A Novel RSA-Like Cryptosystem Based on a Generalization of the Rédei Rational Functions

@inproceedings{Murru2017ANR,
  title={A Novel RSA-Like Cryptosystem Based on a Generalization of the R{\'e}dei Rational Functions},
  author={Nadir Murru and Francesco M. Saettone},
  booktitle={NuTMiC},
  year={2017}
}
In this paper we present a novel RSA-like cryptosystem. Specifically, we define a novel product that arises from a cubic field connected to the cubic Pell equation. We discuss some interesting properties and remarks about this product that can also be evaluated through a generalization of the Redei rational functions. We then exploit these results to construct a novel RSA-like scheme that is more secure than RSA in broadcast applications. Moreover, our scheme is robust against the Wiener attack… 
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Topics from this paper

Classical Attacks on a Variant of the RSA Cryptosystem
TLDR
It is shown that the proposed variant of RSA can be broken if d < N, which shows that their scheme is in reality more vulnerable than RSA, where the bound of vulnerability is d <N.
Tangent-Chebyshev rational maps and Redei functions
TLDR
It is shown that this new class of rational functions over odd-order finite fields are conjugate to the classical family of Rédei rational functions, so that the properties of the new functions follow from properties of RéDei functions.
Cryptanalysis of the RSA variant based on cubic Pell equation
Rédei permutations with cycles of the same length
TLDR
It is shown that there exists a Redei permutation over $\mathbb{P}^1(\ mathbb{F}_q)$ with $1$- and $p$-cycles if and only if $q-1$ or $q+1$ has a prime factor of the form $pk+1 $ or is divisible by $p^2$.

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