Recent Talks

• Invited lecture at the S3 – Summer School (SAC 2016): “Software Implementation of Public-Key Cryptography”, St. John’s, Canada, August 2016.
• Slides (opens in new tab) from my talk at SAC 2016: “FourQNEON: faster elliptic curve scalar multiplications on ARM processors”, St. John’s, Canada, August 2016.
• Slides (opens in new tab) from my invited talk at the University of Luxembourg: “FourQ: pushing the limits of curve-based cryptography”, Luxembourg, November 2015.
• Slides (opens in new tab) from my invited talk at COSIC – KU Leuven: “FourQ and FourQlib: faster curve-based scalar multiplications”, Leuven, Belgium, November 2015.
• Slides (opens in new tab) from my talk at the NIST Workshop on Elliptic Curve Cryptography Standards, “An Analysis of High-Performance Primes at High-Security Levels”, Gaithersburg, MD, June 2015.
• Slides (opens in new tab) from my talk at the Real World Cryptography Workshop 2015, “Post-Snowden Elliptic Curve Cryptography”, London, UK, January 2015.
• Slides (opens in new tab) from my invited talk at the University of Washington (Tacoma): “NUMS Elliptic Curves and their Implementation”, Tacoma, WA, November 2014.
• Slides (opens in new tab) from my presentation for the IETF Crypto Forum Research Group (CFRG), “Selecting Elliptic Curves for Cryptography”, interim teleconference meeting, April 2014.
• Slides (opens in new tab) from my talk at CT-RSA 2014: “Efficient and Secure Methods for GLV-Based Scalar Multiplication and their Implementation on GLV-GLS Curves”, San Francisco, USA, February 2014.
• Slides (opens in new tab) from my talk at ASIACRYPT2012: “Four-Dimensional Gallant-Lambert-Vanstone Scalar Multiplication”, Beijing, China, December 2012.
• Slides (opens in new tab) from my invited talk at the Peking University: “Highly-Efficient and Secure Elliptic Curve Scalar Multiplication using the 4-GLV Method”, Beijing, China, December 2012.
• Slides (opens in new tab) from my invited talk at the 15th Workshop on Elliptic Curve Cryptography (ECC2011): “Elliptic Curve Cryptography at High Speeds”, Nancy, France, September 2011.
• Slides (opens in new tab) from my talk at EUROCRYPT2011: “Faster Explicit Formulas for Computing Pairings over Ordinary Curves”, Tallinn, Estonia, May 2011.
• Slides (opens in new tab) from my talk at CHES2010: “Efficient Techniques for High-Speed Elliptic Curve Cryptography”, University of California, Sta. Barbara, California, USA, August 2010.
• Slides (opens in new tab) from my talk at the Centre for Applied Cryptographic Research (CACR): “Record-Breaking Implementations of Elliptic Curve Scalar Multiplication on x86-64 Processors”, University of Waterloo, Waterloo, Canada, July 2010.
• Slides (opens in new tab) from my invited talk at the MITACS Workshop on Network Security and Cryptography 2010: “High-Speed Elliptic Curve Cryptography: New Records in Software”, Toronto, Canada, June 2010.

Recent Publications

• Patrick Longa, “FourQNEON: Faster Elliptic Curve Scalar Multiplications on ARM Processors”, Selected Areas in Cryptography (SAC 2016), August 2016. Posted as Cryptology ePrint Report 2016/645, June 2016. [paper] (opens in new tab)
• Kimmo Järvinen, Andrea Miele, Reza Azarderakhsh and Patrick Longa, “FourQ on FPGA: New Hardware Speed Records for Elliptic Curve Cryptography over Large Prime Characteristic Fields”, Workshop on Cryptographic Hardware and Embedded Systems (CHES 2016), August 2016. Posted as Cryptology ePrint Report 2016/569, June 2016. [paper] (opens in new tab)
• Patrick Longa and Michael Naehrig, “Speeding up the Number Theoretic Transform for Faster Ideal Lattice-Based Cryptography”, posted as Cryptology ePrint Report 2016/504, May 2016. [paper] (opens in new tab)
• Craig Costello, Patrick Longa and Michael Naehrig, “Efficient algorithms for supersingular isogeny Diffie-Hellman”, Advances in Cryptology – CRYPTO 2016, 2016. Extended version posted as Cryptology ePrint Report 2016/413, April 2016. [paper] (opens in new tab)
• R. Azarderakhsh, D. Fishbein, G. Grewal, S. Hu, D. Jao, P. Longa and R. Verma, “Fast Software Implementations of Bilinear Pairings”, IEEE Transactions on Dependable and Secure Computing, 2015. Posted as CACR Technical Report, CACR 2016-03, January 2016. [paper] (opens in new tab)
• Craig Costello and Patrick Longa, “FourQ: four-dimensional decompositions on a Q-curve over the Mersenne prime”, Advances in Cryptology – ASIACRYPT 2015, December 2015. Full paper version posted as Cryptology ePrint Report 2015/565, June 2015. [paper] (opens in new tab)
• Craig Costello, Patrick Longa, and Michael Naehrig, “A brief discussion on selecting new elliptic curves (opens in new tab)“, no. MSR-TR-2015-46, 8 June 2015.
• Joppe Bos, Craig Costello, Patrick Longa, and Michael Naehrig, “Specification of Curve Selection and Supported Curve Parameters in MSR ECCLib (opens in new tab)“, no. MSR-TR-2015-49, June 2015.
• Joppe Bos, Craig Costello, Patrick Longa, and Michael Naehrig, “Selecting Elliptic Curves for Cryptography: An Efficiency and Security Analysis”, Journal of Cryptographic Engineering (to appear), May 2015. Posted as Cryptology ePrint Report 2013/130, February 2014. [paper] (opens in new tab)
• A. Faz-Hernandez, P. Longa, and A.H. Sanchez, “Efficient and Secure Methods for GLV-Based Scalar Multiplication and their Implementation on GLV-GLS Curves (Extended Version)”, Journal of Cryptographic Engineering, April 2015. Posted as Cryptology ePrint Report 2013/158, March 2013. [paper] (opens in new tab)
• A. Faz-Hernandez, P. Longa, and A.H. Sanchez, “Efficient and Secure Methods for GLV-Based Scalar Multiplication and their Implementation on GLV-GLS Curves”, RSA Conference Cryptographers’ Track (CT-RSA 2014), February 2014. [paper] (opens in new tab)
• D.F. Aranha, P.S.L.M. Barreto, P. Longa, and J. Ricardini, “The Realm of The Pairings” (Invited Paper), Selected Areas in Cryptography (SAC 2013), 2013. Posted as Cryptology ePrint Report 2013/722, November 2013. [paper] (opens in new tab)
• P. Longa, and F. Sica, “Four-Dimensional Gallant-Lambert-Vanstone Scalar Multiplication” (Full Version), Journal of Cryptology, April 2014. Posted as Cryptology ePrint Report 2011/608, November 2011. [paper] (opens in new tab)
• P. Longa, and F. Sica, “Four-Dimensional Gallant-Lambert-Vanstone Scalar Multiplication”, Advances in Cryptology – ASIACRYPT 2012, 2012. [paper] (opens in new tab)
• G. Grewal, R. Azarderakhsh, P. Longa, S. Hu, and D. Jao, “Efficient Implementation of Bilinear Pairings on ARM Processors”, Selected Areas in Cryptography (SAC 2012), 2012. The full version is posted as Cryptology ePrint Report 2012/408, July 2012. [paper] (opens in new tab)
• Z. Hu, P. Longa, and M. Xu, “Implementing 4-Dimensional GLV Method on GLS Elliptic Curves with j-Invariant 0”, Designs, Codes and Cryptography, June 2012. The full version is posted as Cryptology ePrint Report 2011/315, June 2011. [paper] (opens in new tab)
• D.F. Aranha, K. Karabina, P. Longa, C. Gebotys, and J. Lopez, “Faster Explicit Formulas for Computing Pairings over Ordinary Curves”, Advances in Cryptology – EUROCRYPT 2011, 2011. The full version is posted as Cryptology ePrint Report 2010/526, October 2010. [paper] (opens in new tab)
• P. Longa, and C. Gebotys, “Efficient Techniques for High-Speed Elliptic Curve Cryptography”, Workshop on Cryptographic Hardware and Embedded Systems (CHES 2010), 2010. The full version is posted as Cryptology ePrint Report 2010/315, May 2010. [paper] (opens in new tab)
• P. Longa, C. Gebotys, “Fast Multibase Methods and Other Several Optimizations for Elliptic Curve Scalar Multiplication”, Public-Key Cryptography (PKC 2009), 2009. The full version is posted as Cryptology ePrint Report 2009/173, April 2009. [paper] (opens in new tab)
• P. Longa, C. Gebotys, “Novel Precomputation Schemes for Elliptic Curve Cryptosystems”, Applied Cryptography and Network Security (ACNS 2009), 2009. The full version is posted as Cryptology ePrint Report 2008/526, Dec 2008. [paper] (opens in new tab)
• P. Longa, A. Miri, “New Composite Operations and Precomputation Scheme for Elliptic Curve Cryptosystems over Prime Fields”, Public-Key Cryptography (PKC 2008), 2008. The full version is posted as Cryptology ePrint Report 2008/051, Jan 2008. [paper] (opens in new tab)
• P. Longa, A. Miri, “Fast and Flexible Elliptic Curve Point Arithmetic over Prime Fields”, IEEE Transactions on Computers, 2008. [paper] (opens in new tab)

Theses

• P. Longa, “High-Speed Elliptic Curve and Pairing-Based Cryptography”, Ph.D. Thesis, University of Waterloo, April 2011. The full text can be accessed in [Ph.D. Thesis] (opens in new tab).
• P. Longa, “Accelerating the Scalar Multiplication on Elliptic Curve Cryptosystems over Prime Fields”. Master’s Thesis, University of Ottawa, June 2007. The full text can be accessed in [Master’s Thesis] (opens in new tab).

Professional Activities

I serve(d) on the following program committees:

• 19th Information Security Conference (ISC 2016 (opens in new tab)).
• 3rd International Conference on Cryptology and Information Security in Latin America (LATINCRYPT 2014 (opens in new tab)).
• XVIII IEEE International Conference of Electrical, Electronics and Systems Engineering (INTERCON 2011).

I reviewed papers for the following journals: Journal of Cryptology, IEEE Transactions on Computers, IEEE Transactions on Very Large Scale Integration Systems (VLSI), Journal of Cryptographic Engineering (JCEN), IET Circuits, Devices & Systems, International Journal of Computer Mathematics, Integration – The VLSI Journal, International Journal of Electronics.

I reviewed papers for the following conferences and workshops: ACNS 2016, PKC 2015, LATINCRYPT 2015, ACISP 2015, LightSec 2015, SPACE 2015, PST 2015, ASIACRYPT 2014, PKC 2013, PKC 2011, CHES 2010, PKC 2010, CCECE 2009.

Interns

I have been lucky to work with the following bright interns at MSR:

• Angshuman Karmakar (Ph.D. student at KULeuven, Belgium), Summer 2016.
• Zhe Liu (former Ph.D. student at University of Luxembourg, Luxembourg; currently postdoc at University of Waterloo, Canada), Summer 2015.
• Michael Wesolowski (former master Student at University of Waterloo, Canada; currently at Deloitte Canada), Summer 2014.
• Armando Faz-Hernandez (former master student at CINVESTAV-IPN, Mexico; currently Ph.D. student at University of Campinas, Brazil), Summer 2012.