Group-based cryptography is a use of

groups 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 ...

to construct

cryptographic primitive Cryptographic primitives are well-established, low-level cryptographic algorithms that are frequently used to build cryptographic protocols for computer security systems. These routines include, but are not limited to, one-way hash functions and ...

s. A group is a very general algebraic object and most cryptographic schemes use groups in some way. In particular

Diffie–Hellman key exchange Diffie–Hellman key exchangeSynonyms of Diffie–Hellman key exchange include: * Diffie–Hellman–Merkle key exchange * Diffie–Hellman key agreement * Diffie–Hellman key establishment * Diffie–Hellman key negotiation * Exponential key exc ...

uses finite

cyclic group In group theory, a branch of abstract algebra in pure mathematics, a cyclic group or monogenous group is a group, denoted C''n'', that is generated by a single element. That is, it is a set of invertible elements with a single associative bina ...

s. So the term ''group-based cryptography'' refers mostly to

cryptographic protocol A security protocol (cryptographic protocol or encryption protocol) is an abstract or concrete protocol that performs a security-related function and applies cryptographic methods, often as sequences of cryptographic primitives. A protocol describe ...

s that use infinite

non-abelian group In mathematics, and specifically in group theory, a non-abelian group, sometimes called a non-commutative group, is a group (''G'', ∗) in which there exists at least one pair of elements ''a'' and ''b'' of ''G'', such that ''a'' ∗ '' ...

s such as a

braid group A braid (also referred to as a plait) is a complex structure or pattern formed by interlacing two or more strands of flexible material such as textile yarns, wire, or hair. The simplest and most common version is a flat, solid, three-strande ...

Examples

* Shpilrain–Zapata public-key protocols * Magyarik–Wagner public key protocol *

Anshel–Anshel–Goldfeld key exchange Anshel–Anshel–Goldfeld protocol, also known as a commutator key exchange, is a key-exchange protocol using nonabelian groups. It was invented by Drs. Michael Anshel, Iris Anshel, and Dorian M. Goldfeld, Dorian Goldfeld. Unlike other group-based ...

* Ko–Lee et al. key exchange protocol

References

* * * * * *

External links

Cryptography and Braid Groups page
(archived version 7/17/2017) Theory of cryptography Braid groups {{crypto-stub

Examples

See also

References

Further reading

External links