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Research Output

2000

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)
2001

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

Interpolation of the discrete logarithm in finite fields by Boolean functions

Lange, T. & Winterhof, A., 2001, Proceedings International Workshop on Coding and Cryptography (WCC 2001, Paris, France, January 8-12, 2001). Augot, D. & Carlet, C. (eds.). p. 498-506 (Electronic Notes in Discrete Mathematics; vol. 6).

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

Speeding up the arithmetic on hyperelliptic Koblitz curves of genus two

Günther, C., Lange, T. & Stein, A., 2001, Selected areas in cryptography : 7th Annual International Workshop, SAC 2000 Waterloo, Ontario, Canada, August 14–15, 2000 : proceedings. Stinson, D. R. & Tavares, S. (eds.). Berlin: Springer, p. 106-117 (Lecture Notes in Computer Science; vol. 2012).

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

19 Citations (Scopus)
2002

Efficient arithmetic on genus 2 hyperelliptic curves over finite fields via explicit formulae

Lange, T., 2002, IACR. (Cryptology ePrint Archive; vol. 2002/021)

Research output: Book/ReportReportAcademic

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)

Inversion-free arithmetic on genus 2 hyperelliptic curves

Lange, T., 2002, IACR. (Cryptology ePrint Archive; vol. 2002/147)

Research output: Book/ReportReportAcademic

Polynomial interpolation of the elliptic curve and XTR discrete logarithm

Lange, T. & Winterhof, A., 2002, Computing and combinatorics : 8th annual international conference, COCOON 2002, Singapore, August 15-17, 2002 : proceedings. Ibarra, O. H. & Zhang, L. (eds.). Berlin: Springer, p. 137-143 (Lecture Notes in Computer Science; vol. 2387).

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

16 Citations (Scopus)

Weighted coordinates on genus 2 hyperelliptic curves

Lange, T., 2002, IACR. (Cryptology ePrint Archive; vol. 2002/153)

Research output: Book/ReportReportAcademic

2003

Improved algorithms for efficient arithmetic on elliptic curves using fast endomorphisms

Ciet, M., Lange, T., Sica, F. & Quisquater, J. J., 2003, Advances in Cryptology - EUROCRYPT 2003 (Proceedings International Conference on the Theory and Application of Cryptographic Techniques, Warsaw, Poland, May 4-8, 2003). Biham, E. (ed.). p. 387-400 (Lecture Notes in Computer Science; vol. 2656).

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

22 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)

Interpolation of the elliptic-curve Diffie-Hellman mapping

Lange, T. & Winterhof, A., 2003, Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (Proceedings 15th International Conference, AAECC-15, Toulouse, France, May 12-16, 2003). Fossorier, M. P. C., Hoholdt, T. & Poli, A. (eds.). Berlin: Springer, p. 51-60 (Lecture Notes in Computer Science; vol. 2643).

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

6 Citations (Scopus)

Koblitz curve cryptosystems

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

Research output: Contribution to journalArticleProfessional

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)

Trace zero subvariety for cryptosystems

Lange, T., 2003, IACR. (Cryptology ePrint Archive; vol. 2003/094)

Research output: Book/ReportReportAcademic

2004

A note on López-Dahab coordinates

Lange, T., 2004, IACR. (Cryptology ePrint Archive; vol. 2004/323)

Research output: Book/ReportReportAcademic

Efficient doubling on genus two curves over binary fields

Lange, T. & Stevens, M., 1 Dec 2004, Selected areas in cryptography : 11th Annual Workshop, SAC 2004, Waterloo ON, Canada, August 9-10, 2004 : revised selected papers. Handschuh, H., Hasan, M. A., Wainwright, R. L. & Liebrock, L. M. (eds.). Berlin: Springer, p. 170-181 12 p. (Lecture Notes in Computer Science; vol. 3357).

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

21 Citations (Scopus)

Montgomery addition for genus two curves

Lange, T., 2004, Algorithmic number theory : 6th international symposium, ANTS-VI, Burlington VT, USA, June 13-18, 2004 : proceedings. Buell, D. A. (ed.). Berlin: Springer, p. 309-317 (Lecture Notes in Computer Science; vol. 3076).

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

6 Citations (Scopus)

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)

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)
2005

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

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)

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)

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)

Mathematical background of public key cryptography

Frey, G. & Lange, T., 2005, Proceedings 9th Meeting on Arithmetic, Geometry and Coding Theory (AGCT-9, Marseilles, France, May 19-23, 2003), Séminaires et Congrès 11. Aubry, Y. & Lachaud, G. (eds.). Paris: Societe Mathematique de France, p. 41-73 (Séminaires et Congrès; vol. 11).

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

SCA resistant parallel explicit formula for addition and doubling of divisors in the Jacobian of hyperelliptic curves of genus 2

Lange, T. & Mishra, P. K., 2005, Progress in cryptology - INDOCRYPT 2005 : 6th international conference on Cryptology in India, Bangalore, India, December 10-12, 2005 : proceedings. Maitra, S., Madhavan, C. E. V. & Venkatesan, R. (eds.). Berlin: Springer, p. 403-416 (Lecture Notes in Computer Science; vol. 3797).

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

2 Citations (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., 2005, Advances in Cryptology - CRYPTO 2005 (Proceedings 25th Annual International Cryptology Conference, Santa Barbara CA, USA, August 14-18, 2005). Shoup, V. (ed.). Berlin: Springer, p. 205-222 (Lecture Notes in Computer Science; vol. 3621).

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

2006

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

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 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)

Fast bilinear maps from the Tate-Lichtenbaum pairing on hyperelliptic curves

Frey, G. & Lange, T., 2006, Algorithmic Number Theory (Proceedings 7th International Symposium, ANTS-VII, Berlin, Germany, July 23-28, 2006). Hess, F., Pauli, S. & Pohst, M. (eds.). Berlin: Springer, p. 466-479 14 p. (Lecture Notes in Computer Science (LNCS); vol. 4076).

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

9 Citations (Scopus)

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

On the non-linearity and sparsity of Boolean functions related to the discrete logarithm in finite fields of characteristic two

Brandstätter, N., Lange, T. & Winterhof, A., 2006, Coding and cryptography international workshop, WCC'05, Bergen, Norway, March 14-18, 2005 : revised selected papers). Ytrehus, Ø. (ed.). Berlin: Springer, p. 135-143 (Lecture Notes in Computer Science; vol. 3969).

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

10 Citations (Scopus)

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

Pairing based threshold cryptography improving on Libert-Quisquater and Baek-Zheng

Desmedt, Y. & Lange, T., 2006, Financial cryptography and data security : 10th international conference, FC'06, Anguilla, British West Indies, February 27-March 2, 2006 : revised selected papers. Di Crescenzo, G. & Rubin, A. (eds.). Berlin: Springer, p. 154-159 (Lecture Notes in Computer Science; vol. 4107).

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

2 Citations (Scopus)

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

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)

Scalable authenticated tree based group key exchange for ad-hoc groups

Desmedt, Y., Lange, T. & Burmester, M., 2006, s.n. 16 p. (Cryptology ePrint Archive; vol. 2006/443)

Research output: Book/ReportReportAcademic

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)
2007

Analysis and optimization of elliptic-curve single-scalar multiplication

Bernstein, D. J. & Lange, T., 2007, IACR. 19 p. (Cryptology ePrint Archive; vol. 2007/455)

Research output: Book/ReportReportAcademic

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)