NEW TRAP DOOR ONE-WAY FUNCTION ON ELLIPTICAL CURVE, AND ITS APPLICATION TO SHORTER SIGNATURE AND ASYMMETRIC ENCRYPTION

摘要

PROBLEM TO BE SOLVED: To provide a new trap door one-way function.;SOLUTION: In general meaning, some secondary algebraic integer z is used. A curve E and a rational map for determining (z) on E are found. The rational map (z) is a trap door one-way function. The wise selection of z guarantees that (z) can be efficiently calculated, that it is difficult to invert (z), that it is difficult to determine (z) from a rational function determined by (z), and that it is possible to invert (z) on a fixed set of elliptical curve points if z is known. All rational maps are a combination of translation and self-homomorphic mapping. Since the translation is easily inverted, the most secure portion of a rational map is self-homomorphic mapping. If the self-homomorphic mapping, that is, the problem of inverting (z) is difficult in the same way as a discrete logarithm problem in E, the size of an encryption group can be smaller than a group used for an RSA trap door one-way function.;COPYRIGHT: (C)2012,JPO&INPIT