On an Improved Definition of Embedding Degree
نویسنده
چکیده
We demonstrate a fundamental flaw in the present definition of embedding degree for curves of any genus, and we present examples of elliptic curves and genus 2 curves which highlight the error. We explain how this can yield a dramatic (unbounded) difference between the size of the actual and presumed embedding fields. This observation has serious implications for the security of pairing-based cryptosystems, as curves are no longer as secure as expected. We discuss the appropriate understanding of embedding degree, the bounds that yield sub-exponential attacks, and offer a way of measuring the discrepancy in security.
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تاریخ انتشار 2006