Lecture

Diffie-Hellman Cryptography: Key Exchange and ElGamal Encryption

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In course

COM-401: Cryptography and security

This course introduces the basics of cryptography. We review several types of cryptographic primitives, when it is safe to use them and how to select the appropriate security parameters. We detail how they work and sketch how they can be implemented. ...

Description

This lecture covers the Diffie-Hellman key exchange protocol, the ElGamal public-key cryptosystem, and related security problems. It explains the CDH and EGD problems, the EIGamal key recovery and decryption problems, and the importance of the discrete logarithm and computational number theory in cryptography.

Instructor

Serge Vaudenay

Serge Vaudenay entered at the Ecole Normale Supérieure in 1989 with a major in mathematics. He earned his agrégation (secondary teaching degree) in mathematics in 1992, then a PhD in Computer Science at the University of Paris 7 - Denis Diderot in 1995. He subsequently became a senior research fellow at the CNRS, prior to being granted his habilitation à diriger des recherches (a postdoctoral degree authorizing the recipient to supervise doctoral students). In 1999, he was appointed as a Professor at the EPFL, where he created the Security and Cryptography Laboratory.

Official source

Ontological neighbourhood

Mathematics

Algebra: Abstract algebra

Computer engineering

Computer security: Public-key cryptography

Related concepts (32)

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.

RSA Factoring Challenge

The RSA Factoring Challenge was a challenge put forward by RSA Laboratories on March 18, 1991 to encourage research into computational number theory and the practical difficulty of factoring large integers and cracking RSA keys used in cryptography. They published a list of semiprimes (numbers with exactly two prime factors) known as the RSA numbers, with a cash prize for the successful factorization of some of them. The smallest of them, a 100-decimal digit number called RSA-100 was factored by April 1, 1991.

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.

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.

Public key fingerprint

In public-key cryptography, a public key fingerprint is a short sequence of bytes used to identify a longer public key. Fingerprints are created by applying a cryptographic hash function to a public key. Since fingerprints are shorter than the keys they refer to, they can be used to simplify certain key management tasks. In Microsoft software, "thumbprint" is used instead of "fingerprint." A public key fingerprint is typically created through the following steps: A public key (and optionally some additional data) is encoded into a sequence of bytes.

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Public-Key Cryptography: Key Exchange and Signatures

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RSA Encryption: Principles and Applications

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