Abstract
In this paper we derive lower bounds for the degree of polynomials that approximate the square root of the discrete logarithm for Elliptic Curves with orders of various specific types. These bounds can serve as evidence for the difficulty in the computation of the square root of discrete logarithms for such elliptic curves, with properly chosen parameters that result in the curve having order of any of types studied in this paper. The techniques are potentially applicable to elliptic curves of order of any specific, allowable (by Hasse’s bounds), order type that is of interest for the application in hand.
This work was partially supported by the European Union project ABC4Trust (Attribute-based Credentials for Trust) funded within the context of the 7th Research Framework Program (FP7).
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Meletiou, G.C., Stamatiou, Y.C., Tsiakalos, A. (2011). Lower Bounds for Interpolating Polynomials for Square Roots of the Elliptic Curve Discrete Logarithm. In: Kim, Th., Adeli, H., Robles, R.J., Balitanas, M. (eds) Information Security and Assurance. ISA 2011. Communications in Computer and Information Science, vol 200. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23141-4_17
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