This paper presents Xoodoo, a 48-byte cryptographic permutation with excellent propagation properties. Its design approach is inspired by Keccak-*p*, while it is dimensioned like Gimli for efficiency on low-end processors. The structure consists of three planes of 128 bits each, which interact per 3-bit columns through mixing and nonlinear operations, and which otherwise move as three independent rigid objects. We analyze its differential and linear propagation properties and, in particular, prove lower bounds on the weight of trails using the tree search-based technique of Mella et al. (ToSC 2017). Xoodoo’s primary target application is in the Farfalle construction that we instantiate for the doubly-extendable cryptographic keyed (or deck) function Xoofff. Combining a relatively narrow permutation with the parallelism of Farfalle results in very efficient schemes on a wide range of platforms, from low-end devices to high-end processors with vector instructions.

This note defines Kravatte-SANE and Kravatte-SANSE. Both are session authenticated encryption schemes and differ in their robustness with respect to nonce misuse. They are defined as instances of modes on top of the deck function Kravatte, where a deck function is a keyed function with variable-length input strings, an arbitrary-length output and certain incrementality properties.

## J. Daemen, S. Hoffert, G. Van Assche and R. Van Keer, Xoodoo cookbook, IACR ePrint Archive, 2018 [pdf]

This document presents Xoodoo, a 48-byte cryptographic permutation that allows very efficient symmetric crypto on a wide range of platforms and a suite of cryptographic functions built on top of it. The central function in this suite is Xoofff, obtained by instantiating Farfalle with Xoodoo. Xoofff is what we call a *deck function* and can readily be used for MAC computation, stream encryption and key derivation. The suite includes two session authenticated encryption (SAE) modes: Xoofff-SANE and Xoofff-SANSE. Both are built on top of Xoofff and differ in their robustness with respect to nonce misuse. The final members of the suite are a tweakable wide block cipher Xoofff-WBC and authenticated encryption mode Xoofff-WBC-AE, obtained by instantiating the Farfalle-WBC and Farfalle-WBC-AE constructions with Xoofff. This paper is a specification and security claim reference for the Xoodoo suite. It is a *standing document*: over time, we may extend the Xoodoo suite, e.g., with a hash function or a dedicated lightweight MAC function and we will update it accordingly.

In this paper, we introduce *Farfalle*, a new permutation-based construction for building a pseudorandom function (PRF). The PRF takes as input a key and a sequence of arbitrary-length data strings, and returns an arbitrary-length output. It has a *compression layer* and an *expansion layer*, each involving the parallel application of a permutation. The construction also makes use of LFSR-like *rolling functions* for generating input and output masks and for updating the inner state during expansion. On top of the inherent parallelism, Farfalle instances can be very efficient because the construction imposes less requirements on the underlying primitive than, e.g., the duplex construction or typical block cipher modes. Farfalle has an *incremental* property: compression of common prefixes of inputs can be factored out. Thanks to its input-output characteristics, Farfalle is really versatile. We specify simple modes on top of it for authentication, encryption and authenticated encryption, as well as a wide block cipher mode. As a showcase, we present Kravatte, a very efficient instance of Farfalle based on Keccak-*p*[1600, *n*_{r}] permutations and formulate concrete security claims against classical and quantum adversaries. The permutations in the compression and expansion layers of Kravatte have only 6 rounds apiece and the rolling functions are lightweight. We provide a rationale for our choices and report on software performance.