VCS

San Cao Vo, Ph.D. sancaovo@stanfordalumni.org 


Stanford University, Stanford, California, 1990-1995

- Doctor of Philosophy (Ph.D.) in Mathematics, conferred in June 1995.

- Areas of Interest: Applied Number Theory, Real Analysis, Complex Analysis, Algebra, - Automorphic Forms and Representation Theory.

- Advisor: Professor Daniel W. Bump. Dissertation: “The Spin L-function on the Symplectic Group GSp(6)”, published by the Israel Journal of Mathematics, Volume 101, 1997. (Article of Thesis)

- Master of Science (M.S.) in Mathematics, conferred in June 1992.

     PhD. Defense Lecture         Stanford's Ph.D Thesis

 


University of California at Berkeley, Berkeley, California, 1987-1990

Bachelor of Arts in three majors: Astronomy - Mathematics - Physics, in May 1990 with “High Distinction.

Phi Beta Kappa, Alpha Chapter of California (U. C. Berkeley), April 1989.

University of Technology, Saigon, Vietnam, 1980-1984

Bachelor of Science in Electrical Engineering, in 1984.

Field Major: Automatization & Electrification in Industry.

Graduation Thesis: Designing a microprocessor system to control an electronic bulletin board.


Articles Published

01. Stanford University, Department of Mathematics, Ph.D. Dissertation, 1995. Advisor: Professor Daniel W. Bump.

02. Ph.D. Dissertation: “The Spin L-function on the Symplectic Group GSp(6)”, published by the Israel Journal of Mathematics, Volume 101, 1997.(Article of Thesis, Thesis Summary)

03. NIST, Information Technology Laboratory, Invited lecture, Basic properties of the Riemann Zeta-Functions and L-functions, 1997. (Link/Doc)

04. NIST, Information Technology Laboratory, Computer Security Division, Internal lecture, Elliptic Curve Cryptography in Information Systems Security, 1998. (link)

05. White paper, “Recommendations on Key Agreement and Key Transport Schemes Using Elliptic Curve Cryptography for Government Use”, on the ANSI Standard and FIPS X9.63-1999, “Public Key Cryptography for the Financial Services Industry: Key Agreement and Key Transport Using Elliptic Curve Cryptography”, submitted to Computer Security Division, Information Technology Laboratory, NIST, U. S. Department of Commerce, December 1999. (Notes)

06. NIST (National Institute of Standards& Technology) Random Number Generator and Testing Technical Working Group, Special Publication 800-22, co-author, A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications.

Information Technology Laboratory (ITL), Random Number Generator Working Group of Computer Security Division & Statistical Engineering Division, 2001: Random Number Generator Resources(Links to Information Technology Laboratory's NIST Special Publications 800 on Computer Security Series)

07. NASA Ames Research Center, NASA Technical ReportsSome Improvements on Signed Window Algorithms for Scalar Multiplications in Elliptic Curve Cryptosystems, 2001. Document ID #20010062806, (*.pdf).

08. NASA Special Technical Report, NAS-03-012, “A Surveys to Elliptic Curve Cryptosystems. Part I: An Introduction”, NAS Tech-Reports-03-012.pdf, NASA Ames Research Center, 2003.

09. NIST, Information Technology Laboratory, Invited lecture, Information-to-Knowledge Strategic Reversal Problem, 2005. (link)


Books In Progress

10. “Theory and Application of Elliptic Curve Cryptosystems”, potentially as a text book for a university course in Elliptic Curve Cryptography, 2008-... (link)

10. “Numeropedia - The Special Encyclopedia of Interesting Numbers in Science, Technology and Life”, 2008-... (link)

11. Information Systems Security Engineering Handbook”, on Information Systems Security and System Lifecycle, for IT/ISS program managers of the FAA National Airspace System (NAS), 2009-...  (link)


White Papers Unpublished

1. White Paper on X9.63 (Submitted Dec.1999)

2. Elliptic Curve Cryptography in Information Systems Security (PowerPoint, 2000)

3. Secure Air-Ground Communication System (Stevens Institute of Technology - System Engineering SDOE 625, 2006)

4. Cyber Hacking Methodology 100.9.9.9 (PowerPoint, 2007)

5. Information-to-Knowledge Inversion Problem (IKIP), (PowerPoint, 2009).


References Links

A. The Spin L-Function on the Symplectic Group GSp(6)

01. Stanford University, Mathematics Department Ph.D. Dissertation, San C. Vo, “The Spin L-Function on the Symplectic Group GSp(6)”, 1995 (Link)

02. Israel Journal of Mathematics, San C. Vo, The Spin L-Function on the Symplectic Group GSp(6), (Article, Preview), 1997.

03. Prof. Daniel W. Bump & David Ginzburg, Spin L-functions on GSp8 and GSp10, 1999.

04. Daniel Bump, Solomon Friedberg & David Ginzburg, Rankin-Selberg integrals in two complex variables, Mathematische Annalen 313 (1999), 731--761.

05. San C. Vo’s Dissertation Review & Summary by Professor Solomon Friedberg for Math Database, 1931-2008 of the European Mathematical Society, FIZ Karlsruhe & Springer-Verlag, (Link). & Zentralblaa MATH.

06. David Ginzburg& Dihua Jiang, Periods and Liftings from G2 to C3, 2000.

07. Professor Daniel W. Bump, The Rankin-Selberg Method: An Introduction and Survey, 2004.

08. David Ginzburg& Joseph Hundley, Multivariable Rankin-Selberg Integrals for Orthogonal Groups, International Mathematics Research Notices, 2004.

90. David Ginzburg& Erez Lapid, On a Conjecture of Jacquet-Lai-Rallis; Some Exceptional Cases, 2005.

10. Miki Hirano, Taku Ishii & Takayuki Oda, Whittaker Functions for PJ-principal Series Representations of Sp(3,R), 2006, UTMS 2006-16, Graduate School of Mathematical Sciences, University of Tokyo, Japan. (Download: *.Pdf)

11. Alexei Panchishkin& Kirill Vankov, Explicit Shimura's Conjecture for Sp(3) on ..., Mathematical Research Letters, 14, No.2, pp. 173-187, 2007.

12. Dihua Jiang, OnSome Topics in Automorphic Representations, ICCM 2007, Vol. I, 165-18

13. Dihua Jiang, Poles of Certain Automorphic L-Functions, October 2007.

14. Gordan Savin & Martin H. Weissman, “Dichotomy for Generic Supercuspidal Representation of G2”, 2009. Cornell University Library.


B. Advance Encryption Standard (AES) & Random Number Generation (RNG)

1. NIST Random Number Generators: NIST/CSD RNG-SP800-22b.pdf or Links.

2. Juan Soto, Empirical Statistical Testing Of Cryptographic PRNGs”, 1998. Link & PPT presentation by Juan Soto.

3. Status Report of the First Round of the Development of the Advance Encryption Standard, Journal of Research of the National Institute of Standards and Technology (NIST), Vol.104, No.5, September-October 1999. (Link & .pdf)

4. Status Report of the First Round of the Development of the Advance Encryption Standard, Journal of Research of the National Institute of Standards and Technology (NIST), Vol. 104, No.5, September-October 1999. (Link & .pdf)


C. Survey on the Elliptic Curve Cryptosystems

1. NASA Ames Research Center, NASA Advanced Supercomputing Division, NASA Technical Reports, A Survey of Elliptic Curve Cryptosystems, Part I: Introductory, 2003. (Survey on ECC, NAS-03-012.pdf)

2. NASA Ames Research Center, NASA Technical ReportsSome Improvements on Signed Window Algorithms for Scalar Multiplications in Elliptic Curve Cryptosystems, 2001. Document ID #20010062806, (*.pdf).

3. Legendre-form Elliptic Curve's Research, (形式椭圆曲线的生成研究),Network & Computer Security (计算机安全), Vol.05, pp. 18-21, 2007.

4. Elliptic Curve Encryption Algorithm of Hidden Information (椭圆曲线加密算法中的信息隐藏)


Mathematics Genealogy Tree

Each person’s Philosophical Dissertation Advisor(s) in Mathematics is (are) listed in the very next line (by Name, School and Year of Ph.D. degree)

San Cao Vo (Stanford University, 1995)

Prof. Daniel W. Bump (University of Chicago, 1982)

Prof. Walter L. Baily, Jr. (Princeton University, 1955)

Prof. Kunihiko Kodaira (Tokyo Imperial University, 1949, Fields Medalist 1954).

Prof. Shokichi Iyanaga (Tokyo Imperial University, 1931)

Prof. Taiji Tagaki (Tokyo Imperial University, 1903)

Prof. David Hilbert (Universität Königsberg , 1885) 

Prof. C. L. Ferdinand Lindemann (Friedrich-Alexander-Universität Erlangen-Nürnberg, 1873)

Prof. C. Felix Klein (Rheinische Friedrich-Wilhelms-Universität Bonn, 1868).

Prof. Rudolf Otto Sigismund Lipschitz (Universität Berlin, 1853) and Prof. Julius Plücker (Philipps-Universität Marburg, 1823).

     * Mathematics Genealogy Tree for Prof. Rudolf Otto Sigismund Lipschitz

Prof. Rudolf Otto Sigismund Lipschitz (Universität Berlin, 1853)

Prof. Gustav Peter Lejeune Dirichlet (Honorary, Rheinische Friedrich-Wilhelms-Universität Bonn 1827) and Prof. Martin Ohm (Friedrich-Alexander-Universität Erlangen-Nürnberg, 1811).

Prof. Ohm’s advisor is Prof. Karl Christian von Langsdorf (Universität Erfurt, 1781, Advisor: unknown!)

Prof. Simeon Poisson, (École Polytechnique) & Prof. Jean-Baptiste Joseph Fourier.

Prof. Joseph Louis Lagrange (No degree!)

Prof. Leonhard Euler (Universität Basel, 1726)

Prof. Johann Bernoulli (Universität Basel, 1694)

Prof. Jacob Bernoulli (Universität Basel, 1684)

Prof. Gottfried Wilhelm Leibniz (Universität Altdorf, 1666)

Prof. Erhard Weigel (Universität Leipzig, 1650, Advisor: unknown!)

     * Mathematics Genealogy Tree for Prof. Julius Plücker

Prof. Julius Plücker (Philipps-Universität Marburg, 1823). 

Prof. Christian Ludwig Gerling (Georg-August-Universität Göttingen, 1812)

Prof. Carl Friedrich Gauß (Universität Helmstedt, 1799)

Prof. Johann Friedrich Pfaff (Georg-August-Universität Göttingen, 1786)

Prof. Abraham Gotthelf Kästner (Universität Leipzig, 1739)

Prof. Christian Hausen (Martin-Luther-Universität Halle-Wittenberg, 1713)

Prof. Johann Christoph Wichmannshausen (Universität Leipzig, 1685)

Prof. Otto Mencke (Universität Leipzig, 1665-1666, Advisor: unknown!)