On the arithmetic complexity of euler function

Authors:
Manindra Agrawal
Affiliations:
Department of Computer Science, IIT Kanpur, Kanpur, India
Venue:
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
Year:
2011

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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.