Cryptology ePrint Archive: Report 2013/246

A Lever Function to a New Codomain with Adequate Indeterminacy

Shenghui Su and Maozhi Xu and Shuwang Lv

Abstract: The key transform of the REESSE1+ cryptosystem is Ci = (Ai * W^l(i))^d (% M) with l(i) in O = {5, 7, , 2n + 3} for i = 1, , n, where l(i) is called a lever function. In this paper, the authors give a simplified transform Ci = Ai * W^l(i) (% M) and a new lever function l(i) from {1, , n} toO+- = {+/-5, , +/-(n + 4)}, where +/- means the selection of the + or - sign, and discuss the necessity of the new ℓ(i) that a simplified private key is insecure if l(i) is only some fixed integer and the sufficiency that a simplified private key is secure at present if l(i) is a one-to-one function. The sufficiency is expounded from four aspects: indeterminacy of the new l(i), every condition for the counteraction of powers of W and W^-1 being only necessary with even O+- = {5, , n + 4}, verification by examples, and running times of continued fraction attack and parameter intersection attack which are two most efficient algorithms so far but not determinate polynomial time ones. Last, elaborate a relation between a lever function and a random oracle.

Category / Keywords: Public key cryptosystem; Coprime sequence; Lever function; Continued fraction attack; Random oracle

Date: received 1 May 2013, last revised 1 Nov 2014

Contact author: reesse at 126 com

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Note: The content has no essential change.

Version: 20141101:084204 (All versions of this report)

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