Abstract
Perfect nonlinear functions are of importance in cryptography. By using Galois rings and investigating the character values of corresponding relative difference sets, we construct a perfect nonlinear function from \(\mathbb{Z}^{n}_{p_{2}}\) to \(\mathbb{Z}^{m}_{p_{2}}\) where 2m is possibly larger than the largest divisor of n. Meanwhile we prove that there exists a perfect nonlinear function from \(\mathbb{Z}^{2}_{2_{p}}\) to \(\mathbb{Z}_{2_{p}}\) if and only if p=2, and that there doesn’t exist a perfect nonlinear function from \(\mathbb{Z}^{2n}_{2k_{l}}\) to \(\mathbb{Z}^{m}_{2k_{l}}\) if m>n and l(l is odd) is self-conjugate modulo 2k(k≥1) .
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Zhang, X., Guo, H., Yuan, J. (2006). A Note of Perfect Nonlinear Functions. In: Pointcheval, D., Mu, Y., Chen, K. (eds) Cryptology and Network Security. CANS 2006. Lecture Notes in Computer Science, vol 4301. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11935070_18
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DOI: https://doi.org/10.1007/11935070_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-49462-1
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