Abstract
Supersingular elliptic curves have played an important role in the development of elliptic curve crytography. Scott Vanstone introduced the first author to elliptic curve cryptography, a subject that continues to be a rich source of interesting problems, results and applications. One important fact about supersingular elliptic curves is that the number of rational points is tightly constrained to a small number of possible values. In this paper we present some similar results for curves of higher genus. We also present an application to the problem of determining abelian varieties that occur as jacobians.
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Acknowledgments
Gary McGuire and Emrah Sercan Yılmaz was supported by Science Foundation Ireland Grant 13/IA/1914.
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Dedicated to the memory of Scott Vanstone.
This is one of several papers published in Designs, Codes and Cryptography comprising the “Special Issue on Cryptography, Codes, Designs and Finite Fields: In Memory of Scott A. Vanstone”.
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McGuire, G., Yılmaz, E.S. Further results on the number of rational points of hyperelliptic supersingular curves in characteristic 2. Des. Codes Cryptogr. 77, 653–662 (2015). https://doi.org/10.1007/s10623-015-0102-6
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DOI: https://doi.org/10.1007/s10623-015-0102-6