Research Statement v1.11 - thank Victor R. Jose for proofreading

Kuan-ming Lin
Nov. 29, 2004. All Rights Reserved. 

1. A Great Challenge on Cryptography

  Ten years ago, the definition of computer in most people's minds was the
standalone PC in their home, where most tasks they want to do was accomplished
be done without significant communication. Cryptography therefore was not
urgent for personal use, and was only of interest in the military and the 
academia. However, as the Internet has become indispensable in
most people's work and life, many personal data stored in the computer are 
exposed either willingly or unwillingly to all other users. It is known 
that many computer crackers (most of who are malicious and some criminal) 
have been continuously targeting and attacking vulnerable systems on
the Internet. Therefore, electronic data protection research 
ranging from encryption algorithms to anti-virus/firewall solutions has
played an active role both in the academia and industry.

  The security/privacy crisis has become even more serious with the
popularity of E-commerce like Internet shopping, unmanned bank transaction,
and so forth. Because current solutions in practice, for example MD5
hashing, PGP signature, 3-DES encryption, and SSL transaction protocol,
have been proven unsafe in certain cases, public acceptance for on-line
transaction has improved much slower than expected. Advanced computational
technologies like long-key RSA/ECC encryption are still experimental and
are still reliant on unproved hypotheses. (An example of such a hypothesis
is "Factorizing a huge integer is computationally intractable.")

2. Alternative Cryptographic Schemes

  My primary interest is cryptography, so I try to set my short-term career
goal to improve the reliability and applicability of some advanced
cryptography researches. Before I used to relate cryptography to only
computational number theory and complexity theory, but now I find cryptography
to be a wide interdisciplinary area of research. Even for theoretical
cryptography in which I am most interested, there is a variety of active
research branches. For example, some imaginative yet promisingly realizable
computation models have been proposed to beat the computational limitation
of current von-Neumann computer architecture. These models, including
quantum computing, DNA self-assembly computing, and neural computation,
have the potential to be extended to cryptographic systems which are more 
secure than state-of-the-art implementations.  

  The mathematical research branch on finite field algebra may also
contribute in novel algorithms for cryptography. Discrete logarithm, for
example, has been proven to be at least as secure as the RSA approach. Also,
biological identification processes such as fingerprints and iris
scanning are also being applied to confidential data access; however, the
success of such processes relies on efficient database searching and
machine learning from noisy sensors. Hence, I am equally interested in doing
research related to combining efficient computations with biological
techniques. Finally, studies in computational complexity, such as attempts
to address the famous $(P=NP)?$ question, may help define the
complexity of various cryptographic tasks.