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Many cryptographic protocols which are based on the elliptic curves, require to efficiently encode massages or bit strings into the points of a given elliptic curve in such a way that they can be decoded to the originated massage or bit string. In this paper we modify the simplified SWU-encoding to present a uniform encoding map from the elements of a finite field into the set of points of an elliptic curve of odd characteristic. In particular, an injective encoding map is given for elliptic curves with
a point of order two.
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