# 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…

## Topics from this paper

## 4 Citations

Classical Attacks on a Variant of the RSA Cryptosystem

- Computer ScienceLATINCRYPT
- 2021

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

- Computer ScienceArXiv
- 2021

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

- Computer ScienceTheor. Comput. Sci.
- 2021

Rédei permutations with cycles of the same length

- Computer Science, MathematicsDes. Codes Cryptogr.
- 2020

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 $p^2$.

## References

SHOWING 1-10 OF 25 REFERENCES

An efficient and secure RSA-like cryptosystem exploiting Rédei rational functions over conics

- Computer Science, MathematicsFinite Fields Their Appl.
- 2016

The decryption operation of the proposed scheme turns to be two times faster than RSA, and involves the lowest number of modular inversions with respect to other RSA-like schemes based on curves.

New Public-Key Schemes Based on Elliptic Curves over the Ring Zn

- Mathematics, Computer ScienceCRYPTO
- 1991

Three new trapdoor one-way functions are proposed that are based on elliptic curves over the ring Zn, which seem to be more secure than those schemes from the viewpoint of attacks without factoring such as low multiplier attacks.

A New Elliptic Curve Based Analogue of RSA

- Mathematics, Computer ScienceEUROCRYPT
- 1993

A new public key cryptosystem based on elliptic curves over the ring Zn is described. The scheme can be used for both digital signature and encryption applications, does not expand the amount of data…

A Public Key Cryptosystem Based on Pell Equation

- Mathematics, Computer ScienceIACR Cryptol. ePrint Arch.
- 2006

It is shown that the proposed RSA type public key cryptosystems based on the Pell’s equation are more secure than the RSA scheme when purely common plaintexts are encrypted in the broadcast application and are as secure as the RSA schemes against ciphertext attack.

Protocol Failures for RSA-Like Functions Using Lucas Sequences and Elliptic Curves

- Computer ScienceSecurity Protocols Workshop
- 1996

We show that the cryptosystems based on Lucas sequences and on elliptic curves over a ring are insecure when a linear relation is known between two plaintexts that are encrypted with a “small” public…

On Using RSA with Low Exponent in a Public Key Network

- Mathematics, Computer ScienceCRYPTO
- 1985

The problem of solving systems of equations Pi(x) ? 0 (mod ni) i = 1... k where Pi are polynomials of degree d and the ni are distinct relatively prime numbers is considered and it is shown that x can recover x in polynomial time provided ni ? 2k.

Fast RSA-type Schemes Based on Singular Cubic Curves y2+axy=m³(mod n)

- Mathematics, Computer ScienceEUROCRYPT
- 1995

It is proved that the proposed RSA-type public-key schemes based on singular cubic curves y2 + axy = x3 over the ring Zn have the same security as the RSA scheme against the Hastad attack when linearly related plaintexts are encrypted i n broadcast applications.

A cubic RSA code equivalent to factorization

- Mathematics, Computer ScienceJournal of Cryptology
- 2004

A version of the RSA scheme is presented with encryption exponent e ≡ 3 (mod 6) and the equivalence of decryption and factorization of R can be demonstrated.

Continued fractions and RSA with small secret exponent

- Computer Science, MathematicsArXiv
- 2004

A modification of Verheul and van Tilborg variant of Wiener's attack on RSA cryptosystem with small secret exponent is described.

A New Public-Key Cryptosystem

- Mathematics, Computer ScienceEUROCRYPT
- 1997

This paper describes a new public-key cryptosystem where the ciphertext is obtained by multiplying the public-keys indexed by the message bits and the cleartext is recovered by factoring the…