references.bib

@misc{eea,
  key = {extendedeuclideanalgorithm},
  title = {{The Extended Euclidean Algorithm explained with examples}},
  howpublished = {\url{https://extendedeuclideanalgorithm.com/xea.php}},
  year = {2018},
  note = {Accessed: 2025-08-29}
}

@misc{Bernstein_Lange_2007_EFD,
  author = {Daniel J. Bernstein and Tanja Lange},
  title = {Explicit-Formulas Database},
  howpublished = {\url{https://www.hyperelliptic.org/EFD}},
  year = {2007},
  note = {Accessed: 2025-07-05}
}

@misc{rust_generic_const_args_pr,
  author = {Noah Lev Bartell-Mangel},
  title = {Implement {MVP} for opaque generic const arguments},
  howpublished = {\url{https://github.com/rust-lang/rust/pull/150823}},
  year = {2026},
  note = {Accessed: 2026-04-12}
}

@article{diffie_hellman_1976,
  author = {Whitfield Diffie and Martin E. Hellman},
  title = {{New Directions in Cryptography}},
  journal = {IEEE Transactions on Information Theory},
  volume = {22},
  number = {6},
  pages = {644-654},
  year = {1976}
}

@InProceedings{bernstein_curve25519_2006,
  author = {Daniel J. Bernstein},
  title = {{Curve25519: New Diffie-Hellman Speed Records}},
  booktitle = {Public Key Cryptography - PKC 2006},
  isbn = {978-3-540-33852-9},
  pages = {207-228},
  publisher = {Springer Berlin Heidelberg},
  year = {2006}
}

@misc{rfc7748,
  series = {Request for Comments},
  number = 7748,
  howpublished = {RFC 7748},
  publisher = {RFC Editor},
  doi = {10.17487/RFC7748},
  url = {https://www.rfc-editor.org/info/rfc7748},
  author = {Adam Langley and Mike Hamburg and Sean Turner},
  title = {{Elliptic Curves for Security}},
  pagetotal = 22,
  year = 2016,
  month = jan
}

@misc{flaticon_avatars,
  author = {microstd},
  title = {Avatar and Hacker Free Icons},
  howpublished = {\url{https://www.flaticon.com/free-icon/avatar_12172300}, \url{https://www.flaticon.com/free-icon/hacker_7039004}, \url{https://www.flaticon.com/free-icon/avatar_12171001}},
  note = {Accessed: 2026-04-16}
}

@misc{sec2v1,
  author = {{Standards for Efficient Cryptography Group (SECG)}},
  title = {{SEC 2: Recommended Elliptic Curve Domain Parameters}},
  institution = {Certicom Research},
  year = {2000},
  number = {Version 1.0},
  howpublished = {\url{https://www.secg.org/SEC2-Ver-1.0.pdf}}
}

@misc{sec2v2,
  author = {{Standards for Efficient Cryptography Group (SECG)}},
  title = {{SEC 2: Recommended Elliptic Curve Domain Parameters}},
  institution = {Certicom Research},
  year = {2010},
  number = {Version 2.0},
  howpublished = {\url{https://www.secg.org/sec2-v2.pdf}}
}

@article{montgomery1987,
  author = {Montgomery, Peter L},
  title = {Speeding the {Pollard} and elliptic curve methods of factorization},
  journal = {Mathematics of computation},
  volume = {48},
  number = {177},
  pages = {243--264},
  year = {1987}
}

@article{pollard1978monte,
  author = {Pollard, John M},
  title = {Monte {Carlo} Methods for Index Computation (mod p)},
  journal = {Mathematics of computation},
  volume = {32},
  number = {143},
  pages = {918--924},
  year = {1978}
}

@article{schoof1995,
  author = {Schoof, Ren{\'e}},
  title = {Counting points on elliptic curves over finite fields},
  journal = {Journal de th{\'e}orie des nombres de Bordeaux},
  volume = {7},
  number = {1},
  pages = {219--254},
  year = {1995}
}

@misc{FHTWTeschlEC,
  author = {Susanne Teschl and Gerald Teschl},
  title = {Studienbrief {Kryptographie} 10: {Public-Key Verfahren: Elliptische Kurven}},
  year = {2024},
  month = {aug},
  publisher = {University of Applied Sciences Technikum Wien}
}

@misc{FHTWTeschlAlgebra1,
  author = {Susanne Teschl and Gerald Teschl},
  title = {Studienbrief {Kryptographie} 1: {Algebra 1: Elemente der Zahlentheorie}},
  year = {2024},
  month = {aug},
  publisher = {University of Applied Sciences Technikum Wien}
}

@misc{FHTWTeschlAlgebra3,
  author = {Susanne Teschl and Gerald Teschl},
  title = {Studienbrief {Kryptographie} 7: {Algebra 3: Zyklische Gruppen}},
  year = {2024},
  month = {oct},
  publisher = {University of Applied Sciences Technikum Wien}
}

@article{Hasse1936,
  author = {Helmut Hasse},
  title = {Zur {Theorie} der abstrakten elliptischen {Funktionenk\"orper I, II, III}},
  journal = {Journal f\"ur die Reine und Angewandte Mathematik},
  pager = {55--62, 69--88, 193--208},
  issn = {0075-4102},
  year = {1936}
}

@article{cornacchia1908,
  author = {Giuseppe Cornacchia},
  title = {Su di un metodo per la risoluzione in numeri interi dell' equazione $\sum_{h=0}^{n}c_hx^{n-h}y^h=P$},
  journal = {Giornale di Matematiche di Battaglini. II. Serie},
  volume = {15},
  pages = {33--90},
  year = {1908}
}

@book{coolidge1959treatise,
  author = {Julian Lowell Coolidge},
  title = {A Treatise on Algebraic Plane Curves},
  year = {1959},
  publisher = {New York, Dover Publications}
}

@misc{openssl,
  author = {{OpenSSL Project}},
  title = {{OpenSSL Cryptography and SSL/TLS Toolkit}},
  howpublished = {\url{https://github.com/openssl/openssl/releases/tag/openssl-3.5.5}},
  year = {2026},
  note = {Accessed: 2026-04-15}
}

@misc{libsecp256k1,
  author = {{Bitcoin Core Developers}},
  title = {libsecp256k1},
  howpublished = {\url{https://github.com/bitcoin-core/secp256k1/releases/tag/v0.7.1}},
  year = {2026},
  note = {Accessed: 2026-04-18}
}

@misc{miracl,
  author = {{MIRACL Ltd.}},
  title = {{MIRACL Cryptographic SDK}},
  howpublished = {\url{https://github.com/miracl/MIRACL}},
  year = {2018},
  note = {Accessed: 2025-12-11}
}

@inproceedings{shanks1973,
  author = {Daniel Shanks},
  title = {Five number-theoretic algorithms},
  pages = {51--70},
  year = {1973},
  note = {Scanned copy: \url{https://cr.yp.to/bib/1973/shanks.html}}
}