CODING AND CRYPTOGRAPHY RESEARCH GROUP
Coding Theory and Cryptography
The rapid
growth of the Internet and World Wide Web has brought tremendous
opportunities for online commercial activities, business transactions and
government services, delivered over open (and increasingly mobile) computer and
communications networks. This is possible only so long as
communications can be conducted in a secure and reliable way. The mathematical theory and practice of coding theory and cryptography underpins
the provision of effective security and reliability for data communication,
processing and storage. In the Coding and Cryptography Research Group, we are constantly pursuing further theoretical and practical advances in the field, which is crucial for supporting the growth of data communications and data networks of various
types. Our research helps to support the operations of rapidly growing e-commerce services, as well as helping to
strengthen the national safeguard capability of Singapore’s digital systems and
infrastructure, and consolidate Singapore’s leading position in the
telecommunication and information industries.
Coding and Cryptography: Two Sides of the Same Coin
The fields of Coding and Cryptography both stem from Claude Shannon’s pioneering work in the late 1940s.
Coding Theory
is the branch of mathematics that investigates how to encode information in such a way that it
becomes resistant to transmission errors. It is concerned with the properties
of various codes (including cyclic codes, BCH codes, MDS codes and
algebraic-geometric codes), and their efficient decoding algorithms.
Cryptography
is the mathematical theory of data confidentiality, authentication,
nonrepudiation, data integrity, privacy and access control and availability. It
protects information against unauthorised access and determines if a message
has been altered by a third party.
Applications of coding theory and
cryptography range from correcting errors (e.g., allowing music and data discs to function despite scratches and dust), protecting mobile phone conversations from fading, cancelling out the noise associated
with high frequency radio transmission, as well as safeguarding ATM cards, computer passwords and online payments.
Future Challenges
Today, high
speed and broad bandwidth is the dictum for modern computer and communications
systems. However, the proliferation of low-cost devices –
the enablers of the pervasive computing paradigm – has brought along the
threat of exploitation by potential adversaries. New techniques, methods and tools for coding
theory and cryptography must be developed to tackle new and emerging
technologies.
The last
decade has witnessed exciting developments emerging from coding and
cryptography research, such as the invention of zero-knowledge proofs, completeness results for multi-party computations, and the renewal of
lattice-based cryptography. The combination of these results is extremely
powerful, as it denotes that virtually any cryptographic problem can be solved
by making some reasonable assumptions.
In
today’s applications, even a simple public-key operation is sometimes
considered too slow in relations to the speed required by the application. It
is therefore urgent to develop special solutions offering
high efficiency for specific computational tasks. This 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 today the implementation
of an algorithm is often the weakest link of a security system and, hence,
needs thorough investigation. In our research on cryptanalysis, we analyse
proposed cryptographic schemes and try to invalidate them as a way to detect
security weaknesses and new threats. Our research harnesses diverse,
sophisticated mathematical tools, ranging from algebra to combinatorics and number theory, and applies them
to the development of new cryptographic and coding techniques.