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Anshel–Anshel–Goldfeld key exchange
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Anshel–Anshel–Goldfeld key exchange : ウィキペディア英語版
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.
== 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 } and their inverses: a_^, \ldots, a_^, where a_\in^ \ldots a_^.
Bob's public/private information:
* ''Bob's public key'' is a tuple of elements } and their inverses: b_^, \ldots, b_^, where b_\in^ \ldots b_^.
Transitions:
* Alice sends a tuple b_1A,\ldots,A^b_nA) to Bob.
* Bob sends a tuple a_1B,\ldots,B^a_nB) to Alice.
Shared key:
The key shared by Alice and Bob is the group element K = A^ B^ A B \in G called the commutator of A and B.
* Alice computes K as a product A^ \cdot B^a_^B\cdots B^a_^B.
* Bob computes K as a product (A^b_^A \cdots A^ b_^A)^ \cdot B = A^ B^ A B.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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