Paper 2013/246
A New Lever Function with Adequate Indeterminacy
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, we 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)}. 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) the running time of continued fraction attack and running time of W-parameter intersection attack which are the two most efficient of the probabilistic polytime attack algorithms so far. Last, we detail the relation between a lever function and a random oracle.
Note: The content has no essential change.
Metadata
- Available format(s)
-
PDF
- Category
- Foundations
- Publication info
- Preprint.
- Keywords
- Asymmetric cryptosystemCoprime sequenceLever functionContinued fraction attackRandom oracle
- Contact author(s)
- idology98 @ gmail com
- History
- 2023-04-23: last of 8 revisions
- 2013-05-03: received
- See all versions
- Short URL
- https://ia.cr/2013/246
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2013/246,
author = {Shenghui Su and Ping Luo and Shuwang Lv and Maozhi Xu},
title = {A New Lever Function with Adequate Indeterminacy},
howpublished = {Cryptology {ePrint} Archive, Paper 2013/246},
year = {2013},
url = {https://eprint.iacr.org/2013/246}
}
