



@article {1554,
	title = {Optimal quantum algorithm for polynomial interpolation},
	journal = {43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
	volume = {55},
	year = {2016},
	month = {2016/03/01},
	pages = {16:1--16:13},
	abstract = {<p>We consider the number of quantum queries required to determine the coefficients of a degree-d polynomial over GF(q). A lower bound shown independently by Kane and Kutin and by Meyer and Pommersheim shows that d/2+1/2 quantum queries are needed to solve this problem with bounded error, whereas an algorithm of Boneh and Zhandry shows that d quantum queries are sufficient. We show that the lower bound is achievable: d/2+1/2 quantum queries suffice to determine the polynomial with bounded error. Furthermore, we show that d/2+1 queries suffice to achieve probability approaching 1 for large q. These upper bounds improve results of Boneh and Zhandry on the insecurity of cryptographic protocols against quantum attacks. We also show that our algorithm\&$\#$39;s success probability as a function of the number of queries is precisely optimal. Furthermore, the algorithm can be implemented with gate complexity poly(log q) with negligible decrease in the success probability.</p>},
	isbn = {978-3-95977-013-2},
	issn = {1868-8969},
	doi = {http://dx.doi.org/10.4230/LIPIcs.ICALP.2016.16},
	url = {http://arxiv.org/abs/1509.09271},
	author = {Andrew M. Childs and Wim van Dam and Shih-Han Hung and Igor E. Shparlinski}
}
