Abstract
We extend the area of applications of our methods to lower bounds on the circuit and decision tree complexity of Boolean functions related to some number-theoretic problems. In particular, we show that deciding whether a given integer is square-free and testing co-primality of two integers by unbounded fan-in circuits of bounded depth requires superpolynomial size, see [9, 38, 39, 40, 41, 460]. This method can be applied to other number-theoretic problems related to arithmetical properties of integers. Unfortunately this approach does not seem to apply to the complexity of the primality testing problem, for which an alternative approach has been developed in [9], which in fact implies stronger but less explicit results (which apply to square-freeness and co-primality testing as well).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer Basel AG
About this chapter
Cite this chapter
Shparlinski, I. (2003). Square-Freeness Testing and Other Number-Theoretic Problems. In: Shparlinski, I. (eds) Cryptographic Applications of Analytic Number Theory. Progress in Computer Science and Applied Logic, vol 22. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8037-4_29
Download citation
DOI: https://doi.org/10.1007/978-3-0348-8037-4_29
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9415-9
Online ISBN: 978-3-0348-8037-4
eBook Packages: Springer Book Archive