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My question pertains to the proof of Ajtai's main theorem in his groundbreaking 1996 paper, Generating hard instances of lattice problems, which indicates a connection between worst-case hard and average-case hard lattice problems. This proof is difficult for me to understand. Is there a clear exposition of this proof in the literature?

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You can try reading more recent papers such as Worst-case to Average-case Reductions based on Gaussian Measures by Miccancio and Regev, or Regev's lecture notes on the subject (you might want to read through the entire course).

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