Lecture

Diffie-Hellman and El Gamal Cryptosystems

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In course

COM-102: Advanced information, computation, communication II

Text, sound, and images are examples of information sources stored in our computers and/or communicated over the Internet. How do we measure, compress, and protect the informatin they contain? ...

Description

This lecture covers the Diffie-Hellman key exchange protocol, the concept of trapdoor one-way functions, and El Gamal's cryptosystem. It explains how these systems work, the importance of large prime factors, and the difficulty of breaking Diffie-Hellman. The lecture also delves into the idea of one-way functions and the significance of trapdoor functions in cryptography.

Instructors (2)

Bixio Rimoldi

Bixio Rimoldi received the Dipl. El.-Ing degree as well as the Dr. ès Sciences degree from the ETHZ, Switzerland. Since 1997, he holds a full professor position at the School of Computer and Communication Sciences at EPFL and he is the director of EPFL's Mobile Communications Laboratory (LCM). Prior to joining EPFL, he was in the faculty of the Electrical Engineering department of Washington University. In 1993, he received a US National Science Foundation Young Investigator Award. In 2000, he was elected to the grade of Fellow of the IEEE. During the period 2002-2009 he has been on the Board of Governors of the IEEE Information Theory Society, where he served in several offices including President. He was co-chairman with Bruce Hajek of the 1995 IEEE Information Theory Workshop on Information Theory, Multiple Access, and Queueing (St Louis, MO), and co-chairman with Jim Massey of the 2002 IEEE International Symposium in Information Theory (Lausanne, Switzerland). He has been a member of the editorial board of "Foundations and Trends on Communications and Information Theory," and was an editor of the European Transactions on Telecommunications. During 2005 and 2006 he was the Director of EPFL's Bachelor program in Communication Systems. His interests are in various aspects of digital communications, information theory, and software-defined radio.

Michael Christoph Gastpar

Michael Gastpar is a (full) Professor at EPFL. From 2003 to 2011, he was a professor at the University of California at Berkeley, earning his tenure in 2008. He received his Dipl. El.-Ing. degree from ETH Zürich, Switzerland, in 1997 and his MS degree from the University of Illinois at Urbana-Champaign, IL, USA, in 1999. He defended his doctoral thesis at EPFL on Santa Claus day, 2002. He was also a (full) Professor at Delft University of Technology, The Netherlands. His research interests are in network information theory and related coding and signal processing techniques, with applications to sensor networks and neuroscience. He is a Fellow of the IEEE. He is the co-recipient of the 2013 Communications Society & Information Theory Society Joint Paper Award. He was an Information Theory Society Distinguished Lecturer (2009-2011). He won an ERC Starting Grant in 2010, an Okawa Foundation Research Grant in 2008, an NSF CAREER award in 2004, and the 2002 EPFL Best Thesis Award. He has served as an Associate Editor for Shannon Theory for the IEEE Transactions on Information Theory (2008-11), and as Technical Program Committee Co-Chair for the 2010 International Symposium on Information Theory, Austin, TX.

Official source

Ontological neighbourhood

Computer engineering

Computer security: Public-key cryptography

Related concepts (24)

One-way function

In computer science, a one-way function is a function that is easy to compute on every input, but hard to invert given the of a random input. Here, "easy" and "hard" are to be understood in the sense of computational complexity theory, specifically the theory of polynomial time problems. Not being one-to-one is not considered sufficient for a function to be called one-way (see Theoretical definition, below). The existence of such one-way functions is still an open conjecture.

Diffie–Hellman key exchange

Diffie–Hellman key exchange is a mathematical method of securely exchanging cryptographic keys over a public channel and was one of the first public-key protocols as conceived by Ralph Merkle and named after Whitfield Diffie and Martin Hellman. DH is one of the earliest practical examples of public key exchange implemented within the field of cryptography. Published in 1976 by Diffie and Hellman, this is the earliest publicly known work that proposed the idea of a private key and a corresponding public key.

Cryptography

Cryptography, or cryptology (from κρυπτός "hidden, secret"; and γράφειν graphein, "to write", or -λογία -logia, "study", respectively), is the practice and study of techniques for secure communication in the presence of adversarial behavior. More generally, cryptography is about constructing and analyzing protocols that prevent third parties or the public from reading private messages. Modern cryptography exists at the intersection of the disciplines of mathematics, computer science, information security, electrical engineering, digital signal processing, physics, and others.

Key (cryptography)

A key in cryptography is a piece of information, usually a string of numbers or letters that are stored in a file, which, when processed through a cryptographic algorithm, can encode or decode cryptographic data. Based on the used method, the key can be different sizes and varieties, but in all cases, the strength of the encryption relies on the security of the key being maintained. A key's security strength is dependent on its algorithm, the size of the key, the generation of the key, and the process of key exchange.

Key exchange

Key exchange (also key establishment) is a method in cryptography by which cryptographic keys are exchanged between two parties, allowing use of a cryptographic algorithm. If the sender and receiver wish to exchange encrypted messages, each must be equipped to encrypt messages to be sent and decrypt messages received. The nature of the equipping they require depends on the encryption technique they might use. If they use a code, both will require a copy of the same codebook. If they use a cipher, they will need appropriate keys.

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