A New Lever Function with Adequate Indeterminacy
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The key transform of the REESSE1+ asymmetrical cryptosystem is Ci = (Ai * W ^ l(i)) ^ d ( where l(i) is called a lever function. In this paper, the authors give a simplified key transform Ci = Ai * W ^ l(i) ( l(i) from 1, ..., n to Omega = +/-5, +/-6, ..., +/-(n + 4), where "+/-" means the selection of the "+" or "-" sign. Discuss the necessity of the new l(i), namely that a simplified private key is insecure if the new l(i) is a constant but not one-to-one function. Further, expound the sufficiency of the new l(i) from four aspects: (1) indeterminacy of the new l(i), (2) insufficient conditions for neutralizing the powers of W and W ^-1 even if Omega = 5, 6, ..., n + 4, (3) verification by examples, and (4) running times of the continued fraction attack and W-parameter intersection attack which are the two most efficient of the probabilistic polytime attack algorithms so far. Last, the authors elaborate the relation between a lever function and a random oracle.
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