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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 Goldfeld. Unlike other group-based protocols, it does not employ any commuting or commutative subgroups of a given platform group and can use any nonabelian group with efficiently computable normal forms. It is often discussed specifically in application of braid groups, which notably are infinite (and the group elements can take variable quantities of space to represent). The computed shared secret is an element of the group, so in practice this scheme must be accompanied with a sufficiently secure compressive hash function to normalize the group element to a usable bitstring. Description Let G be a fixed nonabelian group called a ''platform group''. Alice's public/private information: * ''Alice's public key'' is a tuple of elements =(a_1,\ldots,a_n) in G. * ''Alice's private key'' is a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nonabelian 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'' ∗ ''b'' ≠ ''b'' ∗ ''a''. This class of groups contrasts with the abelian groups. (In an abelian group, all pairs of group elements commute). Non-abelian groups are pervasive in mathematics and physics. One of the simplest examples of a non-abelian group is the dihedral group of order 6. It is the smallest finite non-abelian group. A common example from physics is the rotation group SO(3) in three dimensions (for example, rotating something 90 degrees along one axis and then 90 degrees along a different axis is not the same as doing them in reverse order). Both discrete groups and continuous groups may be non-abelian. Most of the interesting Lie groups are non-abelian, and these play an important role in gauge theory. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dorian M
Dorian may refer to: Ancient Greece * Dorians, one of the main ethnic divisions of ancient Greeks * Doric Greek, or Dorian, the dialect spoken by the Dorians Art and entertainment Films * ''Dorian'' (film), the Canadian title of the 2004 film ''Pact with the Devil'' * ''Dorian Blues'', a 2004 film Literature * ''Dorian, an Imitation'', a 2002 novel by Will Self * ''Dorian'', a 1921 novel by Nephi Anderson Music * Dorians (band), from Armenia * Dorian (Spanish band), a Spanish band * Dorian (Turkish band), a Turkish rock band * Dorian mode, various musical modes * Dorian Recordings, a label noted for early music recordings * Toccata and Fugue in D minor, BWV 538, or "Dorian", an organ piece by Johann Sebastian Bach * Ukrainian Dorian scale, a musical mode * "Dorian," a song by Demons and Wizards on their album ''Touched by the Crimson King'' People * Dorian (name), a given name (includes a list of people with the name) * Dorian (rapper) (born 1984), American hip-hop artis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Braid Groups
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-stranded structure. More complex patterns can be constructed from an arbitrary number of strands to create a wider range of structures (such as a fishtail braid, a five-stranded braid, rope braid, a French braid and a waterfall braid). The structure is usually long and narrow with each component strand functionally equivalent in zigzagging forward through the overlapping mass of the others. It can be compared with the process of weaving, which usually involves two separate perpendicular groups of strands (warp and weft). Historically, the materials used have depended on the indigenous plants and animals available in the local area. During the Industrial Revolution, mechanized braiding equipment was invented to increase production. The braiding te ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Group (mathematics)
In mathematics, a group is a Set (mathematics), set and an Binary operation, operation that combines any two Element (mathematics), elements of the set to produce a third element of the set, in such a way that the operation is Associative property, associative, an identity element exists and every element has an Inverse element, inverse. These three axioms hold for Number#Main classification, number systems and many other mathematical structures. For example, the integers together with the addition operation form a group. The concept of a group and the axioms that define it were elaborated for handling, in a unified way, essential structural properties of very different mathematical entities such as numbers, geometric shapes and polynomial roots. Because the concept of groups is ubiquitous in numerous areas both within and outside mathematics, some authors consider it as a central organizing principle of contemporary mathematics. In geometry groups arise naturally in the study of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Commutator
In mathematics, the commutator gives an indication of the extent to which a certain binary operation fails to be commutative. There are different definitions used in group theory and ring theory. Group theory The commutator of two elements, and , of a group , is the element : . This element is equal to the group's identity if and only if and commute (from the definition , being equal to the identity if and only if ). The set of all commutators of a group is not in general closed under the group operation, but the subgroup of ''G'' generated by all commutators is closed and is called the ''derived group'' or the ''commutator subgroup'' of ''G''. Commutators are used to define nilpotent and solvable groups and the largest abelian quotient group. The definition of the commutator above is used throughout this article, but many other group theorists define the commutator as :. Identities (group theory) Commutator identities are an important tool in group theory. The expr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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-stranded structure. More complex patterns can be constructed from an arbitrary number of strands to create a wider range of structures (such as a fishtail braid, a five-stranded braid, rope braid, a French braid and a waterfall braid). The structure is usually long and narrow with each component strand functionally equivalent in zigzagging forward through the overlapping mass of the others. It can be compared with the process of weaving, which usually involves two separate perpendicular groups of strands (warp and weft). Historically, the materials used have depended on the indigenous plants and animals available in the local area. During the Industrial Revolution, mechanized braiding equipment was invented to increase production. The braiding te ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebraic Eraser
Algebraic Eraser (AE)Also referred to as the colored Burau key agreement protocol (CBKAP), Anshel–Anshel–Goldfeld–Lemieux key agreement protocol, Algebraic Eraser key agreement protocol (AEKAP), and Algebraic Eraser Diffie–Hellman (AEDH). is an anonymous key agreement protocol that allows two parties, each having an AE public–private key pair, to establish a shared secret over an insecure channel. This shared secret may be directly used as a key, or to derive another key that can then be used to encrypt subsequent communications using a symmetric key cipher. Algebraic Eraser was developed by Iris Anshel, Michael Anshel, Dorian Goldfeld and Stephane Lemieux. SecureRF owns patents covering the protocol and unsuccessfully attempted (as of July 2019) to standardize the protocol as part of ISO/IEC 29167-20, a standard for securing radio-frequency identification devices and wireless sensor networks. Keyset parameters Before two parties can establish a key they ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Group-based Cryptography
Group-based cryptography is a use of groups to construct cryptographic primitives. A group is a very general algebraic object and most cryptographic schemes use groups in some way. In particular Diffie–Hellman key exchange uses finite cyclic groups. So the term ''group-based cryptography'' refers mostly to cryptographic protocols that use infinite non-abelian groups such as a braid group. 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 Non-commutative cryptography is the area of cryptology where the cryptographic primitives, methods and systems are based on algebraic structures like semigroups, Group (mathematics), groups and Ring (mathematics), rings which are non-commutative. On ... References * * * * * * Further reading * Paul, Kamakhya; Goswami, Pinkimani; Singh, Madan Mohan. (2022)"ALGEBRAIC BRAID GR ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
