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In this chapter, we will use the result obtained in Chap.  16 in order to prove some security results on Generic balanced Feistel ciphers \(\varPsi ^k\) . The main results will be the proof of security for \(\varPsi ^4\) in KPA, for \(\varPsi ^5\) in CPA and CCA, and for \(\varPsi ^6\) in CCA, when \(q \ll 2^n\) . We will also see what kind of bound we obtain from the results on \(\varPsi ^6\) for \(\varPsi ^k\) , \(k \ge 6\) , by using some compositions theorem. Finally, at the end of this chapter, we will compare the results obtained with proofs from Mirror theory and H-coefficient technique from the results obtained in Chap.  14 with the coupling technique.

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Proofs Beyond the Birthday Bound on \(\varPsi ^k\) with the H-Coefficient Method

  • 章节

  • 发表日期：

    2026年

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  • Jacques Patarin,
  • Emmanuel Volte,
  • Benoît Cogliati

摘要

In this chapter, we will use the result obtained in Chap.  16 in order to prove some security results on Generic balanced Feistel ciphers \(\varPsi ^k\) . The main results will be the proof of security for \(\varPsi ^4\) in KPA, for \(\varPsi ^5\) in CPA and CCA, and for \(\varPsi ^6\) in CCA, when \(q \ll 2^n\) . We will also see what kind of bound we obtain from the results on \(\varPsi ^6\) for \(\varPsi ^k\) , \(k \ge 6\) , by using some compositions theorem. Finally, at the end of this chapter, we will compare the results obtained with proofs from Mirror theory and H-coefficient technique from the results obtained in Chap.  14 with the coupling technique.