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Bellare, Mihir, Hoang, Viet Tung, Tessaro, Stefano.  2016.  Message-Recovery Attacks on Feistel-Based Format Preserving Encryption. Proceedings of the 2016 ACM SIGSAC Conference on Computer and Communications Security. :444–455.

We give attacks on Feistel-based format-preserving encryption (FPE) schemes that succeed in message recovery (not merely distinguishing scheme outputs from random) when the message space is small. For \$4\$-bit messages, the attacks fully recover the target message using \$2textasciicircum1 examples for the FF3 NIST standard and \$2textasciicircum5 examples for the FF1 NIST standard. The examples include only three messages per tweak, which is what makes the attacks non-trivial even though the total number of examples exceeds the size of the domain. The attacks are rigorously analyzed in a new definitional framework of message-recovery security. The attacks are easily put out of reach by increasing the number of Feistel rounds in the standards.