Events
Department of Mathematics and Statistics
Texas Tech University
In 1948/1949 Claude Shannon wrote two papers [Sha48, Sha49] which became the foundation of modern information theory. The papers showed that information can be compressed up to the entropy, that data can be transmitted error free at a rate below the capacity and that there exist provable secure cryptographic systems. These were all fundamental theoretical results. The challenge remained to build practical systems which came close to the theoretical optimal systems predicted by Shannon.
In this overview talk we will explain how the first two challenges concerning coding theory have resulted in practical solutions which are very close to optimal. Then we explain why the gap between the practical implementation of cryptographic protocols with the theoretical result of Shannon is largest.
[Sha48] C.E. Shannon, A mathematical theory of communication, Bell System Tech. J. 27, (1948), 379--423 and 623--656.
[Sha49] C.E. Shannon, Communication theory of secrecy systems, Bell System Tech. J. 28, (1949), 656--715.
Biography: Joachim Rosenthal received a Diploma in mathematics from the University of Basel in 1986 and his Ph.D. in mathematics from Arizona State University in 1990. From 1990 to 2006, he was with the University of Notre Dame, USA, where he held the Endowed Chair of applied mathematics and a Concurrent Professor of electrical engineering. Since 2004, he has been a Professor of applied mathematics with the University of Zurich. He is a fellow of IEEE, a fellow of SIAM and an Honorary Professor at Universidad del Norte, Colombia. He currently serves as President of the Swiss Mathematical Society.
This presentation may be viewed in the TTU Mediasite catalog via eraider login.
Coding theory plays a crucial role in modern communication devices. The lecture will provide an overview to the mathematical constructions and decoding techniques used in coding theory. First we will show how techniques from algebra and algebraic geometry led to the construction of block codes with large distance and efficient decoding techniques. Second, we will cover classes of different type of codes such as LDPC codes and convolutional codes. The latter can be seen as discrete linear systems defined over a finite field and techniques from systems theory play an important role in their construction.
Please attend the second of this year's three Dayawansa Memorial Lecture Series at 4 PM (UT-5) in the Experimental Sciences Building 1, room 120.
This presentation may be viewed in the TTU Mediasite catalog via eraider login.
Public key cryptography has been at the center of modern cryptography. It is not only used for the exchange of secret keys but also for the authentication of entities on the Internet, for digital signatures and for the construction of digital currencies.
Until a few years ago most public key systems were based on the hardness of factoring integers or on the hardness of the discrete logarithm problem in an elliptic curve. With the realization that a quantum computer would make many practically used public key cryptographic systems obsolete it became an important research topic to design public key systems which are expected to be secure even if a powerful quantum computer would exist.
This new area of research is called post-quantum cryptography and there has been in the last couple of years a lot of effort to come up with new standards to be used in everyday applications. The National Institute of Standards and Technology (NIST) currently conducts a standardization process.
The main part of the lecture will overview this recent development and will explain the underlying mathematical problems.
Please attend the second of this year's three Dayawansa Memorial Lecture Series at 4 PM (UT-5) in the Experimental Sciences Building 1, room 120.
This presentation may be viewed in the TTU Mediasite catalog via eraider login.