Abstract
In this paper, we respond to the proposal of the Permutation Polynomial Encryption Scheme, introduced by Singh, Sarma, and Saikia in 2020. We simplify the private key and prove the scheme can be completely broken by a direct attack. Furthermore, we show that the direct attack also completely breaks the \(\ell \)IC cryptosystem. Although other attacks on this scheme were known, it was previously incorrectly asserted that Gröbner basis method is not feasible against \(\ell \)IC. We also highlight that this attack is effective against any generalization of these schemes that contain specific properties necessary for inversion.
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Cartor, M., Cartor, R., Lewis, M., Smith-Tone, D. (2023). Total Break of a Public Key Cryptosystem Based on a Group of Permutation Polynomials. In: Shikata, J., Kuzuno, H. (eds) Advances in Information and Computer Security. IWSEC 2023. Lecture Notes in Computer Science, vol 14128. Springer, Cham. https://doi.org/10.1007/978-3-031-41326-1_8
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DOI: https://doi.org/10.1007/978-3-031-41326-1_8
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