Cryptography – Particular algorithmic function encoding – Public key
Reexamination Certificate
2005-11-14
2010-11-30
Parthasarathy, Pramila (Department: 2436)
Cryptography
Particular algorithmic function encoding
Public key
C713S150000, C713S176000
Reexamination Certificate
active
07844051
ABSTRACT:
The present invention provides a new trapdoor one-way function. In a general sense, some quadratic algebraic integer z is used. One then finds a curve E and a rational map defining [z] on E. The rational map [z] is the trapdoor one-way function. A judicious selection of z will ensure that [z] can be efficiently computed, that it is difficult to invert, that determination of [z] from the rational functions defined by [z] is difficult, and knowledge of z allows one to invert [z] on a certain set of elliptic curve points. Every rational map is a composition of a translation and an endomorphism. The most secure part of the rational map is the endomorphism as the translation is easy to invert. If the problem of inverting the endomorphism and thus [z] is as hard as the discrete logarithm problem in E, then the size of the cryptographic group can be smaller than the group used for RSA trapdoor one-way functions.
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Brown Daniel R. L.
Gallant Robert P.
Struik Marinus
Vanstone Scott A.
Blake Cassels & Graydon LLP
Certicom Corp.
Orange John R. S.
Parthasarathy Pramila
Slaney Brett J.
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