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There is a statement in the article of "Public-Key Cryptosystems from Lattice Reduction Problems" that presents GGH encryption scheme:

"The cryptanalytic problem underlying our scheme is to approximate the closest vector problem (CVP) in a lattice, given a "non-reduced" basis for that lattice"

On the other hand, in his survey Peikert says:

" Unlike the works of Ajtai and Ajtai-Dwork [AD97], the GGH proposals did not come with any worst-case security guarantees; their conjectured security was merely heuristic. "

Also he says "Because no cryptosystem has yet been proved secure based on CVPγ, we do not formally define that problem here"

Which one is true?

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If you look at the GGH paper, they explicitly say that they reduce to a random instance of CVP. At the end of the paragraph on CVP in Section 2.1, it explicitly says: "As we explain in Section 3, an attack against our trapdoor function amounts to finding an exact solution for some random instance of CVP." Peikert is referring to worst-case guarantees (i.e., hardness for any instance of CVP) whereas GGH considered an average-case problem (when the instance is generated at random).

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