International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: Identifying Ideal Lattices

Jintai Ding
Richard Lindner
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Abstract: Micciancio defined a generalization of cyclic lattices, called ideal lattices. These lattices can be used in cryptosystems to decrease the number of parameters necessary to describe a lattice by a square root, making them more efficient. He proves that the computational intractability of classic lattice problems for these lattices gives rise to provably secure one-way and collision-resistant hash functions. This provable security relies on the assumption that reducing bases of ideal lattices is similar to reducing bases of random lattices. We give an indication that lattice problems in ideal lattices do not represent the general case by providing a distinguisher, which decides in time $O(n^4)$ whether a given basis of rank $n$ spans an ideal lattice or not. Using this algorithm we perform a statistical analysis for several dimensions and show that randomly generated lattices are practically never ideal.
  title={Identifying Ideal Lattices},
  booktitle={IACR Eprint archive},
  keywords={foundations / decision problems, lattices, complexity, NTRU},
  note={ 13740 received 15 Aug 2007},
  author={Jintai Ding and Richard Lindner},