# Extended meet-in-the-middle attacks on some Feistel constructions

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## Abstract

We show key recovery attacks on generic balanced Feistel ciphers. The analysis is based on the meet-in-the-middle technique and exploits truncated differentials that are present in the ciphers due to the Feistel construction. Depending on the type of round function, we differentiate and show attacks on two types of Feistels. For the first type, which is one of the most practical Feistels, we show a 5-round distinguisher based on a truncated differential, which allows to launch 6-round and 10-round attacks, for single-key and double-key sizes, respectively. For the second type of Feistels, with round functions that follow the SPN structure composed of linear layers with maximal branch number, based on a 7-round distinguisher we show attacks that reach up to 14 rounds. Our attacks outperform all the known attacks for any key sizes and provide new lower bounds on the number of rounds required to achieve a practical and a secure Feistel. The attacks on first type have been experimentally verified with computer implementations of the attacks on small-state ciphers.

## Keywords

Feistel Generic attack Key recovery Meet-in-the-middle## Mathematics Subject Classification

94A60 (cryptography)## Notes

### Acknowledgments

Jérémy Jean and Ivica Nikolić were supported by the Singapore National Research Foundation Fellowship 2012 NRF-NRFF2012-06.

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