Abstract
We introduce Targeted Ciphers, which typically encipher points on domain \documentclass[12pt]{minimal}
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\begin{document}$$\mathcal {X}$$\end{document}, but can be easily modified to instead encipher points on some subset \documentclass[12pt]{minimal}
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\begin{document}$$\mathcal{S}\subseteq \mathcal {X}$$\end{document}. Ciphers that can directly support this domain targeting are useful in Format-Preserving Encryption, where one wishes to encipher points on a potentially complex domain \documentclass[12pt]{minimal}
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\begin{document}$$\mathcal{S}$$\end{document}. We propose two targeted ciphers and analyze their security. The first, Targeted Swap-or-Not, is a modification of the Swap-or-Not cipher proposed by Hoang, Morris, and Rogaway (CRYPTO 2012). The second, a new cipher we call Mix-Swap-Unmix, achieves the stronger notion of full security. Our targeted ciphers perform domain targeting more efficiently than the recently proposed Cycle Slicer algorithm of Miracle and Yilek (ASIACRYPT 2017).