Publications on Computational Number Theory

2012

• Thomas Lansdall-Welfare, Vasileios Lampos, Nello Cristianini, The Effect of the Recession on Collective Mood in the UK. Proceedings of Internet, Politics, Policy 2012. July 2012. PDF, 623 Kbytes. External information

2010

• Luo Sun, Jimson Mathew, Dhiraj Pradhan, S. P. Mohanty, Algorithms for Rare Event Analysis in Nano-CMOS Circuits Using Statistical Blockade. Proceedings of the International SoC Design Conference (ISOCC). May 2010. No electronic version available.

2009

• Robert Granger, Andrew Moss, Nigel Smart, Efficient Arithmetic Modulo Minimal Redundancy Cyclotomic Primes. CSTR-09-004, Claude Shannon Institute, Ireland and University of Bristol. August 2009. PDF, 273 Kbytes.

2008

• Robert Granger, Andrew Moss, Nigel Smart, Efficient Arithmetic Modulo Cyclotomic Primes. CSTR-08-001, University of Bristol. February 2008. PDF, 109 Kbytes.

2007

• Nigel Smart, Y. Tourigny, A multidimensional continued fraction based on a high-order recurrence relation. . Math. Comp., 76, pp. 1995–2022. August 2007. No electronic version available.
• Robert Granger, Florian Hess, Roger Oyono, Nicolas Theriault, Fre Vercauteren, Ate Pairing on Hyperelliptic Curves. Advances in Cryptology - EUROCRYPT 2007, pp. 430–447. May 2007. No electronic version available.

2006

• J. Denef, Fre Vercauteren, Computing zeta functions of C_{ab} curves using Monsky-Washnitzer cohomology. Finite fields and their Applications, 12, pp. 78–102. August 2006. No electronic version available.
• Robert Granger, Nigel Smart, On Computing Products of Pairings. CSTR-06-013, University of Bristol. May 2006. No electronic version available.
• Robert Granger, Dan Page, Martijn Stam, On Small Characteristic Algebraic Tori in Pairing Based Cryptography. LMS Journal of Computation and Mathematics, 9, pp. 64–85. March 2006. No electronic version available.

2005

• Robert Granger, On Small Degree Extension Fields in Cryptology. PhD thesis. University of Bristol. November 2005. PDF, 802 Kbytes.
• Robert Granger, Fre Vercauteren, On the Discrete Logarithm Problem on Algebraic Tori. Advances in Cryptology (CRYPTO 2005), pp. 66–85. August 2005. No electronic version available.
• Robert Granger, Dan Page, Martijn Stam, Hardware and Software Normal Basis Arithmetic for Pairing-Based Cryptography in Characteristic Three. IEEE Transactions on Computers, 54(7), pp. 852–860. July 2005. No electronic version available.
• Marten van Dijk, Robert Granger, Dan Page, Karl Rubin, Alice Silverberg, Martijn Stam, David Woodruff, Practical Cryptography in High Dimensional Tori. Advances in Cryptology (EUROCRYPT 2005), pp. 234–250. May 2005. No electronic version available.

2004

• Robert Granger, Andrew Holt, Dan Page, Nigel Smart, Fre Vercauteren, Function Field Sieve in Characteristic Three. Algorithmic Number Theory, 6th International Symposium, ANTS-VI. ISBN 3-540-22156-5, pp. 223–234. June 2004. PDF, 198 Kbytes.
• Robert Granger, Dan Page, Martijn Stam, A Comparison of CEILIDH and XTR. Algorithmic Number Theory, 6th International Symposium, ANTS-VI. ISBN 3-540-22156-5, pp. 235–249. June 2004. PDF, 287 Kbytes.

2003

• Robert Granger, Estimates for Discrete Logarithm Computations in Finite Fields of Small Characteristic. Cryptography and Coding. ISSN 0302-9743, pp. 190–206. December 2003. PDF, 235 Kbytes.
• Florian Hess, S. Pauli, M.E. Pohst, Computing the multiplicative group of residue class rings. Math. Comp., 72, pp. 1531–1548. August 2003. No electronic version available.

2002

• Keith Harrison, Dan Page, Nigel Smart, Software Implementation of Finite Fields of Characteristic Three. LMS JCM, 5 (-). ISSN x, pp. 181–193. November 2002. No electronic version available. External information
• Frederik Vercauteren, Computing zeta functions of hyperelliptic curves over finite fields of characteristic 2. Advances in Cryptology - Crypto 2002. Moti Yung, (eds.). ISSN 0302-9743, pp. 369–384. August 2002. No electronic version available.
• Jan Denef, Frederik Vercauteren, An extension of Kedlaya's algorithm to Artin-Schreier curves in characteristic 2. Algorithmic Number Theory, 5th International Symposium, ANTS-V. Claus Fieker, David R. Kohel, (eds.). ISBN 3-540-43863-7, pp. 369–384. July 2002. No electronic version available.
• F. Hess, Computing Riemann-Roch Spaces in Algebraic Function Fields and Related Topics. Journal of Symbolic Computation, 33 (4). ISSN 0747-7171, pp. 425–445. April 2002. PDF, 317 Kbytes.
• Steven Galbraith, S. Paulus, N. P. Smart, Arithmetic on superelliptic curves . Mathematics of Computation, 71 (?). ISSN 0025-5718, pp. 393–405. January 2002. No electronic version available. External information

2001

• Frederik Vercauteren, Bart Preneel, Joos Vandewalle, A Memory Efficient Version of Satoh's Algorithm. Advances in Cryptology - Eurocrypt 2001. Birgit Pfitzmann, (eds.). ISSN 0302-9743, pp. 1–13. May 2001. No electronic version available.