My research interests can be roughly divided into the following areas: Effective Crypto Algorithms (especially for Low-Resource and Pervasive Applications); Cryptology (including Post-Quantum Cryptosystems and Algebraic Cryptanalysis) and other Combinatorial Studies (including Analysis of Algorithms and other topics).
1. Effective Crypto Algorithms especially for Low-Resource and Pervasive Applications: It seems that computers are everywhere, working invisibly and seamlessly. As it is getting more and more ubiquitous, security and privacy becomes pressing issues. RSA may be on its way out within 5-10 years even without the advance of Quantum Computing. Indeed, NATO is standardizing on ECC (ECIES, ECDSA) as the next standard. This is due to the need for security in pervasive or ubiquitous computing. RSA is simply too heavy-weight to fit all occasions. Even the proponents concede this point. We study topics ranging from restricted linear algebra, resource-limited arithmetic, fast arithmetic to efficient primitives. Our recent work in this area includes designing a module that can do a signature for a low power RFID tag within the standard constraints of power and current. Today we are now investigating flexible optimizations with domain knowledge, with an eye toward applications on the possibility of software-hardware codesign with a scalable co-processor for security (of which we hoping to produce a prototype incorporating ECC and post-quantum crypto this year).
2. Cryptology: In this area, we concentrate in the following areas: a. Post-Quantum Cryptography: There are two major meanings for this term: One is the study of cryptosystems using quantum effects to establish security and privacy, such as the famous BB84 protocol; the other is the study of cryptography that resists the advent of Quantum Computers, which are rumored to arrive within two decades. Our research in MPKCs (Multivariate Public-Key Cryptosystems) which depends on the difficulty of instances in EIP (Extended Isomorphism of Polynomials) and Multivariate Quadratic problems, has advanced the understanding of the field in both theoretical and practical viewpoints. MPKCs operate on a vector of variables over a small field as opposed to an element in a huge algebraic structure (as in RSA or ECC). This key characteristic makes MPKCs faster at comparable design security. This is useful for low-resource environments, such as embedded systems and smart cards. Recently we have proposed several analysis and improvements in the design of such primitives. b. Algebraic Cryptanalysis We have made practical advances to equation-solving and algebraic cryptanalysis, especially those including Gröbner Bases and the related XL (eXtended Linearization) method and its variants. Such methods of attack has revolutionized the field of stream ciphers and led the European Ecrypt project to reissue a call for primitives; at the moment they are still in their shakeout phase in looking for a replacement to the venerable RC4 cipher. We are still working on faster implementations of such work.
3. Other Combinatorial Studies I work on many other combinatorial problems especially those dealing with enumeration and analysis of algorithms that deals with iterative or recursive structures that can be handled by standard combinatorial methods.