Kleinjung, Thorsten; Wesolowski, Benjamin Discrete logarithms in quasi-polynomial time in finite fields of fixed characteristic. (English) Zbl 1487.11113 J. Am. Math. Soc. 35, No. 2, 581-624 (2022). Reviewer: Juan Tena Ayuso (Valladolid) MSC: 11Y16 14H52 11T71 PDFBibTeX XMLCite \textit{T. Kleinjung} and \textit{B. Wesolowski}, J. Am. Math. Soc. 35, No. 2, 581--624 (2022; Zbl 1487.11113) Full Text: DOI arXiv
Bos, Joppe W.; Kleinjung, Thorsten; Page, Dan Efficient modular arithmetic. (English) Zbl 1483.94036 Bos, Joppe W. (ed.) et al., Computational cryptography. Algorithmic aspects of cryptology. A tribute to Arjen K. Lenstra on the occasion of his 65th birthday. Cambridge: Cambridge University Press. Lond. Math. Soc. Lect. Note Ser. 469, 223-250 (2021). MSC: 94A60 94-03 94-02 PDFBibTeX XMLCite \textit{J. W. Bos} et al., Lond. Math. Soc. Lect. Note Ser. 469, 223--250 (2021; Zbl 1483.94036) Full Text: DOI Link
Granger, Robert; Kleinjung, Thorsten; Lenstra, Arjen K.; Wesolowski, Benjamin; Zumbrägel, Jens Computation of a 30750-bit binary field discrete logarithm. (English) Zbl 1472.11319 Math. Comput. 90, No. 332, 2997-3022 (2021). MSC: 11Y16 11T71 94A60 PDFBibTeX XMLCite \textit{R. Granger} et al., Math. Comput. 90, No. 332, 2997--3022 (2021; Zbl 1472.11319) Full Text: DOI arXiv
Kaluđerović, Novak; Kleinjung, Thorsten; Kostić, Dušan Cryptanalysis of the generalised Legendre pseudorandom function. (English) Zbl 1472.94052 Galbraith, Steven D. (ed.), ANTS XIV. Proceedings of the fourteenth algorithmic number theory symposium, Auckland, New Zealand, virtual event, June 29 – July 4, 2020. Berkeley, CA: Mathematical Sciences Publishers (MSP). Open Book Ser. 4, 267-282 (2020). MSC: 94A60 11T71 PDFBibTeX XMLCite \textit{N. Kaluđerović} et al., Open Book Ser. 4, 267--282 (2020; Zbl 1472.94052) Full Text: DOI
Kleinjung, Thorsten; Wesolowski, Benjamin A new perspective on the powers of two descent for discrete logarithms in finite fields. (English) Zbl 07721134 Scheidler, Renate (ed.) et al., ANTS XIII. Proceedings of the thirteenth algorithmic number theory symposium, University of Wisconsin-Madison, WI, USA, July 16–20, 2018. Berkeley, CA: Mathematical Sciences Publishers (MSP). Open Book Ser. 2, 343-352 (2019). MSC: 11T71 11Y16 PDFBibTeX XMLCite \textit{T. Kleinjung} and \textit{B. Wesolowski}, Open Book Ser. 2, 343--352 (2019; Zbl 07721134) Full Text: DOI arXiv
Beullens, Ward; Kleinjung, Thorsten; Vercauteren, Frederik CSI-FiSh: efficient isogeny based signatures through class group computations. (English) Zbl 1456.94050 Galbraith, Steven D. (ed.) et al., Advances in cryptology – ASIACRYPT 2019. 25th international conference on the theory and application of cryptology and information security, Kobe, Japan, December 8–12, 2019. Proceedings. Part I. Cham: Springer. Lect. Notes Comput. Sci. 11921, 227-247 (2019). MSC: 94A60 94A62 PDFBibTeX XMLCite \textit{W. Beullens} et al., Lect. Notes Comput. Sci. 11921, 227--247 (2019; Zbl 1456.94050) Full Text: DOI
Granger, Robert; Kleinjung, Thorsten; Zumbrägel, Jens Indiscreet logarithms in finite fields of small characteristic. (English) Zbl 1414.11166 Adv. Math. Commun. 12, No. 2, 263-286 (2018). MSC: 11Y16 11T71 94A60 PDFBibTeX XMLCite \textit{R. Granger} et al., Adv. Math. Commun. 12, No. 2, 263--286 (2018; Zbl 1414.11166) Full Text: DOI arXiv
Granger, Robert; Kleinjung, Thorsten; Zumbrägel, Jens On the discrete logarithm problem in finite fields of fixed characteristic. (English) Zbl 1428.11210 Trans. Am. Math. Soc. 370, No. 5, 3129-3145 (2018). MSC: 11Y16 11T71 PDFBibTeX XMLCite \textit{R. Granger} et al., Trans. Am. Math. Soc. 370, No. 5, 3129--3145 (2018; Zbl 1428.11210) Full Text: DOI arXiv
Kleinjung, Thorsten Polynomial selection for the number field sieve. (English) Zbl 07677662 Bos, Joppe W. (ed.) et al., Topics in computational number theory inspired by Peter L. Montgomery. Cambridge: Cambridge University Press. 161-174 (2017). MSC: 11Y16 11Y05 PDFBibTeX XMLCite \textit{T. Kleinjung}, in: Topics in computational number theory inspired by Peter L. Montgomery. Cambridge: Cambridge University Press. 161--174 (2017; Zbl 07677662) Full Text: DOI
Gélin, Alexandre; Kleinjung, Thorsten; Lenstra, Arjen K. Parametrizations for families of ECM-friendly curves. (English) Zbl 1458.11092 Burr, Michael (ed.), Proceedings of the 42nd international symposium on symbolic and algebraic computation, ISSAC 2017, Kaiserslautern, Germany, July 25–28, 2017. New York, NY: Association for Computing Machinery (ACM). 165-171 (2017). MSC: 11G05 68W30 PDFBibTeX XMLCite \textit{A. Gélin} et al., in: Proceedings of the 42nd international symposium on symbolic and algebraic computation, ISSAC 2017, Kaiserslautern, Germany, July 25--28, 2017. New York, NY: Association for Computing Machinery (ACM). 165--171 (2017; Zbl 1458.11092) Full Text: DOI HAL
Franke, Jens; Kleinjung, Thorsten; Büthe, Jan; Jost, Alexander A practical analytic method for calculating \(\pi(x)\). (English) Zbl 1431.11142 Math. Comput. 86, No. 308, 2889-2909 (2017). MSC: 11Y35 11Y70 PDFBibTeX XMLCite \textit{J. Franke} et al., Math. Comput. 86, No. 308, 2889--2909 (2017; Zbl 1431.11142) Full Text: DOI
Kleinjung, Thorsten; Diem, Claus; Lenstra, Arjen K.; Priplata, Christine; Stahlke, Colin Computation of a 768-bit prime field discrete logarithm. (English) Zbl 1411.11135 Coron, Jean-Sébastien (ed.) et al., Advances in cryptology – EUROCRYPT 2017. 36th annual international conference on the theory and applications of cryptographic techniques, Paris, France, April 30 – May 4, 2017. Proceedings. Part I. Cham: Springer. Lect. Notes Comput. Sci. 10210, 185-201 (2017). MSC: 11T71 11Y16 94A60 PDFBibTeX XMLCite \textit{T. Kleinjung} et al., Lect. Notes Comput. Sci. 10210, 185--201 (2017; Zbl 1411.11135) Full Text: DOI
Kleinjung, Thorsten Quadratic sieving. (English) Zbl 1362.11108 Math. Comput. 85, No. 300, 1861-1873 (2016). Reviewer: Alexander Hulpke (Fort Collins) MSC: 11Y05 11Y40 11Y16 PDFBibTeX XMLCite \textit{T. Kleinjung}, Math. Comput. 85, No. 300, 1861--1873 (2016; Zbl 1362.11108) Full Text: DOI
Barbulescu, Razvan; Gaudry, Pierrick; Kleinjung, Thorsten The tower number field sieve. (English) Zbl 1375.94096 Iwata, Tetsu (ed.) et al., Advances in cryptology – ASIACRYPT 2015. 21st international conference on the theory and application of cryptology and information security, Auckland, New Zealand, November 29 – December 3, 2015. Proceedings. Part II. Berlin: Springer (ISBN 978-3-662-48799-0/pbk; 978-3-662-48800-3/ebook). Lecture Notes in Computer Science 9453, 31-55 (2015). MSC: 94A60 11Y16 PDFBibTeX XMLCite \textit{R. Barbulescu} et al., Lect. Notes Comput. Sci. 9453, 31--55 (2015; Zbl 1375.94096) Full Text: DOI
Kleinjung, Thorsten; Bos, Joppe W.; Lenstra, Arjen K. Mersenne factorization factory. (English) Zbl 1306.11098 Sarkar, Palash (ed.) et al., Advances in cryptology – ASIACRYPT 2014. 20th international conference on the theory and application of cryptology and information security, Kaoshiung, Taiwan, R.O.C., December 7–11, 2014. Proceedings, Part I. Berlin: Springer (ISBN 978-3-662-45610-1/pbk). Lecture Notes in Computer Science 8873, 358-377 (2014). MSC: 11Y05 94A60 PDFBibTeX XMLCite \textit{T. Kleinjung} et al., Lect. Notes Comput. Sci. 8873, 358--377 (2014; Zbl 1306.11098) Full Text: DOI
Granger, Robert; Kleinjung, Thorsten; Zumbrägel, Jens Breaking ‘128-bit secure’ supersingular binary curves. (Or how to solve discrete logarithms in \({\mathbb F}_{2^{4 \cdot 1223}}\) and \({\mathbb F}_{2^{12 \cdot 367}}\)). (English) Zbl 1334.94080 Garay, Juan A. (ed.) et al., Advances in cryptology – CRYPTO 2014. 34th annual cryptology conference, Santa Barbara, CA, USA, August 17–21, 2014. Proceedings, Part II. Berlin: Springer (ISBN 978-3-662-44380-4/pbk). Lecture Notes in Computer Science 8617, 126-145 (2014). MSC: 94A60 14G50 11Y16 11T71 PDFBibTeX XMLCite \textit{R. Granger} et al., Lect. Notes Comput. Sci. 8617, 126--145 (2014; Zbl 1334.94080) Full Text: DOI arXiv
Barbulescu, Razvan; Bos, Joppe W.; Bouvier, Cyril; Kleinjung, Thorsten; Montgomery, Peter L. Finding ECM-friendly curves through a study of Galois properties. (English) Zbl 1344.11043 Howe, Everett W. (ed.) et al., ANTS X. Proceedings of the tenth algorithmic number theory symposium, San Diego, CA, USA, July 9–13, 2012. Berkeley, CA: Mathematical Sciences Publishers (MSP) (ISBN 978-1-935107-00-2/hbk; 978-1-935107-01-9/ebook). The Open Book Series 1, 63-86 (2013). MSC: 11G05 11Y05 11G15 PDFBibTeX XMLCite \textit{R. Barbulescu} et al., Open Book Ser. 1, 63--86 (2013; Zbl 1344.11043) Full Text: arXiv
Lenstra, Arjen K.; Kleinjung, Thorsten; Thomé, Emmanuel Universal security. From bits and mips to pools, lakes – and beyond. (English) Zbl 1320.94072 Fischlin, Marc (ed.) et al., Number theory and cryptography. Papers in honor of Johannes Buchmann on the occasion of his 60th birthday. Berlin: Springer (ISBN 978-3-642-42000-9/pbk). Lecture Notes in Computer Science 8260, 121-124 (2013). MSC: 94A60 PDFBibTeX XMLCite \textit{A. K. Lenstra} et al., Lect. Notes Comput. Sci. 8260, 121--124 (2013; Zbl 1320.94072) Full Text: DOI
Büthe, J.; Franke, Jens; Jost, Alexander; Kleinjung, Thorsten Some applications of the Weil-Barner explicit formula. (English) Zbl 1339.11079 Math. Nachr. 286, No. 5-6, 536-549 (2013). Reviewer: Tatyana L. Todorova (Sofia) MSC: 11M06 11N05 11Y35 PDFBibTeX XMLCite \textit{J. Büthe} et al., Math. Nachr. 286, No. 5--6, 536--549 (2013; Zbl 1339.11079) Full Text: DOI
Ding, Jintai; Kleinjung, Thorsten Degree of regularity for HFE Minus (HFE\(-\)). (English) Zbl 1302.94042 J. Math-for-Ind. 4, No. A, 97-104 (2012). MSC: 94A60 PDFBibTeX XMLCite \textit{J. Ding} and \textit{T. Kleinjung}, J. Math-for-Ind. 4, No. A, 97--104 (2012; Zbl 1302.94042)
Kleinjung, Thorsten; Lenstra, Arjen K.; Page, Dan; Smart, Nigel P. Using the cloud to determine key strengths. (English) Zbl 1295.94093 Galbraith, Steven (ed.) et al., Progress in cryptology – INDOCRYPT 2012. 13th international conference on cryptology in India, Kolkata, India, December 9–12, 2012. Proceedings. Berlin: Springer (ISBN 978-3-642-34930-0/pbk). Lecture Notes in Computer Science 7668, 17-39 (2012). MSC: 94A60 PDFBibTeX XMLCite \textit{T. Kleinjung} et al., Lect. Notes Comput. Sci. 7668, 17--39 (2012; Zbl 1295.94093) Full Text: DOI
Bos, Joppe W.; Kleinjung, Thorsten ECM at work. (English) Zbl 1292.94036 Wang, Xiaoyun (ed.) et al., Advances in cryptology – ASIACRYPT 2012. 18th international conference on the theory and application of cryptology and information security, Beijing, China, December 2–6, 2012. Proceedings. Berlin: Springer (ISBN 978-3-642-34960-7/pbk). Lecture Notes in Computer Science 7658, 467-484 (2012). MSC: 94A60 PDFBibTeX XMLCite \textit{J. W. Bos} and \textit{T. Kleinjung}, Lect. Notes Comput. Sci. 7658, 467--484 (2012; Zbl 1292.94036) Full Text: DOI
Bos, Joppe W.; Kaihara, Marcelo E.; Kleinjung, Thorsten; Lenstra, Arjen K.; Montgomery, Peter L. Solving a 112-bit prime elliptic curve discrete logarithm problem on game consoles using sloppy reduction. (English) Zbl 1276.94008 Int. J. Appl. Cryptogr. 2, No. 3, 212-228 (2012). MSC: 94A60 11Y16 PDFBibTeX XMLCite \textit{J. W. Bos} et al., Int. J. Appl. Cryptogr. 2, No. 3, 212--228 (2012; Zbl 1276.94008) Full Text: DOI
Lenstra, Arjen K.; Hughes, James P.; Augier, Maxime; Bos, Joppe W.; Kleinjung, Thorsten; Wachter, Christophe Public keys. (English) Zbl 1296.94127 Safavi-Naini, Reihaneh (ed.) et al., Advances in cryptology – CRYPTO 2012. 32nd annual cryptology conference, Santa Barbara, CA, USA, August 19–23, 2012. Proceedings. Berlin: Springer (ISBN 978-3-642-32008-8/pbk). Lecture Notes in Computer Science 7417, 626-642 (2012). MSC: 94A60 PDFBibTeX XMLCite \textit{A. K. Lenstra} et al., Lect. Notes Comput. Sci. 7417, 626--642 (2012; Zbl 1296.94127) Full Text: DOI
Bos, Joppe W.; Kleinjung, Thorsten; Lenstra, Arjen K. On the use of the negation map in the Pollard rho method. (English) Zbl 1260.11080 Hanrot, Guillaume (ed.) et al., Algorithmic number theory. 9th international symposium, ANTS-IX, Nancy, France, July 19–23, 2010. Proceedings. Berlin: Springer (ISBN 978-3-642-14517-9/pbk). Lecture Notes in Computer Science 6197, 66-82 (2010). MSC: 11Y16 14G50 94A60 PDFBibTeX XMLCite \textit{J. W. Bos} et al., Lect. Notes Comput. Sci. 6197, 66--82 (2010; Zbl 1260.11080) Full Text: DOI Link
Kleinjung, Thorsten; Aoki, Kazumaro; Franke, Jens; Lenstra, Arjen K.; Thomé, Emmanuel; Bos, Joppe W.; Gaudry, Pierrick; Kruppa, Alexander; Montgomery, Peter L.; Osvik, Dag Arne; te Riele, Herman; Timofeev, Andrey; Zimmermann, Paul Factorization of a 768-bit RSA modulus. (English) Zbl 1196.11167 Rabin, Tal (ed.), Advances in cryptology - CRYPTO 2010. 30th annual cryptology conference, Santa Barbara, CA, USA, August 15–19, 2010. Proceedings. Berlin: Springer (ISBN 978-3-642-14622-0/pbk). Lecture Notes in Computer Science 6223, 333-350 (2010). MSC: 11Y05 94A60 PDFBibTeX XMLCite \textit{T. Kleinjung} et al., Lect. Notes Comput. Sci. 6223, 333--350 (2010; Zbl 1196.11167) Full Text: DOI
Bos, Joppe W.; Kleinjung, Thorsten; Niederhagen, Ruben; Schwabe, Peter ECC2K-130 on Cell CPUs. (English) Zbl 1284.94054 Bernstein, Daniel J. (ed.) et al., Progress in cryptology – AFRICACRYPT 2010. Third international conference on cryptology in Africa, Stellenbosch, South Africa, May 3–6, 2010. Proceedings. Berlin: Springer (ISBN 978-3-642-12677-2/pbk). Lecture Notes in Computer Science 6055, 225-242 (2010). MSC: 94A60 11-04 11Y16 94-04 PDFBibTeX XMLCite \textit{J. W. Bos} et al., Lect. Notes Comput. Sci. 6055, 225--242 (2010; Zbl 1284.94054) Full Text: DOI Link
Aoki, Kazumaro; Franke, Jens; Kleinjung, Thorsten; Lenstra, Arjen K.; Osvik, Dag Arne A kilobit special number field sieve factorization. (English) Zbl 1153.11344 Kurosawa, Kaoru (ed.), Advances in cryptology – ASIACRYPT 2007. 13th international conference on the theory and application of cryptology and information security, Kuching, Malaysia, December 2-6, 2007. Proceedings. Berlin: Springer (ISBN 978-3-540-76899-9/pbk). Lecture Notes in Computer Science 4833, 1-12 (2007). MSC: 11Y05 11T71 11Y16 94A60 PDFBibTeX XMLCite \textit{K. Aoki} et al., Lect. Notes Comput. Sci. 4833, 1--12 (2007; Zbl 1153.11344) Full Text: DOI
Kleinjung, Thorsten On polynomial selection for the general number field sieve. (English) Zbl 1183.11079 Math. Comput. 75, No. 256, 2037-2047 (2006). MSC: 11Y05 11Y16 PDFBibTeX XMLCite \textit{T. Kleinjung}, Math. Comput. 75, No. 256, 2037--2047 (2006; Zbl 1183.11079) Full Text: DOI
Franke, Jens; Kleinjung, Thorsten; Morain, François; Wirth, T. Proving the primality of very large numbers with fastECPP. (English) Zbl 1125.11359 Buell, Duncan (ed.), Algorithmic number theory. 6th international symposium, ANTS-VI, Burlington, VT, USA, June 13–18, 2004. Proceedings. Berlin: Springer (ISBN 3-540-22156-5/pbk). Lecture Notes in Computer Science 3076, 194-207 (2004). MSC: 11Y11 PDFBibTeX XMLCite \textit{J. Franke} et al., Lect. Notes Comput. Sci. 3076, 194--207 (2004; Zbl 1125.11359) Full Text: DOI
Lin, Kuang; Kleinjung, Jens; Taylor, William R.; Heringa, Jaap Testing homology with contact accepted mutatiOn (CAO): A contact-based Markov model of protein evolution. (English) Zbl 1024.92007 Comput. Biol. Chem. 27, No. 2, 93-102 (2003). MSC: 92C40 92-08 PDFBibTeX XMLCite \textit{K. Lin} et al., Comput. Biol. Chem. 27, No. 2, 93--102 (2003; Zbl 1024.92007) Full Text: DOI
Kleinjung, Thorsten Framed mixed Tate motives and the value of zeta-functions of number fields at 2 and 3. (Gerahmte gemischte Tate-Motive und die Werte von Zetafunktionen zu Zahlkörpern an den Stellen 2 und 3.) (German) Zbl 0971.14022 Bonner Mathematische Schriften. 340. Bonn: Univ. Bonn, Mathematisch-Naturwissenschaftliche Fakultät, 77 S. (2001). Reviewer: Werner Kleinert (Berlin) MSC: 14G10 11R42 14F42 19E15 19F27 PDFBibTeX XMLCite \textit{T. Kleinjung}, Gerahmte gemischte Tate-Motive und die Werte von Zetafunktionen zu Zahlkörpern an den Stellen 2 und 3. Bonn: Univ. Bonn, Mathematisch-Naturwissenschaftliche Fakultät (2001; Zbl 0971.14022)