Zero-Sum Distinguishers for Iterated Permutations and Application to Keccak-f and Hamsi-256

International audienceThe zero-sum distinguishers introduced by Aumasson and Meier are investigated. First, the minimal size of a zero-sum is established. Then, we analyze the impacts of the linear and the nonlinear layers in an iterated permutation on the construction of zero-sum partitions. Finally, these techniques are applied to the Keccak-f permutation and to Hamsi-256. We exhibit several zero-sum partitions for 20 rounds (out of 24) of Keccak-f and some zero-sum partitions of size 2^{19} and 2^{10} for the finalization permutation in Hamsi-256

Higher Order Differential Analysis of NORX

In this paper, we analyse the higher order differential properties of NORX, an AEAD scheme submitted to CAESAR competition. NORX is a sponge based construction. Previous efforts, by the designers themselves, have focused on the first order differentials and rotational properties for a small number of steps of the NORX core permutation, which turn out to have quite low biases when extended to the full permutation. In our work, the higher order differential properties are identified that allow to come up with practical distinguishers of the 4-round full permutation for NORX64 and half round less than the full permutation (i.e., 3.5-round) for NORX32. These distinguishers are similar to zero-sum distinguishers but are probabilistic in nature rather than deterministic, and are of order as low as four. The distinguishers have very low complexities, and are significantly more efficient than the generic generalized birthday attack for the same configurations of zero-sums. While these distinguishers identify sharper non-randomness than what the designers identified, our results do not lend themselves for cryptanalysis of full-round NORX encryption or authentication

Security of the SHA-3 candidates Keccak and Blue Midnight Wish: Zero-sum property

The SHA-3 competition for the new cryptographic standard was initiated by National Institute of Standards and Technology (NIST) in 2007. In the following years, the event grew to one of the top areas currently being researched by the CS and cryptographic communities. The first objective of this thesis is to overview, analyse, and critique the SHA-3 competition. The second one is to perform an in-depth study of the security of two candidate hash functions, the finalist Keccak and the second round candidate Blue Midnight Wish. The study shall primarily focus on zero-sum distinguishers. First we attempt to attack reduced versions of these hash functions and see if any vulnerabilities can be detected. This is followed by attacks on their full versions. In the process, a novel approach is utilized in the search of zero-sum distinguishers by employing SAT solvers. We conclude that while such complex attacks can theoretically uncover undesired properties of the two hash functions presented, such attacks are still far from being fully realized due to current limitations in computing power

On the influence of the algebraic degree of F−1F^{−1} on the algebraic degree of G∘FG \circ F

We present a study on the algebraic degree of iterated permutations seen as multivari- ate polynomials. Our main result shows that this degree depends on the algebraic degree of the inverse of the permutation which is iterated. This result is also extended to non-injective balanced vectorial functions where the relevant quantity is the minimal degree of the inverse of a permutation expanding the function. This property has consequences in symmetric cryptography since several attacks or distinguishers exploit a low algebraic degree, like higher-order differential attacks, cube attacks and cube testers, or algebraic attacks. Here, we present some applications of this improved bound to a higher-degree variant of the block cipher KN , to the block cipher Rijndael-256 and to the inner permutations of the hash functions ECHO and JH

TurboSHAKE

In a recent presentation, we promoted the use of 12-round instances of Keccak, collectively called “TurboSHAKE”, in post-quantum cryptographic schemes, but without defining them further. The goal of this note is to fill this gap: The definition of the TurboSHAKE family simply consists in exposing and generalizing the primitive already defined inside KangarooTwelve

sLiSCP: Simeck-based Permutations for Lightweight Sponge Cryptographic Primitives

In this paper, we propose a family of lightweight cryptographic permutations called sLiSCP, with the sole aim to provide a realistic minimal design}that suits a variety of lightweight device applications. More precisely, we argue that for such devices the chip area dedicated for security purposes should, not only be consumed by an encryption or hashing algorithm, but also provide as many cryptographic functionalities as possible. Our main contribution is the design of a lightweight permutation employing a 4-subblock Type-2 Generalized-like Structure (GFS) and round-reduced unkeyed Simeck with either 48 or 64-bit block length as the two round functions, thus resulting in two lightweight instances of the permutation, sLiSCP-192 and sLiSCP-256. We leverage the extensive security analysis on both Simeck (Simon-like functions) and Type-2 GFSs and present bounds against differential and linear cryptanalysis. In particular, we provide an estimation on the maximum differential probability of the round-reduced Simeck and use it for bounding the maximum expected differential/linear characteristic probability for our permutation. Due to the iterated nature of the Simeck round function and the simple XOR and cyclic shift mixing layer of the GFS that fosters the propagation of long trails, the long trail strategy}is adopted to provide tighter bounds on both characteristics. Moreover, we analyze sLiSCP against a wide range of distinguishing attacks, and accordingly, claim that there exists no structural distinguishers for sLiSCP with a complexity below $2^{b/2}$ where $b$ is the state size. We demonstrate how sLiSCP can be used as a unified round function in the duplex sponge construction to build (authenticated) encryption and hashing functionalities. The parallel hardware implementation area of the unified duplex mode of sLiSCP-192 (resp. sLiSCP-256) in CMOS $65\,nm$ ASIC is 2289 (resp. 3039) GEs with a throughput of 29.62 (resp. 44.44) kbps, and their areas in CMOS $130\, nm$ are 2498 (resp. 3319) GEs

Zero-Sum Partitions of PHOTON Permutations

We describe an approach to zero-sum partitions using Todo’s division property at EUROCRYPT 2015. It follows the inside-out methodology, and includes MILP-assisted search for the forward and backward trails, and subspace approach to connect those two trails that is less restrictive than commonly done. As an application we choose PHOTON, a family of sponge-like hash function proposals that was recently standardized by ISO. With respect to the security claims made by the designers, we for the first time show zero-sum partitions for almost all of those full 12-round permutation variants that use a 4-bit S-Box. As with essentially any other zero-sum property in the literature, also here the gap between a generic attack and the shortcut is small

Internal Differential Boomerangs: Practical Analysis of the Round-Reduced Keccak-f Permutation

We introduce internal differential boomerang distinguisher as a combination of internal differentials and classical boomerang distinguishers. The new boomerangs can be successful against cryptographic primitives having high-probability round-reduced internal differential characteristics. The internal differential technique, which follow the evolution of differences between parts of the state, is particularly meaningful for highly symmetric functions like the inner permutation Keccak-f of the hash functions defined in the future SHA-3 standard. We find internal differential and standard characteristics for three to four rounds of Keccak-f, and with the use of the new technique, enhanced with a strong message modification, show practical distinguishers for this permutation. Namely, we need $2^{12}$ queries to distinguish 7 rounds of the permutation starting from the first round, and approximately $2^{18}$ queries to distinguish 8 rounds starting from the fourth round. Due to the exceptionally low complexities, all of our results have been completely verified with a computer implementation of the analysis