Xoodoo cookbook

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. Other 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. Finally, for lightweight applications, we define Xoodyak, a cryptographic scheme that can be used for hashing, encryption, MAC computation and authenticated encryption. Essentially, it is a duplex object extended with an interface that allows absorbing strings of arbitrary length, their encryption and squeezing output of arbitrary length. 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, and we will update it accordingly

Interpolation Attacks on Round-Reduced Elephant, Kravatte and Xoofff

We introduce an interpolation attack using the \textsc{Moebius Transform}. This can reduce the time complexity to get a linear system of equations for specified intermediate state bits, which is general to cryptanalysis of some ciphers with update function of low algebraic degree. Along this line, we perform an interpolation attack against \textsc{Elephant-Delirium}, a round 2 submission of the ongoing NIST lightweight cryptography project. This is the first third-party cryptanalysis on this cipher. Moreover, we promote the interpolation attack by applying it to the \textbf{Farfalle} pseudo-random constructions \textsc{Kravatte} and \textsc{Xoofff}. Our attacks turn out to be the most efficient method for these ciphers thus far

Algebraic Key-Recovery Attacks on Reduced-Round Xoofff

Farfalle, a permutation-based construction for building a pseudorandom function (PRF), is really versatile. It can be used for message authentication code, stream cipher, key derivation function, authenticated encryption and so on. Farfalle construction relies on a set of permutations and on so-called rolling functions: it can be split into a compression layer followed by a two-step expansion layer. As one instance of Farfalle, Xoofff is very efficient on a wide range of platforms from low-end devices to high-end processors by combining the narrow permutation Xoodoo and the inherent parallelism of Farfalle. In this paper, we present key-recovery attacks on reduced-round Xoofff. After identifying a weakness in the expanding rolling function, we first propose practical attacks on Xoofff instantiated with 1-/2-round Xoodoo in the expansion layer. We next extend such attack on Xoofff instantiated with 3-/4-round Xoodoo in the expansion layer by making use of Meet-in-the-Middle algebraic attacks and the linearization technique. All attacks proposed here -- which are independent of the details of the compression and/or middle layer -- have been practically verified (either on the real Xoofff or on a toy-version Xoofff with block-size of 96 bits). As a countermeasure, we discuss how to slightly modified the rolling function for free to reduce the number of attackable rounds

Tighter trail bounds for Xoodoo

Determining bounds on the differential probability of differential trails and the squared correlation contribution of linear trails forms an important part of the security evaluation of a permutation. For Xoodoo such bounds were proven with a dedicated tool (XooTools), that scans the space of all r-round trails with weight below a given threshold $T_r$. The search space grows exponentially with the value of $T_r$ and XooTools appeared to have reached its limit, requiring huge amounts of CPU to push the bounds a little further. The bottleneck was the phase called trail extension where short trails are extended to more rounds, especially in the backward direction. In this work, we present a number of techniques that allowed us to make extension much more efficient ant that allowed us to increase the bounds significantly. Notably, we prove that the minimum weight of any 4-round trail is 80, the minimum weight of any 6-round trail is at least 132 and the minimum weight of any 12-round trail is at least 264, both for differential and linear trails

Tighter Trail Bounds for Xoodoo

Determining bounds on the differential probability of differential trails and the squared correlation contribution of linear trails forms an important part of the security evaluation of a permutation. For Xoodoo, such bounds were proven using the trail core tree search technique, with a dedicated tool (XooTools) that scans the space of all r-round trails with weight below a given threshold Tr. The search space grows exponentially with the value of Tr and XooTools appeared to have reached its limit, requiring huge amounts of CPU time to push the bounds a little further. The bottleneck was the phase called trail extension where short trails are extended to more rounds, especially in the backward direction. In this work, we present a number of techniques that allowed us to make extension much more efficient and as such to increase the bounds significantly. Notably, we prove that the minimum weight of any 4-round trail is 80, the minimum weight of any 6-round trail is at least 132 and the minimum weight of any 12-round trail is at least 264, both for differential and linear trails. As a byproduct we found families of trails that have predictable weight once extended to more rounds and use them to compute upper bounds for the minimum weight of trails for arbitrary numbers of rounds

Deck-Based Wide Block Cipher Modes and an Exposition of the Blinded Keyed Hashing Model

We present two tweakable wide block cipher modes from doubly-extendable cryptographic keyed (deck) functions and a keyed hash function: double-decker and docked-double-decker. Double-decker is a direct generalization of Farfalle-WBC of Bertoni et al. (ToSC 2017(4)), and is a four-round Feistel network on two arbitrarily large branches, where the middle two rounds call deck functions and the first and last rounds call the keyed hash function. Docked-double-decker is a variant of double-decker where the bulk of the input to the deck functions is moved to the keyed hash functions. We prove that the distinguishing advantage of the resulting wide block ciphers is simply two times the sum of the pseudorandom function distinguishing advantage of the deck function and the blinded keyed hashing distinguishing advantage of the keyed hash functions. We demonstrate that blinded keyed hashing is more general than the conventional notion of XOR-universality, and that it allows us to instantiate our constructions with keyed hash functions that have a very strong claim on bkh security but not necessarily on XOR-universality, such as Xoofffie (ePrint 2018/767). The bounds of double-decker and docked-double-decker are moreover reduced tweak-dependent, informally meaning that collisions on the keyed hash function for different tweaks only have a limited impact. We describe two use cases that can exploit this property opportunistically to get stronger security than what would be achieved with prior solutions: SSD encryption, where each sector can only be written to a limited number of times, and incremental tweaks, where one includes the state of the system in the variable-length tweak and appends new data incrementally

Gimli Encryption in 715.9 psec

We study the encryption latency of the Gimli cipher, which has recently been submitted to NIST’s Lightweight Cryptography competition. We develop two optimized hardware engines for the 24 round Gimli permutation, characterized by a total latency or 3 and 4 cycles, respectively, in a range of frequencies up to 4.5 GHz. Specifically, we utilize Intel’s 10 nm FinFET process to synthesize a critical path of 15 logic levels, supporting a depth-3 Gimli pipeline capable of computing the result of the Gimli permutation in frequencies up to 3.9 GHz. On the same process technology, a depth-4 pipeline employs a critical path of 12 logic levels and can compute the Gimli permutation in frequencies up to 4.5 GHz. Gimli demonstrates a total unrolled data path latency of 715.9 psec. Compared to our AES implementation, our fastest pipelined Gimli engine demonstrates 3.39 times smaller latency. When compared to the latency of the PRINCE lightweight block cipher, the pipelined Gimli latency is 1.7 times smaller. The paper suggests that the Gimli cipher, and our proposed optimized implementations have the potential to provide breakthrough performance for latency critical applications, in domains such as data storage, networking, IoT and gaming