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 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 codomain Oħ = {+/-5, +/-6, …, +/-(n + 4)}, where “+/-” means the selection of the “+” or “-” sign. Discuss the necessity of l(.) to Oħ that a simplified private key is insecure if l(.) is only a fixed integer, and the sufficiency that a simplified private key is secure (namely Ci = Ai * W ^ l(i) (% M) is not faced with determinate polynomial time attack) if l(.) is a one-to-one function. The sufficiency is expounded from five aspects: indeterminacy of l(.) to Oħ, insufficiency of each of the four judgment conditions for counteraction of powers of W and W ^ -1 even if Oħ = {5, 6, …, n + 4}, verifying by examples, running times of continued fraction attack and indeterministic intersection attack most efficient now, and a relation between a lever function and a random oracle.

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

Date: received 1 May 2013, last revised 8 Oct 2013

Contact author: reesse at 126 com

Available format(s): PDF | BibTeX Citation

Note: Very minor revision.

Version: 20131008:102221 (All versions of this report)

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