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Permutation-based modes have been established for lightweight authenticated encryption, as can be seen from the high interest in the ongoing NIST lightweight competition. However, their security is upper bounded by  O ( σ  2 /2  c  ) bits, where  σ  are the number of calls and  c  is the hidden capacity of the state. The development of more schemes that provide higher security bounds led to the CHES’18 proposal Beetle that raised the bound to  O ( rσ /2  c  ), where  r  is the public rate of the state.

The Oribatida v1.3 Family of Lightweight Authenticated Encryption Schemes