Let p be a prime and k, t be positive integers. Given a quadratic equation Q(x1,x2,...,xn)=t mod p^k in n-variables; we present a polynomial time Las-Vegas algorithm that samples a uniformly random solution of the quadratic equation.
@InProceedings{dubey_et_al:LIPIcs.APPROX-RANDOM.2014.643, author = {Dubey, Chandan and Holenstein, Thomas}, title = {{Sampling a Uniform Solution of a Quadratic Equation Modulo a Prime Power}}, booktitle = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)}, pages = {643--653}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-74-3}, ISSN = {1868-8969}, year = {2014}, volume = {28}, editor = {Jansen, Klaus and Rolim, Jos\'{e} and Devanur, Nikhil R. and Moore, Cristopher}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2014.643}, URN = {urn:nbn:de:0030-drops-47289}, doi = {10.4230/LIPIcs.APPROX-RANDOM.2014.643}, annote = {Keywords: Quadratic Forms, Lattices, Modular, p-adic} }
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