Journal Papers

Conference Papers

Technical Reports

  • Montgomery Multiplication on the Cell, Joppe W. Bos, Marcelo E. Kaihara, Parallel Processing and Applied Mathematics (PPAM 2009), volume 6067 of LNCS, pages 477-485, 2010.
  • Pollard rho on the PlayStation 3, Joppe W. Bos, Marcelo E. Kaihara, Peter L. Montgomery, Handouts of SHARCS 2009, pages 35-50, Sep. 2009.
  • On the Security of 1024-bit RSA and 160-bit Elliptic Curve Cryptography, Joppe W. Bos, Marcelo E. Kaihara, Thorsten Kleinjung, Arjen K. Lenstra and Peter L. Montgomery, Cryptology ePrint Archive: Report 2009/389, Aug. 2009.
  • A Multiplier/Divider for Modular Arithmetic Based on the Extended Euclidean Algorithm, M.E. Kaihara, N. Takagi, Techinical Report of IEICE, VLD2004-1, vol.104, No.78, pg. 1-6., May 2004.
  • A Multiplication Division VLSI Algorithm for Modular Arithmetic, M.E. Kaihara, N. Takagi, LA Symposium, Evolutionary Advancement in Fundamental Theories of Computer Science, pg.201-207, May 2004.
  • A Modular Multiplication/Division Algorithm for VLSI, M.E. Kaihara, N. Takagi, CS Sessions at 2003 IEICE Gen. Conf., Mar. 2003.
  • A Modulo M Multiplier/Divider, M.E. Kaihara, N. Takagi, Technical Report of IEICE, VLD2002-109, vol. 102, No. 476, pg. 163-168, Nov. 2002.

Invited Talks

  • An Implementation of RSA2048 on GPUs Using CUDA, 4es Rencontres Arithmétique de l'Informatique Mathématique (RAIM’11), Perpignan, France, Feb. 2011.(Slides).
  • An Implementation of RSA2048 on GPUs, INRIA Nancy Grand-Est, LORIA, France, Nov. 2010. (Slides).
  • Modular Arithmetic on PlayStation 3, Laboratoire d'Informatique de Paris 6, LIP6, Université Pierre et Marie Curie, CNRS UPMC, Paris, France, Jan. 2010.
  • Pollard Rho sur PlayStation 3, Rencontres Arithmétique de l'Informatique Mathématique (RAIM’09), ENS Lyon, France, Oct. 2009 (Slides).

World Record

  • PlayStation 3 computing breaks 260 barrier: 112-bit prime ECDLP solved (Slides). My contributions to this project: I propose the use of a scaled modulus for fast modular reduction; acceleration by reducing the number of reductions allowing detectable faulty results (sloppy reduction); partial Montgomery reduction for fast normalization modulo p; ECDLP tag-tracing; escaping cycles using doubling to avoid recurring cycles; long integer representation on the Cell and implementation of modular multiplication routines.

Doctoral Dissertation


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