This volume contains almost complete proceedings of the NATO Advanced Study Institute (ASI) organised in 1979 to bring together principal innovators and numerous users of mathematical techniques for analysing the interaction of electromagnetic waves with engineering and biological structures. The mathematical disciplines which can be brought to bear on these problems necessitate examination of effectiveness, convergence and robustness of the derived analytic and num~rical algorithms. The aim of this ASI was to give a clear and up-to-date tutorial presentation of available techniques, and to bring together interested scientists, engineers and mathematiciaris, to discuss together their experience and to ensure wider familiarity with the subject. Our programme consists of three distinct yet related parts. The first two of these reflect two somewhat different methods applicable for different ranges of L/A, where L represents a characteristic dimension of a structure and A is a representative wavelength-of radiation. The third part deals with the specific problem of biological interaction. In the first part (Low and Intermediate Frequency Applications) we offer tutorial texts and user-oriented discussions on main techniques and problems concerning: radiation, scattering, aperture penetration, inverse scattering, using moment methods and their developments. The approach to the high frequency applications forms the subject of the second part of this volume, concentrating mainly on the geometrical theory of diffraction (GTD). There are three main variants of the GTD: uniform theory of diffraction (UTD), uniform asymptotic theory (liAT) , spectral theory of diffraction (STD).

This volu e contains the complete proceedings of the second NATO Advanced Study Institute organised to relate co uni cation theory with allied subjects, and thus to single out themes which, though peripheral at present, are gaining in importance because of recent developments in theoretical investi gations by communication experts. In 1974 we attempted to promote an interchange of ideas between specialists in Signal Processing and in Control and System Sciences *. This time we tried to concentrate on probabilistic aspects of communication theory and practice and of the allied science of random process theory, with its novel and exciting approach to the mathematical foundations of noise phenomena. The topics presented here have been chosen with the above in view, to enlarge ideas and to diffuse results in the two allied subjects, by providing the opportunity for gaining insight in depth into new developments. These topics fall broadly into 10 distinct parts. Each starts with two or more basic presentations of a tutorial nature, followed by one or more detailed exa inations of particular aspects of the subject. In addition, some parts are concluded with reports of panel dis cuss ons organised to consider a particularly pertinent issue."

This volume contains the complete proceedings of a NATO Advanced Study Institute on various aspects of the reliability of electronic and other systems. The aim of the Insti~ute was to bring together specialists in this subject. An important outcome of this Conference, as many of the delegates have pointed out to me, was complementing theoretical concepts and practical applications in both software and hardware. The reader will find papers on the mathematical background, on reliability problems in establishments where system failure may be hazardous, on reliability assessment in mechanical systems, and also on life cycle cost models and spares allocation. The proceedings contain the texts of all the lectures delivered and also verbatim accounts of panel discussions on subjects chosen from a wide range of important issues. In this introduction I will give a short account of each contribution, stressing what I feel are the most interesting topics introduced by a lecturer or a panel member. To visualise better the extent and structure. of the Institute, I present a tree-like diagram showing the subjects which my co-directors and I would have wished to include in our deliberations (Figures 1 and 2). The names of our lecturers appear underlined under suitable headings. It can be seen that we have managed to cover most of the issues which seemed important to us. VI SYSTEM EFFECTIVENESS _---~-I~--_- Performance Safety Reliability ~intenance ~istic Lethality Hazards Support S.N.R. JARDINE Max. Vel. etc.

This volume contains the full proceedings of the Fourth Advanced Study Institute organised by myself and my colleagues in . * the field of Communication Theory and Allied Subjects. In the first Institute we associated the subject of signal processing in communication with that in control engineering. Then we concentrated on noise and random phenomena by bringing in as well the subject of stochastic calculus. The third time our subject was multi-user communication and associated with it, the important problem of assessing algorithmic complexity. This time we are concerned with the vast increase of computational power that is now available in communication systems processors and controllers. This forces a mathematical, algorithmic and structural approach to the solution of computational requirements and design problems, in contrast to previous heuristic and intuitive methods. We are also concerned with the interactions and trade-offs between the structure, speed, and complexity of a process, and between software and hardware implementations. At the previous Advanced Study Institute in this series, on Multi-User Communications, there was a session on computational complexity, applied particularly to network routing problems. It was the aim of this Institute to expand this topic and to link it with information theory, random processes, pattern analysis, and implementation aspects of communication processors. The first part of these proceedings concentrates on pattern and structure in communications processing. In organising this session I was greatly helped and guided by Professor P. G. Farrell and Professor J. L. Massey.

vii Part 1. ULTIMATE PHYSICAL LIMITS IN ELEcrRONIC CCM1UNICATION Breaking the Recursive Bottleneck Professor David G. Messerschmitt 3 Optimum Scales and Limits of Integration Professor Daniel V. McCaughan . . * . 21 On Ultimate Thermodynamic Limitations in Communication and canputation Professor Jerome Rothstein 43 Part 2. STATISTICAL, INFORMATIONAL, COMPUTATIONAL AND CRYPI'OGRAPHIC LIMITS On the Capacity of Peak Power Constrained Gaussian Channels Professor I. Bar-David *...***. 61 Complexity Issues for Public Key Cryptography Professor Ian F. Blake, Dr. Paul C. van Oorschot and Dr. Scott A. Vanstone . . *...*. *...75 Collaborative Coding for Optical Fibre Multi-User Channels Dr. P. Bridge . **. . ***...*. 99 What Happened with Knapsack Cryptographic Schemes? Professor Y. G. Desmedt . **...****. 113 Optical Logic for Computers Dr. Robert W. Keyes ...* 135 Limitations of Queueing Models in Communication Networks 143 Professor Anthony Ephremides . * * . . * * * * * . * Limits to Network Reliability Dr. GUnter G. Weber . *...1 55 Two Non-Standard Paradigms for Computation: Analog Machines and Cellular Automata Professor Kenneth Steiglitz ******** 173 The Capacity Region of the Binary Multiplying Channel - A Converse Professor J. Pieter M. Schalkwijk ...*. * 193 Recent Developments in Cryptography Dr. Fred Piper . * * * . * * * 207 vi The Role of Feedback in Communication Professor Thomas M. Cover * . * . . * 225 The Complexities of Information Transfer with Reference to a Genetic Code Model Mr. G. A. Karpel . . *...

vii Part 1. ULTIMATE PHYSICAL LIMITS IN ELEcrRONIC CCM1UNICATION Breaking the Recursive Bottleneck Professor David G. Messerschmitt 3 Optimum Scales and Limits of Integration Professor Daniel V. McCaughan . . * . 21 On Ultimate Thermodynamic Limitations in Communication and canputation Professor Jerome Rothstein 43 Part 2. STATISTICAL, INFORMATIONAL, COMPUTATIONAL AND CRYPI'OGRAPHIC LIMITS On the Capacity of Peak Power Constrained Gaussian Channels Professor I. Bar-David *...***. 61 Complexity Issues for Public Key Cryptography Professor Ian F. Blake, Dr. Paul C. van Oorschot and Dr. Scott A. Vanstone . . *...*. *...75 Collaborative Coding for Optical Fibre Multi-User Channels Dr. P. Bridge . **. . ***...*. 99 What Happened with Knapsack Cryptographic Schemes? Professor Y. G. Desmedt . **...****. 113 Optical Logic for Computers Dr. Robert W. Keyes ...* 135 Limitations of Queueing Models in Communication Networks 143 Professor Anthony Ephremides . * * . . * * * * * . * Limits to Network Reliability Dr. GUnter G. Weber . *...1 55 Two Non-Standard Paradigms for Computation: Analog Machines and Cellular Automata Professor Kenneth Steiglitz ******** 173 The Capacity Region of the Binary Multiplying Channel - A Converse Professor J. Pieter M. Schalkwijk ...*. * 193 Recent Developments in Cryptography Dr. Fred Piper . * * * . * * * 207 vi The Role of Feedback in Communication Professor Thomas M. Cover * . * . . * 225 The Complexities of Information Transfer with Reference to a Genetic Code Model Mr. G. A. Karpel . . *...