Method and apparatus for constructing efficient elliptic curve cryptosystems
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United States of America Patent
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Issued Date -
Aug 12, 2004
app pub date -
Apr 5, 2004
filing date -
Apr 5, 2001
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Abandoned
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Abstract
Methods and apparatus to construct finite fields over which efficient elliptic curve cryptosystems can be set up. Given a security parameter k, the said methods and apparatus consist of devices for carrying out operations in a small k.sub.0-bit field k.sub.0 and methods to successively build extension fields K.sub.1; K.sub.2, . . . , K.sub.t, where the extension K.sub.1/K.sub.0 has degree 2 or 3 and the other extensions K.sub.i/K.sub.I-1, are quadratic, K.sub.t is the final field over which elliptic curves are defined, and K.sub.t has size k.sub.o2.sup.t or 3k.sub.02.sup.t-1 just exceeding the said security parameter k.
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