , Expander graphs based on GRH with an application to elliptic curve cryptography, Journal of Number Theory, vol.129652, pp.1491-1504, 2009.

J. Jq01a, M. Et, Q. , and J. , « Hessian elliptic curves and side-channel attacks ». In : Cryptographic Hardware and Embedded Systems?CHES, pp.402-410, 2001.

[. , M. Et, Q. , and J. «. , Hessian Elliptic Curves and Side-Channel Attacks, Lecture Notes in Computer Science, vol.40, pp.402-410, 2001.

]. Kar95 and A. A. Karatsuba, « The complexity of computations, Proceedings of the Steklov Institute of Mathematics-Interperiodica Translation, pp.169-183, 1995.

[. Koblitz, N. Et, M. , and A. , Pairing-Based Cryptography at High Security Levels, Cryptography and Coding : 10th IMA International Conference Proceedings. T. 3796, p.13, 2005.
DOI : 10.1007/11586821_2

]. Knu97 and D. E. Knuth, The Art of Computer Programming) : Seminumerical Algorithms, 1997.

]. Kob87 and N. Koblitz, Elliptic curve cryptosystems, Mathematics of computation 48, pp.203-209, 1987.

]. Koh96 and D. Kohel, Endomorphism rings of elliptic curves over finite fields, Thèse de doct, 1996.

[. Lim, C. H. Et, H. , H. S. , H. Et et al., Fast Implementation of Elliptic Curve Arithmetic in GF(p n ), Lecture Notes in Computer Science, vol.75, pp.405-421, 1751.
DOI : 10.1007/978-3-540-46588-1_27

[. , R. Et, N. , and H. , Finite fields. T. 20. Encyclopaedia of mathematics and its applications, 1997.

[. Lenstra, A. K. Et, W. , and B. , « A random zoo : sloth, unicorn, and trx, » In : IACR Cryptology ePrint Archive, vol.2015, pp.366-411, 2015.

]. Mel07 and N. Meloni, « New point addition formulae for ECC applications Arithmetic of Finite Fields, pp.189-201, 2007.

[. Ma, Y. Liu, Z. Pan, W. Et, J. et al., A High-Speed Elliptic Curve Cryptographic Processor for Generic Curves over $$\mathrm{GF}(p)$$, Lecture Notes in Computer Science, vol.8282102, pp.421-437, 2013.
DOI : 10.1007/978-3-662-43414-7_21

M. Mon85 and P. L. , « Modular multiplication without trial division, Mathematics of computation 44, pp.519-521, 1985.

M. Mon87 and P. L. , « Speeding the Pollard and elliptic curve methods of factorization, Mathematics of computation 48, pp.243-264, 1987.

[. Menezes, A. J. Okamoto, T. Vanstone, and S. , Reducing elliptic curve logarithms to logarithms in a finite field, IEEE Transactions on, vol.39549, issue.50, pp.1639-1646, 1993.

[. Orlando, G. Et, P. , C. «. Scalable, and G. , Elliptic Curve Processor Architecture for Programmable Hardware, Lecture Notes in Computer Science Generators, vol.102, pp.348-363, 2001.
DOI : 10.1007/3-540-44709-1_29

URL : http://www.crypto.ruhr-uni-bochum.de/Publikationen/texte/ecpp_ches.pdf

. Oru95 and H. Orup, Simplifying Quotient Determination in High-Radix Modular Multiplication, IEEE Symposium on Computer Arithmetic, pp.193-199, 1995.

J. Plu11-]-plut, On Various Families of Twisted Jacobi Quartics. » In : Selected Areas in Cryptography, Lecture Notes in Computer Science, pp.373-383, 2011.

. Pol78 and J. M. Pollard, Monte Carlo methods for index computation (mod p), Mathematics of computation 32, pp.918-924, 1978.

[. , J. Costello, C. Et, B. , and L. , Complete addition formulas for prime order elliptic curves, » In : IACR Cryptology ePrint Archive, vol.201528, p.1060, 2015.

[. , R. L. Shamir, A. Et, A. , and L. , « A method for obtaining digital signatures and public-key cryptosystems, Commun. ACM, vol.2110, issue.2, pp.120-126, 1978.

[. Satoh, T. , A. , and K. , Fermat quotients and the polynomial time discrete log algorithm for anomalous elliptic curves, pp.81-92, 1998.

. Sem98 and I. Semaev, Evaluation of discrete logarithms in a group of p-torsion points of an elliptic curve in characteristic p », In : Mathematics of Computation of the American Mathematical Society, vol.6722151, pp.353-356, 1998.

]. Sha71 and D. Shanks, Class number, a theory of factorization, and genera, 1969 Number Theory Institute, pp.415-440, 1969.

[. Suzuki, D. Et, M. , and T. , How to Maximize the Potential of FPGA-Based DSPs for Modular Exponentiation, IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, vol.94, issue.1, pp.211-222, 2011.
DOI : 10.1587/transfun.E94.A.211

. Sma99 and N. P. Smart, « The discrete logarithm problem on elliptic curves of trace one, Journal of cryptology, vol.12351, pp.193-196, 1999.

[. , Y. Kim, S. Lim, S. Et, M. et al., « A countermeasure against one physical cryptanalysis may benefit another attack, Information Security and Cryptology?ICISC, vol.27, pp.414-427, 2001.

T. Tat66 and J. , « Endomorphisms of abelian varieties over finite fields, Inventiones mathematicae 2, pp.134-144, 1966.

[. Tenca, A. F. Todorov, G. Et, K. , C. K. Koç et al., High-Radix Design of a Scalable Modular Multiplier, Lecture Notes in Computer Science Generators, pp.185-201, 2001.
DOI : 10.1007/3-540-44709-1_17

[. Tang, S. H. Tsui, K. S. Et, L. , and P. H. , Modular exponentiation using parallel multipliers, Proceedings. 2003 IEEE International Conference on Field-Programmable Technology (FPT) (IEEE Cat. No.03EX798), pp.52-59, 2003.
DOI : 10.1109/FPT.2003.1275731

URL : http://www.cse.cuhk.edu.hk/~phwl/mt/public/archives/papers/me_fpt03.pdf

. Van92 and S. Vanstone, « Responses to NIST's Proposal, Communications of the ACM, vol.3510, pp.50-52, 1992.

]. Was08 and L. C. Washington, Elliptic Curves : Number Theory and Cryptography, Second Edition. 2 e éd, p.50, 2008.

]. Wei49 and A. Weil, « Numbers of solutions of equations in finite fields, In : Bull. Amer. Math. Soc, vol.55521, pp.497-508, 1949.

[. , S. Et, J. , and M. , Checking before output may not be enough against fault-based cryptanalysis, IEEE Transactions on Computers, vol.4927, issue.9, pp.967-970, 2000.

B. Bibliothèques-logicielles-[-cmt-]-designs and S. Metrics, URL : http://www.semdesigns.com/Products

. Complexity, B. Korb, and . Complexity, URL : https://www.gnu.org/software

[. Ida, the multi-processor disassembler and debugger. URL : https://www.hex-rays.com/products

]. Metasm and . Metasm, The METASM assembly manipulation suite URL : http://metasm.cr0.org/. [171] [ply] . PLY (Python Lex-Yacc) URL : http

A. , B. Et, B. , and Z. , Obfuscating Circuits via Composite-Order Graded Encoding

[. , B. Madou, M. Sutter, B. D. Bus, B. D. Bosschere et al., « Program obfuscation : a quantitative approach. » In : QoP. Sous la dir, pp.15-20, 2007.

]. Bar+01, B. Barak, O. Goldreich, R. Impagliazzo, S. Rudich et al., On the (Im)possibility of Obfuscating Programs, Proceedings of the 21st Annual International Cryptology Conference on Advances in Cryptology. CRYPTO '01, pp.1-18, 2001.

]. Bar+12, B. Barak, O. Goldreich, R. Impagliazzo, S. Rudich et al., On the (im)possibility of obfuscating programs, Journal of the ACM, vol.592, pp.6-203, 2012.

O. Billet, H. Gilbert, E. Et, and C. , Cryptanalysis of a White Box AES Implementation, pp.227-240, 2004.
DOI : 10.1007/978-3-540-30564-4_16

[. Barak, B. Garg, S. Kalai, Y. T. Paneth, O. Et et al., Protecting Obfuscation against Algebraic Attacks, Lecture Notes in Computer Science, vol.207, pp.221-238, 2014.
DOI : 10.1007/978-3-642-55220-5_13

[. Brakerski, Z. Et, R. , and G. N. , Virtual Black-Box Obfuscation for All Circuits via Generic Graded Encoding, Theory of Cryptography, pp.1-25, 2014.
DOI : 10.1007/978-3-642-54242-8_1

URL : http://eprint.iacr.org/2013/563.pdf

[. Blazy, S. Riaud, S. Et, S. , T. Godfrey et al., Data tainting and obfuscation: Improving plausibility of incorrect taint, 2015 IEEE 15th International Working Conference on Source Code Analysis and Manipulation (SCAM), pp.111-120, 2015.
DOI : 10.1109/SCAM.2015.7335407

URL : https://hal.archives-ouvertes.fr/hal-01193286

[. Chow, S. Eisen, P. Johnson, H. Van-oorschot, and P. C. , White-Box Cryptography and an AES Implementation, pp.250-270, 2002.
DOI : 10.1007/3-540-36492-7_17

[. Chow, S. Gu, Y. X. Johnson, H. Et, Z. et al., An Approach to the Obfuscation of Control-Flow of Sequential Computer Programs, Lecture Notes in Computer Science, vol.215, pp.144-155, 2001.
DOI : 10.1007/3-540-45439-X_10

[. , C. Ganesh, V. Pawlowski, P. M. Dill, D. L. Et et al., automatically generating inputs of death, ACM Conference on Computer and Communications Security, pp.322-335, 2006.

[. , S. R. Et, K. , and C. F. , « A Metrics Suite for Object Oriented Design, IEEE Trans. Softw. Eng, vol.20177, issue.6, pp.476-493, 1994.

[. Christian, C. Et, N. , and J. , Surreptitious Software : Obfuscation, Watermarking and Tamperproofing for Software Protection, 2009.

[. , J. Et, P. , B. Al-shaer, E. Jin et al., A general model for hiding control flow. » In : Digital Rights Management Workshop, pp.35-42, 2010.

[. , C. Et, T. , and C. Watermarking, tamper-proofing, and obfuscation-tools for software protection, Software Engineering, pp.735-746, 2000.

[. , C. Thomborson, C. Et, L. , and D. , A Taxonomy of Obfuscating Transformations, p.209, 1997.

C. Ctl98a-]-collberg, C. Thomborson, L. Et, and D. , Breaking Abstractions and Unstructuring Data Structures, IEEE International Conference on Computer Languages. Chicago, pp.28-38, 1998.

]. Ctl98b, C. Collberg, C. Thomborson, L. Et, and D. , Manufacturing Cheap, Resilient, and Stealthy Opaque Constructs, Proceedings of the 25th ACM SIGPLAN-SIGACT symposium on Principles of programming languages, pp.184-196, 1998.

. Dra06 and S. Drape, Generalising the array split obfuscation, » In : Information Science, vol.1771209, pp.202-219, 2006.

[. , J. Et, Z. , and H. , Numerical evaluation of algorithmic complexity for short strings : A glance into the innermost structure of randomness, » In : Applied Mathematics and Computation, vol.2191, pp.63-77, 0194.

[. Feist, J. Mounier, L. Et, P. , and M. , Statically detecting use after free on binary code, Journal of Computer Virology and Hacking Techniques, vol.89, issue.3, pp.211-217, 2014.
DOI : 10.1016/S1571-0661(04)81042-9

. Fog16 and A. Fog, Instruction tables : Lists of instruction latencies, throughputs and micro-operation breakdowns for Intel, AMD and VIA CPUs, 2016.

[. Garg, S. Gentry, C. Halevi, S. Raykova, M. Sahai et al., « Candidate indistinguishability obfuscation and functional encryption for all circuits, Foundations of Computer Science (FOCS), 2013 IEEE 54th Annual Symposium on. IEEE. 2013, pp.40-49
DOI : 10.1137/14095772x

[. Garg, S. Gentry, C. Halevi, S. Et, W. et al., On the Implausibility of Differing-Inputs Obfuscation and Extractable Witness Encryption with Auxiliary Input. » In : CRYPTO (1) Sous la dir, Lecture Notes in Computer Science, vol.8616207, pp.518-535, 2014.

[. , S. Et, M. , S. «. Stoc, . Sous-la-dir et al., Probabilistic Encryption and How to Play Mental Poker Keeping Secret All Partial Information, pp.365-377, 1982.

[. Goubin, L. Masereel, J. Et, Q. , and M. , Cryptanalysis of White Box DES Implementations, pp.278-295, 2007.
DOI : 10.1007/978-3-540-77360-3_18

[. , S. Et, R. , G. N. De, V. et al., « On Best-Possible Obfuscation. » In : sous la dir, P. T. Lecture Notes in Computer Science, vol.4392206, issue.207, pp.194-213, 2007.

[. , S. Et, R. , and G. N. , « On Best-Possible Obfuscation, Journal of Cryptology, vol.273206, pp.480-505, 2014.

[. Henry, S. Et, K. , and D. , On the Improvements of Cyclomatic Complexity Metric, IEEE Transactions on Software Engineering SE-7.5 (sept, 1981.

[. Harrison, W. A. Et, M. , and K. I. , A complexity measure based on nesting level, ACM SIGPLAN Notices, vol.16, issue.3, pp.63-74, 1981.
DOI : 10.1145/947825.947829

[. Hopcroft, J. E. Et, U. , and J. D. , Introduction to Automata Theory, Languages, and Computation, 0190.
DOI : 10.1145/568438.568455

[. , Y. Pandey, O. Et, S. , A. et al., Public-Coin Differing-Inputs Obfuscation and Its Applications, Lecture Notes in Computer Science, vol.9015207, issue.2, pp.668-697, 2015.

W. Lan92-]-landi, Undecidability of static analysis, ACM Letters on Programming Languages and Systems, vol.1, issue.4, pp.323-337, 1992.
DOI : 10.1145/161494.161501

. Ld03a, C. Linn, D. Et, and S. , Obfuscation of executable code to improve resistance to static disassembly, Proceedings of the 10th ACM conference on Computer and communications security. CCS '03, pp.290-299, 2003.

. Ld03b, C. Linn, D. Et, S. K. Atluri, V. Et et al., « Obfuscation of executable code to improve resistance to static disassembly, ACM Conference on Computer and Communications Security, pp.290-299, 0218.

[. Linn, C. Debray, S. Et, K. , and J. , Enhancing software tamper-resistance via stealthy address computations, Proceedings of the 19th Annual Computer Security Applications Conference, 2003.

. Lev74 and L. A. Levin, « Laws of information conservation (nongrowth) and aspects of the foundation of probability theory, Problems of Information Transmission, vol.10, pp.206-210, 0194.

[. , T. Et, K. , and Á. , Obfuscating C++ Programs via Control Flow Flattening Dobogók? o, Hungary, Proceedings of the 10th Symposium on Programming Languages and Software Tools, pp.15-29, 2007.

[. Madou, M. Anckaert, B. Sutter, B. D. Et, B. et al., Hybrid static-dynamic attacks against software protection mechanisms, Proceedings of the 5th ACM workshop on Digital rights management , DRM '05, pp.75-82, 0218.
DOI : 10.1145/1102546.1102560

URL : http://www.elis.ugent.be/~mmadou/home/papers/drm05/madou05hybrid.pdf

[. Majumdar, A. Drape, S. J. Et, T. , and C. D. , Slicing obfuscations, Proceedings of the 2007 ACM workshop on Digital Rights Management , DRM '07, pp.70-81, 2007.
DOI : 10.1145/1314276.1314290

]. Mea55 and G. H. Mealy, « A Method for Synthesizing Sequential Circuits, Bell System Technical Journal, vol.345208, pp.1045-1079, 1955.

. Mil72 and H. D. Mills, Mathematical foundations for structured programming. report FSC 72-6012. IBM Federal Systems Division, 1972.

[. , W. Podgurski, A. Et, L. , and D. , Detecting and Debugging Insecure Information Flows, pp.198-209, 2004.

. Mye77 and G. J. Myers, An extension to the cyclomatic measure of program complexity, In : SIGPLAN Not, vol.1210181, pp.61-64, 1977.

[. Madi, A. Zein, O. K. Et, K. , and S. , On the Improvements of Cyclomatic Complexity Metric, International Journal of Software Engineering and its Applications, vol.7, issue.2

[. Ogiso, T. Sakabe, Y. Soshi, M. Et, M. et al., Software Obfuscation on a Theoretical Basis and Its Implementation, IEICE Trans Fundam Electron Commun Comput Sci E86-A, vol.1, pp.176-186, 2003.

[. Ott, L. M. Et, T. , and J. J. , Slice based metrics for estimating cohesion, [1993] Proceedings First International Software Metrics Symposium, pp.71-81, 1993.
DOI : 10.1109/METRIC.1993.263799

[. Preda, M. D. Madou, M. Bosschere, K. D. Et, G. et al., Opaque Predicates Detection by Abstract Interpretation, Lecture Notes in Computer Science, vol.167, pp.81-95, 2006.

[. Shamir, A. Et, S. , and N. Van, Playing ???Hide and Seek??? with Stored Keys, Lecture Notes in Computer Science, vol.208, pp.118-124, 1999.
DOI : 10.1007/3-540-48390-X_9

URL : http://www.ncipher.com/products/files/papers/anguilla/keyhide2.pdf

[. Woodward, M. R. Hennell, M. A. Et, H. , and D. , A Measure of Control Flow Complexity in Program Text, IEEE Transactions on Software Engineering, vol.5, issue.1, pp.45-50, 1979.
DOI : 10.1109/TSE.1979.226497

[. Wang, C. Hill, J. Knight, J. Et, D. et al., Software Tamper Resistance : Obstructing Static Analysis of Programs, 0190.

[. Wang, C. Hill, J. Knight, J. C. Et, D. et al., Protection of Software-Based Survivability Mechanisms, Proceedings of the 2001 International Conference on Dependable Systems and Networks. DSN '01, pp.193-202, 2001.
DOI : 10.21236/ADA466288

. Yao82 and A. C. Yao, « Theory and Applications of Trapdoor Functions (Extended Abstract), pp.80-91, 1982.