HP Labs Technical Reports

Compact Representation of Elliptic Curve Points over F(sub (2 sup n))

Seroussi, Gadiel

HPL-98-94R1

Keyword(s): finite fields; elliptic curves; cryptography

Abstract: A method is described to represent points on elliptic curves over F(sub (2 sup n)), in the context of elliptic curve cryptosystems, using n bits. The method allows for full recovery of the x and y components of the point. This improves on the naive representation using 2n bits, and on a previously known compressed representation using n + 1 bits. Since n bits are necessary to represent a point in the general case of a cryptosystem over F(sub (2 sup n)), the representation described in this note is minimal.

5 Pages

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