Practical Lattice Basis Sampling Reduction
We propose Simple Sampling Reduction (SSR) that makes Schnorr’s Random Sampling Reduction (RSR) practical. We also introduce generalizations of SSR that yield bases with several short basis vectors and that, in combination, generate shorter basis vectors than SSR alone. Furthermore, we give a formula for Pr[||v||2 ≤x] provided v is randomly sampled from SSR’s search space. We describe two algorithms that estimate the probability that a further SSR iteration will find an even shorter vector, one algorithm based on our formula for Pr[||v||2 ≤x], the other based on the approach of Schnorr’s RSR analysis. Finally, we report on some cryptographic applications.
KeywordsSearch Space Base Vector Lattice Reduction Lattice Basis Short Vector
Unable to display preview. Download preview PDF.
- 3.Ludwig, C.: Practical Lattice Basis Sampling Reduction. PhD thesis, TU Darmstadt (2005), Available at: http://elib.tu-darmstadt.de/diss/000640/
- 6.Goldreich, O., Goldwasser, S., Halevi, S.: Public-key cryptosystems from lattice reduction problems. In: Kaliski Jr., B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 112–131. Springer, Heidelberg (1997)Google Scholar
- 12.Shoup, V.: NTL – a library for doing number theory, Release 5.4 (2005)Google Scholar