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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 of a lattice with good properties (such as short nearly orthogonal vectors) and a unimodular matrix . The public key is another basis of the lattice of the form . For some chosen M, the message space consists of the vector in the range . 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「GGH encryption scheme」の詳細全文を読む スポンサード リンク
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