IEEE P1363 Research Contributions:
Supporting Techniques

Compact Representations of Elliptic Curve Points over GF(2ⁿ)
Gadiel Seroussi

A method is described to represent points on elliptic curves over the finite field with 2ⁿ elements, 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 the compressed representation described in draft standard IEEE P1363, which uses n+1 bits. The representation described in this disclosure is optimal for the general case of a cryptosystem over such a field.

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Storage-efficient finite field basis conversion
Burton S.Kaliski, Jr. and Yiqun Lisa Yin

The problem of finite field basis conversion is to convert from the representation of a field element in one basis to the representation of the element in another basis. This paper presents new algorithms for the problem that require much less storage than previous solutions. For the finite field GF(2^m),for example, the storage requirement of the new algorithms is only O(m) bits, compared to O(m²) for previous solutions. With the new algorithms, it is possible to extend an implementation in one basis to support other bases with little additional cost, thereby providing the desired interoperability in many cryptographic applications.

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