# Torus-based cryptography

﻿
Torus-based cryptography

Torus based cryptography involves using algebraic tori to construct a group for use in ciphers based on the discrete logarithm problem. This idea was first introduced by Alice Silverberg and Karl Rubin in 2003 in the form of a public key algorithm by the name of CEILIDH. It improves on conventional cryptosystems by representing some elements of large finite fields compactly and therefore transmitting fewer bits.

References

* Karl Rubin, Alice Silverberg: Torus-Based Cryptography. CRYPTO 2003: 349&ndash;365

* [http://www.math.uci.edu/~asilverb/bibliography/ceilidh.pdf Torus-Based Cryptography] &mdash; the paper introducing the concept (in PDF).

Wikimedia Foundation. 2010.

### Look at other dictionaries:

• Algebraic torus — In mathematics, an algebraic torus is a type of commutative affine algebraic group. These groups were named by analogy with the theory of tori in Lie group theory (see maximal torus). The theory of tori is in some sense opposite to that of… …   Wikipedia

• Hyperelliptic curve cryptography — is similar to elliptic curve cryptography (ECC) insomuch as the algebraic geometry construct of a hyperelliptic curve with an appropriate group law provides an Abelian group on which to do arithmetic. The use of hyperelliptic curves in… …   Wikipedia

• CEILIDH — is a public key cryptosystem based on the discrete logarithm problem in algebraic torus. This idea was first introduced by Alice Silverberg and Karl Rubin in 2003. The main advantage of those schemes is the reduced size of the keys for the same… …   Wikipedia

• CEILIDH — криптосистема с открытым ключом, в основе которой лежат задачи дискретного логарифмирования и алгебраические группы. Впервые эта идея была предложена Алисой Силверберг и Карлом Рубин в 2003 году. Главное преимущество схемы уменьшенный размер… …   Википедия

• Cellular automaton — A cellular automaton (plural: cellular automata) is a discrete model studied in computability theory, mathematics, theoretical biology and microstructure modeling. It consists of a regular grid of cells , each in one of a finite number of states …   Wikipedia

• Riemann surface — For the Riemann surface of a subring of a field, see Zariski–Riemann space. Riemann surface for the function ƒ(z) = √z. The two horizontal axes represent the real and imaginary parts of z, while the vertical axis represents the real… …   Wikipedia

• Carbon nanotube — Not to be confused with Carbon fiber. Part of a series of articles on Nanomaterials Fullerenes …   Wikipedia

• Mathematics and Physical Sciences — ▪ 2003 Introduction Mathematics       Mathematics in 2002 was marked by two discoveries in number theory. The first may have practical implications; the second satisfied a 150 year old curiosity.       Computer scientist Manindra Agrawal of the… …   Universalium

• Mathematics — Maths and Math redirect here. For other uses see Mathematics (disambiguation) and Math (disambiguation). Euclid, Greek mathematician, 3r …   Wikipedia

• List of mathematics articles (C) — NOTOC C C closed subgroup C minimal theory C normal subgroup C number C semiring C space C symmetry C* algebra C0 semigroup CA group Cabal (set theory) Cabibbo Kobayashi Maskawa matrix Cabinet projection Cable knot Cabri Geometry Cabtaxi number… …   Wikipedia