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Title:
A New Lever Function with Adequate Indeterminacy
Authors: Shenghui Su, Ping Luo, Shuwang Lv, Maozhi Xu
Abstract:The key transform of the REESSE1+ asymmetrical cryptosystem is Ci = (Ai * W ^ l(i)) ^ d (% M) with l(i) in Omega = {5, 7, …, 2n + 3} for i = 1, …, n, where l(i) is called a lever function. In this paper, the authors give a simplified key transform Ci = Ai * W ^ l(i) (% M) with a new lever function 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.
ePrint: https://eprint.iacr.org/2013/246
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