David Jao

I am an associate professor in the Faculty of Mathematics (http://www.math.uwaterloo.ca/) at the University of Waterloo (http://www.uwaterloo.ca/). I am a member of the:

• Center for Applied Cryptographic Research (http://www.cacr.math.uwaterloo.ca/)
• Department of Combinatorics and Optimization (http://www.math.uwaterloo.ca/CandO_Dept/)

My research interests are in the areas of number theory (http://en.wikipedia.org/wiki/Number_Theory) and cryptography (http://en.wikipedia.org/wiki/Cryptography), with emphasis on elliptic (http://en.wikipedia.org/wiki/Elliptic_Curve_Cryptography) and hyperelliptic curve cryptography (http://en.wikipedia.org/wiki/Hyperelliptic_Curve_Cryptography).

Prior to joining the University of Waterloo, I was a post-doc researcher in the Cryptography and Anti-Piracy Group (http://research.microsoft.com/en-us/um/redmond/groups/crypto/) at Microsoft Research (http://research.microsoft.com/). I received my Ph.D. in Mathematics (http://www.genealogy.ams.org/id.php?id=71888) from Harvard University (http://www.math.harvard.edu/) under the supervision of Noam Elkies (http://www.math.harvard.edu/~elkies/).

Articles

• Publicly verifiable secret sharing for cloud-based key management (http:../../wiki/images/9/9c/Indocrypt11.pdf), with R. D'Souza, I. Mironov, and O. Pandey, Indocrypt 2011, pp. 290-309, doi:10.1007/978-3-642-25578-6_21 (http://dx.doi.org/10.1007/978-3-642-25578-6_21)

• Towards quantum-resistant cryptosystems from supersingular elliptic curve isogenies (http://eprint.iacr.org/2011/506), with L. De Feo, PQCrypto 2011, pp. 19-34, doi:10.1007/978-3-642-25405-5_2 (http://dx.doi.org/10.1007/978-3-642-25405-5_2)

• Constructing elliptic curve isogenies in quantum subexponential time (http://arxiv.org/abs/1012.4019), with A. Childs and V. Soukharev.

• A subexponential algorithm for evaluating large degree isogenies (http://arxiv.org/abs/1002.4228), with V. Soukharev, ANTS IX, pp. 219-233, doi:10.1007/978-3-642-14518-6_19 (http://dx.doi.org/10.1007/978-3-642-14518-6_19)

• Elliptic curve cryptography (http:../../wiki/images/a/a1/Handbook.pdf), in Handbook of Information and Communication Security, pp. 35-57, doi:10.1007/978-3-642-04117-4_3 (http://dx.doi.org/10.1007/978-3-642-04117-4_3)

• A study of two-party certificateless authenticated key-agreement protocols (http:../../wiki/images/1/1a/Indocrypt09.pdf), with C. Swanson, Indocrypt 2009, pp. 57-71, doi:10.1007/978-3-642-10628-6_4 (http://dx.doi.org/10.1007/978-3-642-10628-6_4).

• Boneh-Boyen signatures and the Strong Diffie-Hellman problem (http://eprint.iacr.org/2009/221), with K. Yoshida, Pairing 2009, pp. 1-16, doi:10.1007/978-3-642-03298-1_1 (http://dx.doi.org/10.1007/978-3-642-03298-1_1).

• Expander graphs based on GRH with an application to elliptic curve cryptography (http://arxiv.org/abs/0811.0647), with S. D. Miller and R. Venkatesan, J. Num. Thy. 129 no. 6, 2009, pp. 1491-1504, doi:10.1016/j.jnt.2008.11.006 (http://dx.doi.org/10.1016/j.jnt.2008.11.006).

• Speeding up pairing computations on genus 2 hyperelliptic curves with efficiently computable automorphisms (http:../../wiki/images/1/1a/Pairing-2008.pdf), with X. Fan and G. Gong, Pairing 2008, pp. 243-264, doi:10.1007/978-3-540-85538-5_17 (http://dx.doi.org/10.1007/978-3-540-85538-5_17).

• Efficient pairing computation on genus 2 curves in projective coordinates (http:../../wiki/images/b/b5/Sac-2008.pdf), with X. Fan and G. Gong, SAC 2008, pp. 18-34, doi:10.1007/978-3-642-04159-4_2 (http://dx.doi.org/10.1007/978-3-642-04159-4_2).

• On the bits of elliptic curve Diffie-Hellman keys (http:../../wiki/images/8/82/Indocrypt-2007.pdf), with D. Jetchev and R. Venkatesan, Indocrypt 2007, pp. 33-47, doi:10.1007/978-3-540-77026-8_4 (http://dx.doi.org/10.1007/978-3-540-77026-8_4).

• Digit set randomization in elliptic curve cryptography (http:../../wiki/images/0/0a/Saga-2007.pdf), with S. R. Raju and R. Venkatesan, SAGA 2007, pp. 105-117, doi:10.1007/978-3-540-74871-7_10 (http://dx.doi.org/10.1007/978-3-540-74871-7_10).

• Do all elliptic curves of the same order have the same difficulty of discrete log? (http:../../wiki/images/9/91/Asiacrypt-2005.pdf), with S. D. Miller and R. Venkatesan, Asiacrypt 2005, pp. 21-40, doi:10.1007/11593447_2 (http://dx.doi.org/10.1007/11593447_2).

• Applications of secure electronic voting to automated privacy-preserving troubleshooting (http:../../wiki/images/2/2e/Ccs-2005.pdf), with Q. Huang and H. J. Wang, CCS 2005, pp. 68-80, doi:10.1145/1102120.1102132 (http://dx.doi.org/10.1145/1102120.1102132).

• Supersingular primes for points on X₀(p) / w_p (http:../../wiki/images/d/df/Jnt-2005.pdf), J. Num. Thy. 113 no. 2, 2005, pp. 208-225, doi:10.1016/j.jnt.2004.09.002 (http://dx.doi.org/10.1016/j.jnt.2004.09.002).

Patents

• Privacy-preserving data aggregation using homomorphic encryption (http://patft.uspto.gov/netacgi/nph-Parser?Sect2=PTO1&Sect2=HITOFF&p=1&u=%2Fnetahtml%2FPTO%2Fsearch-bool.html&r=1&f=G&l=50&d=PALL&RefSrch=yes&Query=PN%2F7856100), with H. J. Wang and Q. Huang, United States patent 7856100, issued December 21, 2010.

• Aggregating information from a cluster of peers (http://patft.uspto.gov/netacgi/nph-Parser?Sect2=PTO1&Sect2=HITOFF&p=1&u=%2Fnetahtml%2FPTO%2Fsearch-bool.html&r=1&f=G&l=50&d=PALL&RefSrch=yes&Query=PN%2F7743123), with H. J. Wang, N. Borisov, and Q. Huang, United States patent 7743123, issued June 22, 2010.

• Randomized sparse formats for efficient and secure computation on elliptic curves (http://patft.uspto.gov/netacgi/nph-Parser?Sect2=PTO1&Sect2=HITOFF&p=1&u=%2Fnetahtml%2FPTO%2Fsearch-bool.html&r=1&f=G&l=50&d=PALL&RefSrch=yes&Query=PN%2F7664258), with R. Venkatesan, P. Montgomery, and S. R. Raju, United States patent 7664258, issued February 16, 2010.

• Systems and methods for generation and validation of isogeny-based signatures (http://patft.uspto.gov/netacgi/nph-Parser?Sect2=PTO1&Sect2=HITOFF&p=1&u=%2Fnetahtml%2FPTO%2Fsearch-bool.html&r=1&f=G&l=50&d=PALL&RefSrch=yes&Query=PN%2F7617397), with P. Montgomery, R. Venkatesan, and V. Boyko, United States patent 7617397, issued November 10, 2009.

• Determining cardinality of a parameter using hash values (http://patft.uspto.gov/netacgi/nph-Parser?Sect2=PTO1&Sect2=HITOFF&p=1&u=%2Fnetahtml%2FPTO%2Fsearch-bool.html&r=1&f=G&l=50&d=PALL&RefSrch=yes&Query=PN%2F7584182), with H. J. Wang, N. Borisov, and Q. Huang, United States patent 7584182, issued September 1, 2009.

• Use of isogenies for design of cryptosystems (http://patft.uspto.gov/netacgi/nph-Parser?Sect2=PTO1&Sect2=HITOFF&p=1&u=%2Fnetahtml%2FPTO%2Fsearch-bool.html&r=1&f=G&l=50&d=PALL&RefSrch=yes&Query=PN%2F7499544), with R. Venkatesan, United States patent 7499544, issued March 3, 2009.

Teaching

I find that teaching and the students keep life going, and I would never accept any position in which somebody has invented a happy situation for me where I don't have to teach. Never.

--Richard P. Feynman

• CO 789
  • Fall 2011
  • Winter 2007
• Math 145
  • Fall 2011
• CO 487
  • Winter 2011
• CO 331
  • Winter 2011
  • Winter 2007
• CO 485/685
  • Fall 2010
  • Fall 2009
  • Fall 2008
  • Fall 2007
• Math 239
  • Fall 2010
  • Fall 2009
  • Spring 2009
  • Fall 2008
  • Fall 2007
• CO 690
  • Winter 2007

Contact information

Address	200 University Ave. W Waterloo, ON, N2L 3G1 Canada
Office	MC 5038
Phone	519-888-4567 x32493
Email	djao@uwaterloo.ca