Abstract
It is shown that the problem of computing the Euler function is closely related to the problem of computing the permanent of a matrix as well as to the derandomization of the Identity Testing problem. Specifically, it is shown that (1) if computing the Euler function over a finite field is hard then computing permanent over the integers is also hard, and (2) if computing any factor of the Euler function over a field is hard then the Identity Testing problem over the field can be derandomized.
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Agrawal, M. (2011). On the Arithmetic Complexity of Euler Function. In: Kulikov, A., Vereshchagin, N. (eds) Computer Science – Theory and Applications. CSR 2011. Lecture Notes in Computer Science, vol 6651. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20712-9_4
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DOI: https://doi.org/10.1007/978-3-642-20712-9_4
Publisher Name: Springer, Berlin, Heidelberg
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