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Division of Mathematical Sciences

CODING AND CRYPTOGRAPHY RESEARCH GROUP
CODING THEORY AND CRYPTOGRAPHY
The rapid growth of the Internet and World-Wide-Web provides fascinating opportunities for online commercial activities, business transactions and government services over open (and increasingly mobile) computer and communications networks. Such developments are only possible if communications can be conducted in a secure and reliable way. The mathematical theory and practice of coding theory and cryptography underpin the provision of effective security and reliability for data communication, processing and storage. Theoretical and practical advances in the fields are therefore a key factor in facilitating the growth of data communications and data networks of various types.
Our research in coding and cryptography is to enhance information protection and communication reliability, which is absolutely crucial for rapidly growing e-commerce services, and to strengthen national safeguard capability of digital systems and infrastructure. It can contribute to strengthening Singapore's leading position in the telecommunication and information industries.
 
TWO SIDES OF THE SAME COIN
Coding theory wants to reveal while cryptography wants to hide, although both stem from Claude Shannon’s pioneering work in the late 1940s. Coding theory is a mathematical branch of encoding information in such a way that it becomes resistant to transmission errors. It is concerned with the properties of various codes (cyclic codes, BCH-codes, MDS-codes, algebraic-geometric codes, etc.) and their efficient decoding algorithms. Cryptography is the mathematical theory of data confidentiality, authentication, nonrepudiation, data integrity, privacy, access control and availability, protecting information against unauthorized access, determining if a message has been altered by a third party, etc. Applications of coding theory and cryptography range from correcting errors due to scratches and dust on a music CD, protecting cellphone conversations from the fading and noise of high frequency radio transmission, to safeguarding ATM cards, computer passwords, and online payments, etc.
 
NEW CHALLENGES

Today, on the one hand, high speed and broad bandwidth have become the keywords for modern computer and communications systems, while on the other hand myriads of low-cost devices, the enablers of the pervasive computing paradigm, are under full physical control of potential adversaries. New techniques, methods and tools for coding theory and cryptography have to keep up in order to adapt to the new and emerging technologies.
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 "Coding is used for the reliability of data storage in data centers"
 
 
The last decades have witnessed exciting developments of research in the areas of cryptography, such as the invention of zero-knowledge proofs, the remarkable completeness results of multi-party computations or the renewal of lattice-based cryptography. The combination of these results is extremely powerful, as they show that virtually any cryptographic problem can be solved under some reasonable assumptions.
However, in today's applications, even a simple public-key operation is sometimes considered too slow in comparison to the speed required by the application. It is therefore a high priority to develop special solutions for various specific computation domains with high efficiency, which is where research on lightweight cryptography and hash functions plays an important role: hash functions are among the fastest cryptography primitives available and have countless security applications.
Furthermore, the discovery of side-channel attacks has shown that nowadays the implementation of an algorithm is often the weakest link of a security system, and, hence, needs thorough investigation. Research on cryptanalysis continues to analyze proposed cryptographic schemes, and tries to invalidate them, as a way to detect security weaknesses and new threats.
Our research will apply diverse, sophisticated mathematical tools from algebra, combinatorics and number theory to develop new cryptographic and coding techniques for the emerging practical applications.
 
RESEARCH LAB
Coding and Cryptography research group
The coding theory and cryptography laboratory is led by a group of seven faculty Professor Chee Yeow Meng, Professor Ling San, NRF Fellow Assistant Professor Thomas Peyrin, Associate Professor Frederique Oggier, Associate Professor Wang Huaxiong, Nanyang Assistant Professor Wu Hongjun and Professor Xing Chaoping.
Research in coding and cryptography is to enhance information protection and communication reliability, which is absolutely crucial for rapidly growing e-commerce services, and to strengthen national safeguard capability of digital systems and infrastructure. It can contribute to strengthening Singapore's leading position in the telecommunication and information industries. Currently, variety of research problems ranging from theoretical aspects of coding and cryptography, like algebraic geometry codes or lattice based cryptography, to practical problems such as cryptanalysis, hash functions, side channel, lightweight cryptography or coding for distributed storage, are being studied.
 
Computational Mathematics Group
The computational Mathematics Group consists of Associate Professors Hoang Viet Ha and Wang Li-Lian, together with 6 PhD students and 3 Research Fellows currently in the Lab.
The research focuses of this group lie in the development and analysis of multi-scale/stochastic finite-element methods, and spectral/spectral-element methods with applications to composites, metamaterials, electromagnetic wave simulations, and among others. The current research of this group is funded by Singapore A*Star, SERC PSF and MOE AcRF Tier 2 with a total amount of around S$900K.