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NEW TRAPDOOR ONE-WAY FUNCTION ON ELLIPTIC CURVES AND THEIR APPLICATIONS TO SHORTER SIGNATURES AND ASYMMETRIC ENCRYPTION
NEW TRAPDOOR ONE-WAY FUNCTION ON ELLIPTIC CURVES AND THEIR APPLICATIONS TO SHORTER SIGNATURES AND ASYMMETRIC ENCRYPTION
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机译:椭圆曲线上的新型陷阱单向函数及其在更短的签名和不对称加密中的应用
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摘要
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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