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12

INDOCRYPT
2001
Springer

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Elliptic Curves of Prime Order over Optimal Extension Fields for Use in Cryptography

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Elliptic Curves of Prime Order over Optimal Extension Fields for Use in Cryptography

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We present an algorithm for generating elliptic curves of prime order over Optimal Extension Fields suitable for use in cryptography. The algorithm is based on the theory of Complex Multiplication. Furthermore, we demonstrate the eﬃciency of the algorithm in practice by giving practical running times. In addition, we present statistics on the number of cryptographically strong elliptic curves of prime order for Optimal Extension Fields of cardinality (232 + c)5 with c < 0. We conclude that there are suﬃciently many curves in this case.

Harald Baier

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Cryptology | Elliptic Curves | INDOCRYPT 2001 | Optimal Extension Fields | Prime Order |

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Added	30 Jul 2010
Updated	30 Jul 2010
Type	Conference
Year	2001
Where	INDOCRYPT
Authors	Harald Baier

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