Abstract
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.
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Buchmann, J., Ludwig, C. (2006). Practical Lattice Basis Sampling Reduction. In: Hess, F., Pauli, S., Pohst, M. (eds) Algorithmic Number Theory. ANTS 2006. Lecture Notes in Computer Science, vol 4076. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11792086_17
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DOI: https://doi.org/10.1007/11792086_17
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