Group-based cryptography is a use of
groups 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 an ...
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 bi ...
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 descr ...
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
* Ko–Lee et al. key exchange protocol
See also
*
Non-commutative cryptography
References
*
*
*
*
*
*
Further reading
* Paul, Kamakhya; Goswami, Pinkimani; Singh, Madan Mohan. (2022)
"ALGEBRAIC BRAID GROUP PUBLIC KEY CRYPTOGRAPHY" Jnanabha', Vol. 52(2) (2022), 218-223. ISSN 0304-9892 (Print) ISSN 2455-7463 (Online)
External links
Cryptography and Braid Groups page(archived version 7/17/2017)
Theory of cryptography
Braid groups
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