Torus-based cryptography involves using algebraic tori 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 b^x=a. Analogously, in any group G, powers b^k can be defined for all integers k, and the discrete logarithm \log_b(a) is an integer k such that b^k=a ...

. 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 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.

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 {{Crypto-stub

See also

References

External links