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Random number generator attack, https:\/\/en.wikipedia.org\/wiki\/random_number_generator_attack<\/ext-link>.<\/p>"},{"key":"key-10.3934\/amc.2025008-5","unstructured":"

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D. F. Aranha, B. Salling Hvass, B. Spitters and M. Tibouchi, Faster constant-time evaluation of the Kronecker symbol with application to elliptic curve hashing, in CCS 2023: ACM SIGSAC Conference on Computer and Communications Security<\/i>, Association for Computing Machinery, New York, (2023), 3228-3238.<\/p>","DOI":"10.1145\/3576915.3616597"},{"key":"key-10.3934\/amc.2025008-10","doi-asserted-by":"crossref","unstructured":"

Y. Aubry and M. Perret, A Weil theorem for singular curves, in Arithmetic, Geometry, and Coding Theory<\/i> (eds. R. Pellikaan, M. Perret and S. G. Vl\u0103du\u0163), Proceedings in Mathematics, De Gruyter, Berlin, (1996), 1-7.<\/p>","DOI":"10.1515\/9783110811056.1"},{"key":"key-10.3934\/amc.2025008-11","unstructured":"

E. Barker and J. Kelsey, Recommendation for random number generation using deterministic random bit generators (NIST Special Publication 800-90A Revision 1), 2015. https:\/\/csrc.nist.gov\/publications\/detail\/sp\/800-90a\/rev-1\/final<\/ext-link>.<\/p>"},{"key":"key-10.3934\/amc.2025008-12","doi-asserted-by":"crossref","unstructured":"

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E. Ben-Sasson, A. Chiesa, E. Tromer and M. Virza, Scalable zero knowledge via cycles of elliptic curves, in Advances in Cryptology\u2013CRYPTO 2014<\/i> (eds. J. A. Garay and R. Gennaro), vol. 8617<\/b> of Lecture Notes in Computer Science, Springer, Berlin, Heidelberg, (2014), 276-294.<\/p>","DOI":"10.1007\/978-3-662-44381-1_16"},{"key":"key-10.3934\/amc.2025008-15","unstructured":"

D. J. Bernstein, Faster square roots in annoying finite fields, 2001. https:\/\/cr.yp.to\/papers.html#sqroot<\/ext-link>.<\/p>"},{"key":"key-10.3934\/amc.2025008-16","doi-asserted-by":"publisher","DOI":"10.46586\/tches.v2019.i3.340-398"},{"key":"key-10.3934\/amc.2025008-17","doi-asserted-by":"crossref","unstructured":"

O. Billet and M. Joye, The Jacobi model of an elliptic curve and side-channel analysis, in Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 2003<\/i> (eds. M. Fossorier, T. H\u00f8holdt and A. Poli), vol. 2643<\/b> of Lecture Notes in Computer Science, Springer, Berlin, Heidelberg, 2003, 34-42.<\/p>","DOI":"10.1007\/3-540-44828-4_5"},{"key":"key-10.3934\/amc.2025008-18"},{"key":"key-10.3934\/amc.2025008-19","unstructured":"

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N. El Mrabet and M. Joye (eds.), Guide to Pairing-Based Cryptography<\/i>, Cryptography and Network Security Series, Chapman and Hall\/CRC, New York, 2017.<\/p>","DOI":"10.1201\/9781315370170"},{"key":"key-10.3934\/amc.2025008-24","unstructured":"

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P. A. Fouque, R. Lercier, D. R\u00e9al and F. Valette, Fault attack on elliptic curve Montgomery ladder implementation, in 2008 5th Workshop on Fault Diagnosis and Tolerance in Cryptography<\/i>, Institute of Electrical and Electronics Engineers, New York, 2008, 92-98.<\/p>","DOI":"10.1109\/FDTC.2008.15"},{"key":"key-10.3934\/amc.2025008-27","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139012843"},{"key":"key-10.3934\/amc.2025008-28","unstructured":"

M. J. Handley and E. Rescorla, Internet denial-of-service considerations (RFC 4732), Internet Architecture Board, 2006. https:\/\/datatracker.ietf.org\/doc\/rfc4732<\/ext-link>.<\/p>"},{"key":"key-10.3934\/amc.2025008-29","doi-asserted-by":"crossref","unstructured":"

R. Hartshorne, Algebraic Geometry<\/i>, vol. 52 of Graduate Texts in Mathematics, 8th edition, Springer, New York, 1977.<\/p>","DOI":"10.1007\/978-1-4757-3849-0"},{"key":"key-10.3934\/amc.2025008-30","unstructured":"

D. Hopwood, The Pasta curves for Halo $2$ and beyond, 2020. https:\/\/electriccoin.co\/blog\/the-pasta-curves-for-halo-2-and-beyond<\/ext-link>.<\/p>"},{"key":"key-10.3934\/amc.2025008-31","unstructured":"

D. Hopwood, Pluto\/Eris supporting evidence, 2021. https:\/\/github.com\/daira\/pluto-eris<\/ext-link>.<\/p>"},{"key":"key-10.3934\/amc.2025008-32","doi-asserted-by":"crossref","unstructured":"

T. Icart, How to hash into elliptic curves, in Advances in Cryptology\u2013CRYPTO 2009<\/i> (ed. S. Halevi), vol. 5677<\/b> of Lecture Notes in Computer Science, Springer, Berlin, Heidelberg, 2009,303-316.<\/p>","DOI":"10.1007\/978-3-642-03356-8_18"},{"key":"key-10.3934\/amc.2025008-33","doi-asserted-by":"publisher","DOI":"10.1049\/el:19960359"},{"key":"key-10.3934\/amc.2025008-34","doi-asserted-by":"publisher","DOI":"10.1109\/TC.2007.47"},{"key":"key-10.3934\/amc.2025008-35","doi-asserted-by":"publisher","DOI":"10.1016\/j.ffa.2024.102517"},{"key":"key-10.3934\/amc.2025008-36","doi-asserted-by":"publisher","DOI":"10.1016\/j.ffa.2020.101774"},{"key":"key-10.3934\/amc.2025008-37","doi-asserted-by":"publisher","DOI":"10.1007\/s10623-022-01012-8"},{"key":"key-10.3934\/amc.2025008-38","doi-asserted-by":"publisher","DOI":"10.1007\/s00200-023-00625-3"},{"key":"key-10.3934\/amc.2025008-39","unstructured":"

D. Koshelev, Generation of \u201cindependent\u201d points on elliptic curves by means of Mordell\u2013Weil lattices<\/ext-link>, Mathematical Cryptology<\/i>, 4<\/b> (2024), 11-22.<\/p>"},{"key":"key-10.3934\/amc.2025008-40","doi-asserted-by":"publisher","DOI":"10.1007\/s00145-024-09490-w"},{"key":"key-10.3934\/amc.2025008-41","unstructured":"

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R. J. Lambert, Method to calculate square roots for elliptic curve cryptography, 2013. https:\/\/patents.google.com\/patent\/US9148282B2\/en<\/ext-link>, United States patent No. 9148282B2.<\/p>"},{"key":"key-10.3934\/amc.2025008-44","unstructured":"

D. H. Lehmer, Computer technology applied to the theory of numbers, in Studies in Number Theory<\/i> (ed. W. J. LeVeque), vol. 6<\/b> of Studies in Mathematics, Mathematical Association of America, Washington, (1969), 117-151.<\/p>"},{"key":"key-10.3934\/amc.2025008-45","doi-asserted-by":"publisher","DOI":"10.1007\/s10623-024-01472-0"},{"key":"key-10.3934\/amc.2025008-46","doi-asserted-by":"crossref","unstructured":"

V. S. Miller, Use of elliptic curves in cryptography, in Advances in Cryptology\u2013CRYPTO 1985<\/i> (ed. H. C. Williams), vol. 218<\/b> of Lecture Notes in Computer Science, Springer, Berlin, Heidelberg, 1986,417-426.<\/p>","DOI":"10.1007\/3-540-39799-X_31"},{"key":"key-10.3934\/amc.2025008-47","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-04-01640-0"},{"key":"key-10.3934\/amc.2025008-48","unstructured":"

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C. Petit, M. Kosters and A. Messeng, Algebraic approaches for the elliptic curve discrete logarithm problem over prime fields, in Public-Key Cryptography\u2013PKC 2016<\/i> (eds. C. M. Cheng, K. M. Chung, G. Persiano and B. Y. Yang), vol. 9615<\/b> of Lecture Notes in Computer Science, Springer, Berlin, Heidelberg, (2016), 3-18.<\/p>","DOI":"10.1007\/978-3-662-49387-8_1"},{"key":"key-10.3934\/amc.2025008-51","unstructured":"

T. Pornin, Optimized discrete logarithm computation for faster square roots in finite fields, 2023. https:\/\/eprint.iacr.org\/2023\/828<\/ext-link>.<\/p>"},{"key":"key-10.3934\/amc.2025008-52","unstructured":"

T. Pornin, A prime-order group with complete formulas from even-order elliptic curves, IACR Communications in Cryptology<\/i>, 1<\/b>.<\/p>"},{"key":"key-10.3934\/amc.2025008-53","doi-asserted-by":"publisher","DOI":"10.3934\/amc.2022007"},{"key":"key-10.3934\/amc.2025008-54","doi-asserted-by":"publisher","DOI":"10.1145\/347127.347137"},{"key":"key-10.3934\/amc.2025008-55","doi-asserted-by":"crossref","unstructured":"

J.-P. Serre, Algebraic Groups and Class Fields<\/i>, vol. 117 of Graduate Texts in Mathematics, Springer, New York, 1988.<\/p>","DOI":"10.1007\/978-1-4612-1035-1"},{"key":"key-10.3934\/amc.2025008-56","unstructured":"

D. Shanks, Five number-theoretic algorithms, in Proceedings of the Second Manitoba Conference on Numerical Mathematics<\/i> (eds. R. S. D. Thomas and H. C. Williams), vol. 7<\/b> of Congressus Numerantium, Utilitas Mathematica Publishing Inc., Winnipeg, (1973), 51-70.<\/p>"},{"key":"key-10.3934\/amc.2025008-57","unstructured":"

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I. E. Shparlinski, Pseudorandom number generators from elliptic curves, in Recent Trends in Cryptography<\/i> (ed. I. Luengo), vol. 477<\/b> of Contemporary Mathematics, American Mathematical Society, Providence, (2009), 121-141.<\/p>","DOI":"10.1090\/conm\/477\/09305"},{"key":"key-10.3934\/amc.2025008-59","doi-asserted-by":"publisher","DOI":"10.1080\/10586458.2011.565253"},{"key":"key-10.3934\/amc.2025008-60","doi-asserted-by":"crossref","unstructured":"

H. Stichtenoth, Algebraic Function Fields and Codes<\/i>, vol. 254 of Graduate Texts in Mathematics, 2nd edition, Springer, Berlin, Heidelberg, 2009.<\/p>","DOI":"10.1007\/978-3-540-76878-4"},{"key":"key-10.3934\/amc.2025008-61","unstructured":"

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