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Research Output

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Article
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)
2002

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)
2003

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

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)
2004

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

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)
2007

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)
2008

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)
2011

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)

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)
2012

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)
2013

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)
2014

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)