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Devoted to information security, this volume begins with a short course on cryptography, mainly basedon lectures given by Rudolf Ahlswede at the University of Bielefeld in the mid1990s. It was the second of his cycle of lectures on information theory whichopened with an introductory course on basic coding theorems, as covered inVolume 1 of this series. In this third volume, Shannon's historical work onsecrecy systems is detailed, followed by an introduction to aninformation-theoretic model of wiretap channels, and such important concepts ashomophonic coding and authentication. Once the theoretical arguments have beenpresented, comprehensive technical details of AES are given. Furthermore, ashort introduction to the history of public-key cryptology, RSA and El Gamalcryptosystems is provided, followed by a look at the basic theory of ellipticcurves, and algorithms for efficient addition in elliptic curves. Lastly, theimportant topic of "oblivious transfer" is discussed, which is stronglyconnected to the privacy problem in communication. Today, the importance ofthis problem is rapidly increasing, and further research and practical realizationsare greatly anticipated.
This is the third of several volumes serving as thecollected documentation of Rudolf Ahlswede's lectures on information theory.Each volume includes comments from an invited well-known expert. In thesupplement to the present volume, Rüdiger Reischuk contributes his insights.
Classicalinformation processing concerns the main tasks of gaining knowledge and thestorage, transmission and hiding of data. The first task is the prime goal ofStatistics. For transmission and hiding data, Shannon developed an impressivemathematical theory called Information Theory, which he based on probabilisticmodels. The theory largely involves the concept of codes with small errorprobabilities in spite of noise in the transmission, which is modeled bychannels. The lectures presentedin this work are suitable for graduatestudents in Mathematics, and also for those working in Theoretical ComputerScience, Physics, and Electrical Engineering with a background in basicMathematics. The lectures can be used as the basis for courses or to supplementcourses in many ways. Ph.D. students will also find research problems, oftenwith conjectures, that offer potential subjects for a thesis. More advancedresearchers may find questions which form the basis of entire researchprograms.
List of contents
Chapter I A Short Course on Cryptography.- Chapter II Authentication and Secret-Key Cryptology.- Chapter III The Mathematical Background of the AdvancedEncryption Standard.- Chapter IV Elliptic Curve Cryptosystems.- Chapter V Founding Cryptography on Oblivious Transfer.- Supplement.
About the author
Rudolf Ahlswede (1938 - 2010) studied Mathematics in Göttingen, and held postdoc positions in Erlangen, Germany and Ohio, USA. From 1977 on he was full Professor of Applied Mathematics at the University of Bielefeld. His work represents an essential contribution to information theory and networking. He developed and contributed to a number of central areas, including network coding, and theory of identification, while also advancing the fields of combinatorics and number theory. These efforts culminated in his research program “Development of a General Theory of Information Transfer”. In recognition of his work, Rudolf Ahlswede received several awards for “Best Paper”, as well as the distinguished “Shannon Award”.
Summary
Devoted to information security, this volume begins with a short course on cryptography, mainly based
on lectures given by Rudolf Ahlswede at the University of Bielefeld in the mid
1990s. It was the second of his cycle of lectures on information theory which
opened with an introductory course on basic coding theorems, as covered in
Volume 1 of this series. In this third volume, Shannon’s historical work on
secrecy systems is detailed, followed by an introduction to an
information-theoretic model of wiretap channels, and such important concepts as
homophonic coding and authentication. Once the theoretical arguments have been
presented, comprehensive technical details of AES are given. Furthermore, a
short introduction to the history of public-key cryptology, RSA and El Gamal
cryptosystems is provided, followed by a look at the basic theory of elliptic
curves, and algorithms for efficient addition in elliptic curves. Lastly, the
important topic of “oblivious transfer” is discussed, which is strongly
connected to the privacy problem in communication. Today, the importance of
this problem is rapidly increasing, and further research and practical realizations
are greatly anticipated.
This is the third of several volumes serving as the
collected documentation of Rudolf Ahlswede’s lectures on information theory.
Each volume includes comments from an invited well-known expert. In the
supplement to the present volume, Rüdiger Reischuk contributes his insights.
Classical
information processing concerns the main tasks of gaining knowledge and the
storage, transmission and hiding of data. The first task is the prime goal of
Statistics. For transmission and hiding data, Shannon developed an impressive
mathematical theory called Information Theory, which he based on probabilistic
models. The theory largely involves the concept of codes with small error
probabilities in spite of noise in the transmission, which is modeled by
channels. The lectures presentedin this work are suitable for graduate
students in Mathematics, and also for those working in Theoretical Computer
Science, Physics, and Electrical Engineering with a background in basic
Mathematics. The lectures can be used as the basis for courses or to supplement
courses in many ways. Ph.D. students will also find research problems, often
with conjectures, that offer potential subjects for a thesis. More advanced
researchers may find questions which form the basis of entire research
programs.
