Exponential increment of RSA attack range via lattice based cryptanalysis

Nitaj, Abderahmanne; Ariffin, Muhammad Rezal Kamel; Adenan, Nurul Nur Hanisah; Merenda, Domenica Stefania; Ahmadian, Ali

doi:10.1007/s11042-021-11335-8

Cited by 3 publications

(1 citation statement)

References 21 publications

(51 reference statements)

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“…These attacks are currently used in much research. According to Boneh and Durfee's heuristic [49], the RSA encryption algorithm is unsafe if exponent d is too small. They demonstrated that, given the public key, an adversary could retrieve the private key when d< N0.292.…”

Section: Rsamentioning

confidence: 99%

A Cryptographic Algorithm using Polynomial Interpolations for Mitigating Key-Size Based Attacks

Kaur

K.R.

2022

Preprint

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Confidentiality is one of the fundamental aspects to consider while securing wireless communication. Endeavouring current developments will catch up with the conventional cryptographic methods soon than expected; therefore, a new path is indispensable. In this context, this article presents an innovative idea of using polynomials to achieve a higher level of data privacy. Polynomials' strength lies in their irreducible property, which makes them plausibly appropriate for cryptography. Thenceforth, two novel schemes are proposed based on root-finding polynomial interpolations such as Bisection, Newton-Raphson, and Secant. Relying on these techniques, while the first scheme performs substitution, the BI-New scheme performs substitution, rotation, replacement, and substitution. Hence, both schemes provide confusion and diffusion, a fundamental security aspect. Besides, these algorithms utilise initial points to extract the exact root of the polynomial p1(y) =0. On the basis thereof, an algorithm is developed to retrieve the initial data points. Consequently, the decryption is accomplished in reverse order by evaluating a function. The proposed scheme has unique characteristics, including non-linear interpolating polynomials, roots of non-linear algebraic equations, and non-linear functions. Due to the amalgamation of various non-linear methods and randomised variables, the methods are one-way functions that can endure several assaults. Lastly, the algorithm's security is illustrated by multiple state-of-the-art quantitative metrics such as time complexity, accuracy, memory usage, key space analysis, key sensitivity analysis, robustness analysis, and statistical analysis.

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Section: Rsamentioning

confidence: 99%