Lecture

Diffie-Hellman Cryptography: Key Exchange & ElGamal

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

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 and the ElGamal Public-Key Cryptosystem. It explains the concept of discrete logarithm problems, the security of Diffie-Hellman against passive adversaries, and the challenges with subgroups. The lecture delves into the Decisional Diffie-Hellman (DDH) problem, the notion of games in cryptography, and the implications of hard cases in DDH. It also discusses the importance of checking group membership, key distribution issues, and the correct Diffie-Hellman key exchange protocol. The lecture concludes with a detailed explanation of the RFC 2631 method for Diffie-Hellman key agreement and exercises related to group parameter generation and key wrapping.

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

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.

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.

Post-quantum cryptography

In cryptography, post-quantum cryptography (PQC) (sometimes referred to as quantum-proof, quantum-safe or quantum-resistant) refers to cryptographic algorithms (usually public-key algorithms) that are thought to be secure against a cryptanalytic attack by a quantum computer. The problem with currently popular algorithms is that their security relies on one of three hard mathematical problems: the integer factorization problem, the discrete logarithm problem or the elliptic-curve discrete logarithm problem.

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.

Elliptic-curve cryptography

Elliptic-curve cryptography (ECC) is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields. ECC allows smaller keys compared to non-EC cryptography (based on plain Galois fields) to provide equivalent security. Elliptic curves are applicable for key agreement, digital signatures, pseudo-random generators and other tasks. Indirectly, they can be used for encryption by combining the key agreement with a symmetric encryption scheme.

Related lectures (64)

Public-Key Cryptography: Key Exchange and Signatures

Explores public-key cryptography, key exchange, and digital signatures, discussing practical applications and security mechanisms.

Cryptography: Fundamentals and Applications

Introduces the fundamentals of cryptography, covering symmetric and asymmetric encryption, hash functions, key infrastructure, and data integrity.

Diffie-Hellman Cryptography: Key Exchange and ElGamal Encryption

Covers the Diffie-Hellman key exchange protocol and the ElGamal public-key cryptosystem.

Public-Key Cryptography: Post-Quantum and Access Control

Explores public-key cryptography, post-quantum systems, and access control mechanisms in depth.

Distributed Randomness: Drand