Abstract
We construct a variant of Weil pairing to reduce the elliptic curve discrete logarithm problem to the discrete logarithm problem in the multiplicative subgroup of a finite field. We propose an explicit reduction algorithm using a new pairing and apply the algorithm to the case of two trace elliptic curves.
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Shim, K. (2001). Reducing Certain Elliptic Curve Discrete Logarithms to Logarithms in a Finite Field. In: Varadharajan, V., Mu, Y. (eds) Information Security and Privacy. ACISP 2001. Lecture Notes in Computer Science, vol 2119. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47719-5_40
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DOI: https://doi.org/10.1007/3-540-47719-5_40
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