Cryptographic Mathematician

Dan joined Certicom in 1999. He researches various areas of cryptology and participates in several information security standards development activities. He also assists Certicom's product development and professional services teams to comply with standards and to implement secure products and solutions.

He was a member of the Canadian team at the 1990 International Mathematics Olympiad in China, a Descartes undergraduate scholar, NSERC postgraduate scholar and Tutte graduate scholar. His Ph.D. thesis concerned algebraic and combinatorial enumeration of maps in surfaces and its applications to quantum physics and to algebraic geometry.

Some of Dan's cryptology research interests include provable security, digital signature schemes, modes of encryption, the transport layer security protocol (TLS), secure email protocol (PGP and S/MIME), virtual private networks (i.e. VPNs, IPSec and IKE), public key infrastructure, wireless link layer security (Bluetooth, 802.11, 802.15, ...), anonymity protocols, digital rights management, biometrics, lattice based cryptography, integer factorization, and identity based encryption.

Dan completed his B. Math in Pure Mathematics at the University of Waterloo in 1994, and received his M. Math in 1995 and PhD in 1999 from the department of Combinatorics and Optimization at U. of Waterloo. In 2001, he completed a two-year NSERC Industrial Research Fellowship that supported his research into cryptology at Certicom. His thesis concerned algebraic and combinatorial enumeration of maps in surfaces and its applications to quantum physics and to algebraic geometry. He also took graduate courses in cryptology such as topics in elliptic curves and unconditional security.

Selected Publications and Presentations:

• Adrian Antipa, Daniel R. L. Brown, Alfred J. Menezes, Rene Struik and Scott A. Vanstone. Validation of Elliptic Curve Public Keys. In Proceedings of Public Key Cryptography 2003, Yvo G. Desmedt, editor, volume 2567 of Lecture Notes in Computer Science, pages 211-223, 2003.

• Daniel R. L. Brown. ECDSA, Generic Groups, and Collision Resistance. In Designs, Codes and Cryptography. To appear.

• Daniel R. L. Brown, Robert P. Gallant, and Scott A. Vanstone. Provably Secure Implicit Certificate Schemes. In Proceedings of Financial Cryptography 2001, Paul F. Syverson, editor, volume 2339 of Lecture Notes in Computer Science, pages 156-165, Springer-Verlag, 2002.

• Daniel R. L. Brown and David M. Jackson. The Quadrangulation Conjecture for Orientable Surfaces. In Journal of Combinatorial Theory, Series B. To appear.

• Daniel R. L. Brown and Donald B. Johnson. Formal Security Proofs for a Signature Scheme with Partial Message Recovery. In Topics in Cryptology --- CT-RSA 2001, David Naccache, editor, volume 2020 of Lecture Notes in Computer Science, pages 126-142. Springer-Verlag, 2001.

• Daniel R. L. Brown and Alfred J. Menezes. A Small Subgroup Attack on a Key Agreement Protocol of Arazi. In Bulletin of the Institute for Combinatorial Applications, volume 37, pages, 45-50, 2003.