Message-Recovery Attacks on Feistel-Based Format Preserving Encryption

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 $2^{21}$ examples for the FF3 NIST standard and $2^{25}$ 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.