Ajtai's Proof of Theorem 1 in 'Generating Hard Instances of Lattice Problems' 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?
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).