Abstract
In this paper, we propose a new version of the Lagrange interpolation applied to binary permutation polynomials and, more generally, permutation polynomials over prime power modular rings. We discuss its application to obfuscation and reverse engineering.
The second-named author was partially supported by a PSC-CUNY grant from the CUNY Research Foundation and by the ONR (Office of Naval Research) grant N000141512164.
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References
Zhou, Y., Main, A., Gu, Y.X., Johnson, H.: Information hiding in software with mixed boolean-arithmetic transforms. In: Kim, S., Yung, M., Lee, H.-W. (eds.) WISA 2007. LNCS, vol. 4867, pp. 61–75. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-77535-5_5
Barthelemy, L., Eyrolles, N., Renault, G., Roblin, R.: Binary permutation polynomial inversion and application to obfuscation techniques. In: Proceedings of the 2nd International Workshop on Software Protection, Vienna, Austria. ACM, October 2016
Biondi, F., Josse, S., Legay, A., Sirvent, T.: Effectiveness of synthesis in concolic deobfuscation. Comput. Secur. 70, 500–515 (2017)
Mullen, G., Stevens, H.: Polynomial functions (mod \(m\)). Acta Math. Hungar. 44(3–4), 237–241 (1984)
Rivest, R.L.: Permutation polynomials modulo \(2^w\). Finite Fields Appl. 7(2), 287–292 (2001)
Hardy, G.H., Wright, E.M.: An Introduction to the Theory of Numbers, 4th edn. Clarendon Press, Oxford (1960)
Oruç, H., Phillips, G.M.: Explicit factorization of the Vandermonde matrix. Linear Algebra Appl. 315(1–3), 113–123 (2000)
Markovski, S., Šunić, Z., Gligoroski, D.: Polynomial functions on the units of \(Z_{2^n}\). Quasigr. Relat. Syst. 18(1), 59–82 (2010)
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Barthelemy, L., Kahrobaei, D., Renault, G., Šunić, Z. (2018). Quadratic Time Algorithm for Inversion of Binary Permutation Polynomials. In: Davenport, J., Kauers, M., Labahn, G., Urban, J. (eds) Mathematical Software – ICMS 2018. ICMS 2018. Lecture Notes in Computer Science(), vol 10931. Springer, Cham. https://doi.org/10.1007/978-3-319-96418-8_3
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