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Research Output

Article

A complete set of addition laws for incomplete Edwards curves

Bernstein, D. J. & Lange, T., 2011, In : Journal of Number Theory. 131, 5, p. 858-872

Research output: Contribution to journalArticleAcademicpeer-review

22 Citations (Scopus)
3 Downloads (Pure)

Certain exponential sums and random walks on elliptic curves

Lange, T. & Shparlinski, I. E., 2005, In : Canadian Journal of Mathematics / Journal Canadien de Mathématiques. 57, 2, p. 338-350

Research output: Contribution to journalArticleAcademicpeer-review

35 Citations (Scopus)
2 Downloads (Pure)

Collisions in fast generation of ideal classes and points on hyperelliptic and elliptic curves

Lange, T. & Shparlinski, I. E., 2005, In : Applicable Algebra in Engineering, Communication and Computing. 15, 5, p. 329-337

Research output: Contribution to journalArticleAcademicpeer-review

10 Citations (Scopus)

Distribution of some sequences of points on elliptic curves

Lange, T. & Shparlinski, I. E., 2007, In : Journal of Mathematical Cryptology. 1, 1, p. 1-11

Research output: Contribution to journalArticleAcademicpeer-review

17 Citations (Scopus)
2 Downloads (Pure)

ECM using Edwards curves

Bernstein, D. J., Birkner, P., Lange, T. & Peters, C. P., 2013, In : Mathematics of Computation. 82, 282, p. 1139-1179

Research output: Contribution to journalArticleAcademicpeer-review

15 Citations (Scopus)

Factoring polynomials over arbitrary finite fields

Lange, T. & Winterhof, A., 2000, In : Theoretical Computer Science. 234, 1-2, p. 301-308

Research output: Contribution to journalArticleAcademicpeer-review

1 Citation (Scopus)

Faster computation of the Tate pairing

Arène, C., Lange, T., Naehrig, M. & Ritzenthaler, C., 2011, In : Journal of Number Theory. 131, 5, p. 842-857

Research output: Contribution to journalArticleAcademicpeer-review

39 Citations (Scopus)

Formulae for arithmetic on genus 2 hyperelliptic curves

Lange, T., 2005, In : Applicable Algebra in Engineering, Communication and Computing. 15, 5, p. 295-328

Research output: Contribution to journalArticleAcademicpeer-review

61 Citations (Scopus)

High-speed high-security signatures

Bernstein, D. J., Duif, N., Lange, T., Schwabe, P. & Yang, B. Y., 2012, In : Journal of Cryptographic Engineering. 2, 2, p. 77-89

Research output: Contribution to journalArticleAcademicpeer-review

164 Citations (Scopus)

Hyper-and-elliptic-curve cryptography

Bernstein, D. J. & Lange, T., 2014, In : LMS Journal of Computation and Mathematics. 17, Spec. Issue A, p. 181-202

Research output: Contribution to journalArticleAcademicpeer-review

6 Citations (Scopus)
14 Downloads (Pure)

Incomplete character sums over finite fields and their application to the interpolation of the discrete logarithm by Boolean functions

Lange, T. & Winterhof, A., 2002, In : Acta Arithmetica. 101, p. 223-229

Research output: Contribution to journalArticleAcademicpeer-review

12 Citations (Scopus)

Interpolation of the discrete logarithm in $F_q$ by Boolean functions and by polynomials in several variables modulo a divisor of $q−1$

Lange, T. & Winterhof, A., 2003, In : Discrete Applied Mathematics. 128, 1, p. 193-206

Research output: Contribution to journalArticleAcademicpeer-review

15 Citations (Scopus)

Koblitz curve cryptosystems

Lange, T., 2003, In : ST Journal of System Research. 4, p. 29-36

Research output: Contribution to journalArticleProfessional

Koblitz curve cryptosystems

Lange, T., 2005, In : Finite Fields and their Applications. 11, 2, p. 200-229

Research output: Contribution to journalArticleAcademicpeer-review

14 Citations (Scopus)

Linear complexity of the discrete logarithm

Konyagin, S., Lange, T. & Shparlinski, I. E., 2003, In : Designs, Codes and Cryptography. 28, 2, p. 135-146

Research output: Contribution to journalArticleAcademicpeer-review

12 Citations (Scopus)
1 Downloads (Pure)

On using expansions to the base of -2

Lange, T., Avanzi, R., Frey, G. & Oyono, R., 2004, In : International Journal of Computer Mathematics. 81, 4, p. 403-406

Research output: Contribution to journalArticleAcademicpeer-review

1 Citation (Scopus)

Searchable encryption revisited : Consistency properties, relation to anonymous IBE, and extensions

Abdalla, M., Bellare, M., Catalano, D., Kiltz, E., Kohno, T., Lange, T., Malone-Lee, J., Neven, G., Paillier, P. & Shi, H., 2008, In : Journal of Cryptology. 21, 3, p. 350-391

Research output: Contribution to journalArticleAcademicpeer-review

209 Citations (Scopus)
4 Downloads (Pure)

Trace zero subvarieties of genus 2 curves for cryptosystems

Lange, T., 2004, In : Journal of the Ramanujan Mathematical Society. 19, 1, p. 15-33

Research output: Contribution to journalArticleAcademicpeer-review

2 Citations (Scopus)
Book editing

Pairing-Based Cryptography - Pairing 2012 : 5th International Conference, Cologne, Germany, May 16-18, 2012, Revised Selected Papers

Abdalla, M. (ed.) & Lange, T. (ed.), 2013, Berlin: Springer. 333 p. (Lecture notes in computer science; vol. 7708)

Research output: Book/ReportBook editingAcademic

Progress in cryptology - AFRICACRYPT 2010 : third international conference on cryptology in Africa, Stellenbosch, South Africa, May 3-6, 2010 : proceedings

Bernstein, D. J. (ed.) & Lange, T. (ed.), 2010, Berlin: Springer. (Lecture notes in computer science; vol. 6055)(Progess in cryptology - AFRICACRYPT; vol. 3)

Research output: Book/ReportBook editingAcademic

Progress in cryptology - INDOCRYPT 2006 : 7th international conference on cryptology in India, Kolkata, India, December 11-13, 2006 : proceedings

Barua, R. (ed.) & Lange, T. (ed.), 2006, Berlin: Springer. 454 p. (Lecture notes in computer science; vol. 4329)

Research output: Book/ReportBook editingAcademic

Selected Areas in Cryptography - SAC 2013 : 20th International Conference, Burnaby BC, Canada, August 14-16, 2013 : Revised Selected Papers

Lange, T. (ed.), Lauter, K. (ed.) & Lisonek, P. (ed.), 2014, Berlin: Springer. 590 p. (Lecture notes in computer science; vol. 8282)

Research output: Book/ReportBook editingAcademic

Chapter

Addition formulas for elliptic curves

Bernstein, D. J. & Lange, T., 2013, Handbook of Finite Fields. Mullen, G. L. & Panario, D. (eds.). London: Chapman & Hall/CRC Press, p. 440-446 (Discrete Mathematics and Its Applications).

Research output: Chapter in Book/Report/Conference proceedingChapterAcademic

1 Citation (Scopus)
4 Downloads (Pure)

Algebraic realizations of DL systems

Frey, G. & Lange, T., 2006, Handbook of Elliptic and Hyperelliptic Curve Cryptography. Cohen, H. & Frey, G. (eds.). Boca Raton FL, USA: Chapman & Hall/CRC Press, p. 547-572 (Discrete Mathematics and Its Applications; vol. 34).

Research output: Chapter in Book/Report/Conference proceedingChapterAcademic

Arithmetic of elliptic curves

Doche, C. & Lange, T., 2006, Handbook of Elliptic and Hyperelliptic Curve Cryptography. Cohen, H. & Frey, G. (eds.). Boca Raton FL, USA: Chapman & Hall/CRC Press, p. 267-302 (Discrete Mathematics and Its Applications; vol. 34).

Research output: Chapter in Book/Report/Conference proceedingChapterAcademic

Arithmetic of hyperelliptic curves

Duquesne, S. & Lange, T., 2006, Handbook of Elliptic and Hyperelliptic Curve Cryptography. Cohen, H. & Frey, G. (eds.). Boca Raton FL, USA: Chapman & Hall/CRC Press, p. 303-353 (Discrete Mathematics and Its Applications; vol. 34).

Research output: Chapter in Book/Report/Conference proceedingChapterAcademic

Arithmetic of special curves

Doche, C. & Lange, T., 2006, Handbook of Elliptic and Hyperelliptic Curve Cryptography. Cohen, H. & Frey, G. (eds.). Boca Raton FL, USA: Chapman & Hall/CRC Press, p. 355-387 (Discrete Mathematics and Its Applications; vol. 34).

Research output: Chapter in Book/Report/Conference proceedingChapterAcademic

Background on curves and Jacobians

Frey, G. & Lange, T., 2006, Handbook of Elliptic and Hyperelliptic Curve Cryptography. Cohen, H. & Frey, G. (eds.). Boca Raton FL, USA: Chapman & Hall/CRC Press, p. 45-85 (Discrete Mathematics and Its Applications; vol. 34).

Research output: Chapter in Book/Report/Conference proceedingChapterAcademic

Background on Weil descent

Frey, G. & Lange, T., 2006, Handbook of Elliptic and Hyperelliptic Curve Cryptography. Cohen, H. & Frey, G. (eds.). Boca Raton FL, USA: Chapman & Hall/CRC Press, p. 125-132 (Discrete Mathematics and Its Applications; vol. 34).

Research output: Chapter in Book/Report/Conference proceedingChapterAcademic

2 Downloads (Pure)

Complex multiplication

Frey, G. & Lange, T., 2006, Handbook of elliptic and hyperelliptic curve cryptography. Cohen, H. & Frey, G. (eds.). Boca Raton FL, USA: Chapman & Hall/CRC Press, p. 455-473 (Discrete Mathematics and Its Applications; vol. 34).

Research output: Chapter in Book/Report/Conference proceedingChapterAcademic

2 Downloads (Pure)

Dual EC: a standardized back door

Bernstein, D. J., Lange, T. & Niederhagen, R., 2016, The New Codebreakers : Essays Dedicated to David Kahn on the Occasion of His 85th Birthday. Ryan, P. Y. A., Naccache, D. & Quisquater, J. J. (eds.). Dordrecht: Springer, p. 256-281 26 p. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); vol. 9100).

Research output: Chapter in Book/Report/Conference proceedingChapterAcademicpeer-review

17 Citations (Scopus)

Hash-based signatures

Lange, T., 2011, Encyclopedia of Cryptography and Security (2nd ed.). Tilborg, van, H. C. A. & Jajodia, S. (eds.). New York: Springer, p. 540-542

Research output: Chapter in Book/Report/Conference proceedingChapterProfessional

Introduction to public-key cryptography

Avanzi, R. & Lange, T., 2006, Handbook of Elliptic and Hyperelliptic Curve Cryptography. Cohen, H. & Frey, G. (eds.). Boca Raton FL, USA: Chapman & Hall/CRC Press, p. 1-15 (Discrete Mathematics and Its Applications; vol. 34).

Research output: Chapter in Book/Report/Conference proceedingChapterAcademic

1 Downloads (Pure)

Mathematical countermeasures against side-channel attacks

Lange, T., 2006, Handbook of elliptic and hyperelliptic curve cryptography. Cohen, H. & Frey, G. (eds.). Boca Raton FL, USA: Chapman & Hall/CRC Press, p. 687-714 (Discrete Mathematics and Its Applications; vol. 34).

Research output: Chapter in Book/Report/Conference proceedingChapterAcademic

Montgomery curves and the Montgomery ladder

Bernstein, D. J. & Lange, T., 2017, Topics in Computational Number Theory Inspired by Peter L. Montgomery. Bos, J. W. . & Lenstra, A. K. (eds.). Cambridge: Cambridge University Press, p. 82-115

Research output: Chapter in Book/Report/Conference proceedingChapterAcademicpeer-review

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156 Downloads (Pure)

Pairing-based cryptography

Duquesne, S. & Lange, T., 2006, Handbook of Elliptic and Hyperelliptic Curve Cryptography. Cohen, H. & Frey, G. (eds.). Boca Raton FL, USA: Chapman & Hall/CRC Press, p. 573-590 (Discrete Mathematics and Its Applications; vol. 34).

Research output: Chapter in Book/Report/Conference proceedingChapterAcademic

Random numbers, generation and testing

Lange, T., Lubicz, D. & Weigl, A., 2006, Handbook of Elliptic and Hyperelliptic Curve Cryptography. Cohen, H. & Frey, G. (eds.). Boca Raton FL, USA: Chapman & Hall/CRC Press, p. 715-735 (Discrete Mathematics and Its Applications; vol. 34).

Research output: Chapter in Book/Report/Conference proceedingChapterAcademic

296 Citations (Scopus)

Transfer of discrete logarithmics

Frey, G. & Lange, T., 2006, Handbook of Elliptic and Hyperelliptic Curve Cryptography. Cohen, H. & Frey, G. (eds.). Boca Raton FL, USA: Chapman & Hall/CRC Press, p. 529-543 (Discrete Mathematics and Its Applications; vol. 34).

Research output: Chapter in Book/Report/Conference proceedingChapterAcademic

Varieties over special fields

Frey, G. & Lange, T., 2006, Handbook of Elliptic and Hyperelliptic Curve Cryptography. Cohen, H. & Frey, G. (eds.). Boca Raton FL, USA: Chapman & Hall/CRC Press, p. 87-113 (Discrete Mathematics and Its Applications; vol. 34).

Research output: Chapter in Book/Report/Conference proceedingChapterAcademic

19 Citations (Scopus)
1 Downloads (Pure)

Vector space

Lange, T., 2011, Encyclopedia of Cryptography and Security (2nd ed.). Tilborg, van, H. C. A. & Jajodia, S. (eds.). New York: Springer, p. 1356-1356

Research output: Chapter in Book/Report/Conference proceedingChapterProfessional

Conference contribution

Algorithms for factoring polynomials over finite fields

Lange, T. & Winterhof, A., 2001, Finite Fields and Applications (Proceedings Fifth International Conference, Fq5, Augsburg, Germany, August 2-9, 1999). Jungnickel, D. & Niederreiter, H. (eds.). Berlin: Springer, p. 319-328

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

Analysis and optimization of elliptic-curve single-scalar multiplication

Bernstein, D. J. & Lange, T., 2008, Finite Fields and Applications (Proceedings 8th International Conference, Fq8, Melbourne, Australia, July 9-13, 2007). Mullen, G. L., Panario, D. & Shparlinski, I. E. (eds.). Providence RI: American Mathematical Society, p. 1-20 (Contemporary Mathematics Series; vol. 461).

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

A note on López-Dahab coordinates

Lange, T., 2006, Proceedings 4th Central European Conference on Cryptology (Wartacrypt 2004, Bedlewo/Poznan, Poland, July 1-3, 2004). Jaworski, J., Kula, M. & Nemoga, K. (eds.). p. 75-81 (Tatra Mountains Mathematical Publications; vol. 33).

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

Arithmetic on binary genus 2 curves suitable for small devices

Lange, T., 2005, Proceedings ECRYPT Workshop on RFID and Lightweight Crypto (Graz, Austria, July 14-15, 2005).

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademic

Attacking and defending the McEliece cryptosystem

Bernstein, D. J., Lange, T. & Peters, C. P., 2008, Post-Quantum Cryptography (2nd International Workshop, PQCrypto 2008, Cincinnati OH, USA, October 17-19, 2008, Proceedings). Buchmann, J. & Ding, J. (eds.). Berlin: Springer, p. 31-46 (Lecture Notes in Computer Science; vol. 5299).

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

133 Citations (Scopus)

Bad directions in cryptographic hash functions

Bernstein, D. J., Hülsing, A., Lange, T. & Niederhagen, R., 2015, Information Security and Privacy : 20th Australasian Conference, ACISP 2015, Brisbane, QLD, Australia, June 29 -- July 1, 2015, Proceedings. Foo, E. & Stebila, D. (eds.). Berlin: Springer, p. 488-508 21 p. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); vol. 9144).

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

2 Citations (Scopus)

Batch NFS

Bernstein, D. J. & Lange, T., 2014, Selected Areas in Cryptography -- SAC 2014: 21st International Conference, Montreal, QC, Canada, August 14-15, 2014, Revised Selected Papers. Joux, A. & Youssef, A. (eds.). Springer, p. 38-58 (Lecture Notes in Computer Science; vol. 8781).

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

7 Citations (Scopus)

Binary Edwards curves

Bernstein, D. J., Lange, T. & Rezaeian Farashahi, R., 2008, Cryptographic Hardware and Embedded Systems - CHES 2008 (10th International Workshop, Washington DC, USA, August 10-13, 2008, Proceedings). Oswald, E. & Rohatgi, P. (eds.). Berlin: Springer, p. 244-265 (Lecture Notes in Computer Science; vol. 5154).

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

76 Citations (Scopus)
2 Downloads (Pure)

Computing small discrete logarithms faster

Bernstein, D. J. & Lange, T., 2012, Progress in Cryptology - INDOCRYPT 2012 (13th International Conference on Cryptology in India, Kolkata, India, December 9-12, 2012. Proceedings). Galbraith, S. & Nandi, M. (eds.). Berlin: Springer, p. 318-338 (Lecture Notes in Computer Science; vol. 7668).

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

17 Citations (Scopus)

CSIDH: An efficient post-quantum commutative group action

Castryck, W., Lange, T., Martindale, C., Panny, L. & Renes, J., 1 Jan 2018, Advances in Cryptology – ASIACRYPT 2018 - 24th International Conference on the Theory and Application of Cryptology and Information Security, Proceedings. Peyrin, T. & Galbraith, S. (eds.). Berlin: Springer, p. 395-427 33 p. (Lecture Notes in Computer Science; vol. 11274).

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

31 Citations (Scopus)