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Paper 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 O± = {+/-5, +/-6, …, +/-(n + 4)}, where “+/-” means the selection of the “+” or “-” sign. Discuss the necessity of l(.) to O± 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 O±, insufficiency of each of the four judgment conditions for counteraction of powers of W and W ^ -1 even if O± = {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.

Note: Very minor revision.

Metadata
Available format(s)
PDF
Category
Public-key cryptography
Publication info
Published elsewhere. Unknown status
Keywords
Public key cryptosystemCoprime sequenceLever functionContinued fraction attackRandom oracle
Contact author(s)
reesse @ 126 com
History
2023-04-23: last of 8 revisions
2013-05-03: received
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Short URL
https://ia.cr/2013/246
License
Creative Commons Attribution
CC BY
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