Lecture

Elliptic Curve Cryptography in Practice

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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 delves into the practical applications of elliptic curve cryptography, exploring its use in various real-world scenarios such as Swiss passports and COVID certificates. The instructor explains the Diffie-Hellman protocol on elliptic curves, its implementation in Bluetooth and biometric passports, and the importance of subgroup membership verification. The lecture also covers the ECIES cryptosystem, digital signature algorithm ECDSA, and the concept of pairings in cryptographic operations.

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 (28)

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.

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.

Elliptic Curve Digital Signature Algorithm

In cryptography, the Elliptic Curve Digital Signature Algorithm (ECDSA) offers a variant of the Digital Signature Algorithm (DSA) which uses elliptic-curve cryptography. As with elliptic-curve cryptography in general, the bit size of the private key believed to be needed for ECDSA is about twice the size of the security level, in bits. For example, at a security level of 80 bits—meaning an attacker requires a maximum of about operations to find the private key—the size of an ECDSA private key would be 160 bits.

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 (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.

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