Related Research Articles
Diffie–Hellman (DH) key exchange is a mathematical method of securely generating a symmetric cryptographic key 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.
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 to provide equivalent security, compared to cryptosystems based on modular exponentiation in Galois fields, such as the RSA cryptosystem and ElGamal cryptosystem.
Public-key cryptography, or asymmetric cryptography, is the field of cryptographic systems that use pairs of related keys. Each key pair consists of a public key and a corresponding private key. Key pairs are generated with cryptographic algorithms based on mathematical problems termed one-way functions. Security of public-key cryptography depends on keeping the private key secret; the public key can be openly distributed without compromising security. There are many kinds of public-key cryptosystems, with different security goals, including digital signature, Diffie-Hellman key exchange, public-key key encapsulation, and public-key encryption.
The Rabin cryptosystem is a family of public-key encryption schemes based on a trapdoor function whose security, like that of RSA, is related to the difficulty of integer factorization.
In cryptography, a cryptosystem is a suite of cryptographic algorithms needed to implement a particular security service, such as confidentiality (encryption).
Hyperelliptic curve cryptography is similar to elliptic curve cryptography (ECC) insofar as the Jacobian of a hyperelliptic curve is an abelian group in which to do arithmetic, just as we use the group of points on an elliptic curve in ECC.
Scott A. Vanstone was a mathematician and cryptographer in the University of Waterloo Faculty of Mathematics. He was a member of the school's Centre for Applied Cryptographic Research, and was also a founder of the cybersecurity company Certicom. He received his PhD in 1974 at the University of Waterloo, and for about a decade worked principally in combinatorial design theory, finite geometry, and finite fields. In the 1980s he started working in cryptography. An early result of Vanstone was an improved algorithm for computing discrete logarithms in binary fields, which inspired Don Coppersmith to develop his famous exp(n^{1/3+ε}) algorithm.
The Centre for Applied Cryptographic Research (CACR) is a group of industrial representatives, professors, and students at the University of Waterloo in Waterloo, Ontario, Canada who work and do research in the field of cryptography.
Provable security refers to any type or level of computer security that can be proved. It is used in different ways by different fields.
In computational number theory, the index calculus algorithm is a probabilistic algorithm for computing discrete logarithms. Dedicated to the discrete logarithm in where is a prime, index calculus leads to a family of algorithms adapted to finite fields and to some families of elliptic curves. The algorithm collects relations among the discrete logarithms of small primes, computes them by a linear algebra procedure and finally expresses the desired discrete logarithm with respect to the discrete logarithms of small primes.
MQV (Menezes–Qu–Vanstone) is an authenticated protocol for key agreement based on the Diffie–Hellman scheme. Like other authenticated Diffie–Hellman schemes, MQV provides protection against an active attacker. The protocol can be modified to work in an arbitrary finite group, and, in particular, elliptic curve groups, where it is known as elliptic curve MQV (ECMQV).
Neal I. Koblitz is a Professor of Mathematics at the University of Washington. He is also an adjunct professor with the Centre for Applied Cryptographic Research at the University of Waterloo. He is the creator of hyperelliptic curve cryptography and the independent co-creator of elliptic curve cryptography.
IEEE P1363 is an Institute of Electrical and Electronics Engineers (IEEE) standardization project for public-key cryptography. It includes specifications for:
The Diffie–Hellman problem (DHP) is a mathematical problem first proposed by Whitfield Diffie and Martin Hellman in the context of cryptography and serves as the theoretical basis of the Diffie–Hellman key exchange and its derivatives. The motivation for this problem is that many security systems use one-way functions: mathematical operations that are fast to compute, but hard to reverse. For example, they enable encrypting a message, but reversing the encryption is difficult. If solving the DHP were easy, these systems would be easily broken.
In cryptography, a key encapsulation mechanism, or KEM, is a public-key cryptosystem that allows a sender to generate a short secret key and transmit it to a receiver securely, in spite of eavesdropping and intercepting adversaries. Modern standards for public-key encryption of arbitrary messages are usually based on KEMs.
Pairing-based cryptography is the use of a pairing between elements of two cryptographic groups to a third group with a mapping to construct or analyze cryptographic systems.
Paul C. van Oorschot is a cryptographer and computer security researcher, currently a professor of computer science at Carleton University in Ottawa, Ontario, where he held a Canada Research Chair in authentication and computer security over the period 2002-2023. He is a Fellow of the Royal Society of Canada (FRSC). He is best known as a co-author of the Handbook of Applied Cryptography (ISBN 0-8493-8523-7), together with Alfred Menezes and Scott Vanstone. He is also the author of Computer Security and the Internet: Tools and Jewels from Malware to Bitcoin (ISBN 978-3-030-83410-4). Van Oorschot was awarded the 2000 J.W. Graham Medal in Computing Innovation. He also helped organize the first Selected Areas in Cryptography (SAC) workshop in 1994.
Multivariate cryptography is the generic term for asymmetric cryptographic primitives based on multivariate polynomials over a finite field . In certain cases, those polynomials could be defined over both a ground and an extension field. If the polynomials have degree two, we talk about multivariate quadratics. Solving systems of multivariate polynomial equations is proven to be NP-complete. That's why those schemes are often considered to be good candidates for post-quantum cryptography. Multivariate cryptography has been very productive in terms of design and cryptanalysis. Overall, the situation is now more stable and the strongest schemes have withstood the test of time. It is commonly admitted that Multivariate cryptography turned out to be more successful as an approach to build signature schemes primarily because multivariate schemes provide the shortest signature among post-quantum algorithms.
Cryptography, or cryptology, 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. Core concepts related to information security are also central to cryptography. Practical applications of cryptography include electronic commerce, chip-based payment cards, digital currencies, computer passwords, and military communications.
In cryptography, security level is a measure of the strength that a cryptographic primitive — such as a cipher or hash function — achieves. Security level is usually expressed as a number of "bits of security", where n-bit security means that the attacker would have to perform 2n operations to break it, but other methods have been proposed that more closely model the costs for an attacker. This allows for convenient comparison between algorithms and is useful when combining multiple primitives in a hybrid cryptosystem, so there is no clear weakest link. For example, AES-128 is designed to offer a 128-bit security level, which is considered roughly equivalent to a RSA using 3072-bit key.
References
- ↑ Cf. Library of Congress catalog data
- ↑ "Alfred Menezes: Mini-biography", Certicom company website
- ↑ Koblitz, Neal (2008). Random Curves: Journeys of a Mathematician. Springer-Verlag. ISBN 9783540740773.
- ↑ "Alfred Menezes" . Retrieved 11 April 2018.
- ↑ Menezes, Alfred J. (1993). Elliptic Curve Public Key Cryptosystems. Kluwer Academic Publisher. ISBN 9780792393689.
- ↑ Menezes, Alfred J.; van Oorschot, Paul; Vanstone, Scott A. (1996). Handbook of Applied Cryptography. CRC Press. ISBN 0-8493-8523-7.
- ↑ "Professional Activities" . Retrieved 11 April 2018.
- ↑ "Another look at provable security". YouTube . 4 July 2012. Archived from the original on 2021-12-22. Retrieved 11 April 2018.
- ↑ Neal, Koblitz; Alfred, Menezes. "Another Look at Provable Security". www.math.uwaterloo.ca.
