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GGH encryption scheme
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GGH encryption scheme : ウィキペディア英語版
GGH encryption scheme

The Goldreich–Goldwasser–Halevi (GGH) lattice-based cryptosystem is an asymmetric cryptosystem based on lattices. There is also a GGH signature scheme.
The Goldreich–Goldwasser–Halevi (GGH) cryptosystem makes use of the fact that the closest vector problem can be a hard problem. It was published in 1997 and uses a trapdoor one-way function that is relying on the difficulty of lattice reduction. The idea included in this trapdoor function is that, given any basis for a lattice, it is easy to generate a vector which is close to a lattice point, for example
taking a lattice point and adding a small error vector. But to return from this erroneous vector to the original lattice point a special basis is needed.
The GGH encryption scheme was cryptanalyzed in 1999 by Phong Q. Nguyen.
==Operation==
GGH involves a private key and a public key.
The private key is a basis B of a lattice L with good properties (such as short nearly orthogonal vectors) and a unimodular matrix U.
The public key is another basis of the lattice L of the form B'=UB.
For some chosen M, the message space consists of the vector (\lambda_1,..., \lambda_n) in the range -M <\lambda_i < M.

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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