Torus-based cryptography involves using
algebraic tori
Algebraic may refer to any subject related to algebra in mathematics and related branches like algebraic number theory and algebraic topology. The word algebra itself has several meanings.
Algebraic may also refer to:
* Algebraic data type, a dat ...
to construct a
group
A group is a number of persons or things that are located, gathered, or classed together.
Groups of people
* Cultural group, a group whose members share the same cultural identity
* Ethnic group, a group whose members share the same ethnic iden ...
for use in
cipher
In cryptography, a cipher (or cypher) is an algorithm for performing encryption or decryption—a series of well-defined steps that can be followed as a procedure. An alternative, less common term is ''encipherment''. To encipher or encode i ...
s based on the
discrete logarithm problem
In mathematics, for given real numbers ''a'' and ''b'', the logarithm log''b'' ''a'' is a number ''x'' such that . Analogously, in any group ''G'', powers ''b'k'' can be defined for all integers ''k'', and the discrete logarithm log''b'' ...
. This idea was first introduced by
Alice Silverberg
Alice Silverberg (born 1958) is professor of Mathematics and Computer Science at the University of California, Irvine. She was faculty at the Ohio State University from 1984 through 2004. She has given over 300 lectures at universities around the ...
and
Karl Rubin
Karl Cooper Rubin (born January 27, 1956) is an American mathematician at University of California, Irvine as Thorp Professor of Mathematics. Between 1997 and 2006, he was a professor at Stanford, and before that worked at Ohio State University b ...
in 2003 in the form of a
public key algorithm
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 alg ...
by the name of
CEILIDH. It improves on conventional cryptosystems by representing some elements of large finite fields compactly and therefore transmitting fewer bits.
See also
*
Torus
In geometry, a torus (plural tori, colloquially donut or doughnut) is a surface of revolution generated by revolving a circle in three-dimensional space about an axis that is coplanar with the circle.
If the axis of revolution does not tou ...
References
* Karl Rubin, Alice Silverberg: Torus-Based Cryptography. CRYPTO 2003: 349–365
External links
Torus-Based Cryptography— the paper introducing the concept (in PDF).
Public-key cryptography
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