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arXiv · 1604.07791

Computational aspects of rational residuosity

Markus Hittmeir
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Abstract

In this paper, we consider an extension of Jacobi's symbol, the so called rational $2^k$-th power residue symbol. In Section 3, we prove a novel generalization of Zolotarev's lemma. In Sections 4, 5 and 6, we show that several hard computational problems are polynomial-time reducible to computing these residue symbols, such as getting nontrivial information about factors of semiprime numbers. We also derive criteria concerning the Quadratic Residuosity Problem.

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Markus Hittmeir. 2017-07-16. Computational aspects of rational residuosity. https://doi.org/10.1142/s1793042118500380

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