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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.
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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.
Post-quantum cryptography (PQC), sometimes referred to as quantum-proof, quantum-safe, or quantum-resistant, is the development of cryptographic algorithms that are thought to be secure against a cryptanalytic attack by a quantum computer. The problem with popular algorithms currently used in the market 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. All of these problems could be easily solved on a sufficiently powerful quantum computer running Shor's algorithm or even faster and less demanding alternatives.
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 . 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.
