Cryptology ePrint Archive: Report 2013/246

A Lever Function to a New Codomain with Adequate Indeterminacy

Shenghui Su and Maozhi Xu and Shuwang Lu

Abstract: The key transforms 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 new codomain O from {5, , (n + 4)} and with x + y != 0 for any x, y in O, where x means the coexistence of +x and -x, which indicates that O is indeterminate. Then, discuss the necessity and sufficiency of l(.) to O for resisting continued fraction attack (CFA), prove indeterminacy and other properties of l(.) to O, illustrate the ineffectualness of CFA by using two examples which show that some conditions are only necessary but not sufficient for the counteraction of powers of W and W ^ -1 even though O = {5, , n + 4} is selected and known, analyze the time complexities of CFA and root finding attack with guess, and expound a relation between a lever function and a random oracle. Our research manifests that l(.) to O makes it generally impossible to extract a private key from a flat public key Ci = Ai * W ^ l(i)(% M) for i = 1, , n in polynomial time.

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

Date: received 1 May 2013, last revised 10 Jun 2013

Contact author: sheenway at 126 com

Available format(s): PDF | BibTeX Citation

Note: The some words are revised.

Version: 20130611:013408 (All versions of this report)

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