Improved Collisions for Reduced ECHO-256

In this work, we present a collision attack on 5 out of 8 rounds of the ECHO-256 hash function with a complexity of $2^{112}$ in time and $2^{85.3}$ memory. In this work, we further show that the merge inbound phase can still be solved in the case of hash function attacks on ECHO. As correctly observed by Jean et al., the merge inbound phase of previous hash function attacks succeeds only with a probability of $2^{-128}$. The main reason for this behavior is the low rank of the linear SuperMixColumns transformation. However, since there is enough freedom in ECHO we can solve the resulting linear equations with a complexity much lower than $2^{128}$. On the other hand, also this low rank of the linear SuperMixColumns transformation allows us to extend the collision attack on the reduced hash function from 4 to 5 rounds. Additionally, we present a collision attack on 6 rounds of the compression function of ECHO-256 and show that a subspace distinguisher is still possible for 7 out of 8 rounds of the compression function of ECHO-256. Both compression function attacks have a complexity of $2^{160}$ with memory requirements of $2^{128}$ and chosen salt

Subspace Distinguisher for 5/8 Rounds of the ECHO-256 Hash Function

In this work we present first results for the hash function of ECHO. We provide a subspace distinguisher for 5 rounds, near-collisions on 4.5 rounds and collisions for 4 out of 8 rounds of the ECHO-256 hash function. The complexities are $2^{96}$ compression function calls for the distinguisher and near-collision attack, and $2^{64}$ for the collision attack. The memory requirements are $2^{64}$ for all attacks. Furthermore, we provide improved compression function attacks on ECHO-256 to get distinguishers on 7 rounds and near-collisions for 6 and 6.5 rounds. The compression function attacks also apply to ECHO-512. To get these results, we consider new and sparse truncated differential paths through ECHO. We are able to construct these paths by analyzing the combined MixColumns and BigMixColumns transformation. Since in these sparse truncated differential paths at most one fourth of all bytes of each ECHO state are active, missing degrees of freedom are not a problem. Therefore, we are able to mount a rebound attack with multiple inbound phases to efficiently find according message pairs for ECHO

Collision Attack on 5 Rounds of Grøstl

In this article, we describe a novel collision attack for up to 5 rounds of the Grøstl hash function. This significantly improves upon the best previously published results on 3 rounds. By using a new type of differential trail spanning over more than one message block we are able to construct collisions for Grøstl on 4 and 5 rounds with complexity of $2^{67}$ and $2^{120}$, respectively. Both attacks need $2^{64}$ memory. Due to the generic nature of our attack we can even construct meaningful collisions in the chosen-prefix setting with the same attack complexity

Improving Local Collisions: New Attacks on Reduced SHA-256

In this paper, we focus on the construction of semi-free-start collisions for SHA-256, and show how to turn them into collisions. We present a collision attack on 28 steps of the hash function with practical complexity. Using a two-block approach we are able to turn a semi-free-start collision into a collision for 31 steps with a complexity of at most $2^{65.5}$. The main improvement of our work is to extend the size of the local collisions used in these attacks. To construct differential characteristics and confirming message pairs for longer local collisions, we had to improve the search strategy of our automated search tool. To test the limits of our techniques we present a semi-free-start collision for 38 steps

Ascon PRF, MAC, and Short-Input MAC

The cipher suite Ascon v1.2 already provides authenticated encryption schemes, hash, and extendable output functions. Furthermore, the underlying permutation is also used in two instances of Isap v2.0, an authenticated encryption scheme designed to provide enhanced robustness against side-channel and fault attacks. In this paper, we enrich the functionality one can get out of Ascon\u27s permutation by providing efficient Pseudorandom Functions (PRFs), a Message Authentication Code (MAC) and a fast short-input PRF for messages up to 128 bits

Branching Heuristics in Differential Collision Search with Applications to SHA-512

In this work, we present practical semi-free-start collisions for SHA-512 on up to 38 (out of 80) steps with complexity $2^{40.5}$. The best previously published result was on 24 steps. The attack is based on extending local collisions as proposed by Mendel et al. in their Eurocrypt 2013 attack on SHA-256. However, for SHA-512, the search space is too large for direct application of these techniques. We achieve our result by improving the branching heuristic of the guess-and-determine approach to find differential characteristics and conforming message pairs. Experiments show that for smaller problems like 27 steps of SHA-512, the heuristic can also speed up the collision search by a factor of $2^{20}$

Cryptanalysis of Ascon

We present a detailed security analysis of the CAESAR candidate Ascon. Amongst others, cube-like, differential and linear cryptanalysis are used to evaluate the security of Ascon. Our results are practical key-recovery attacks on round-reduced versions of Ascon-128, where the initialization is reduced to 5 out of 12 rounds. Theoretical key-recovery attacks are possible for up to 6 rounds of initialization. Moreover, we present a practical forgery attack for 3 rounds of the finalization, a theoretical forgery attack for 4 rounds finalization and zero-sum distinguishers for the full 12-round Ascon permutation. Besides, we present the first results regarding linear cryptanalysis of Ascon, improve upon the results of the design document regarding differential cryptanalysis, and prove bounds on the minimum number of (linearly and differentially) active S-boxes for the Ascon permutation

Efficient Low-Latency Masking of Ascon without Fresh Randomness

In this work, we present the first low-latency, second-order masked hardware implementation of Ascon that requires no fresh randomness using only $d+1$ shares. Our results significantly outperform any publicly known second-order masked implementations of AES and Ascon in terms of combined area, latency and randomness requirements. Ascon is a family of lightweight authenticated encryption and hashing schemes selected by NIST for standardization. Ascon is tailored for small form factors. It requires less power and energy while attaining the same or even better performance than current NIST standards. We achieve the reduction of latency by rearranging the linear layers of the Ascon permutation in a round-based implementation. We provide an improved technique to achieve implementations without the need for fresh randomness. It is based on the concept of changing of the guards extended to the second-order case. Together with the reduction of latency, we need to consider a large set of additional conditions which we propose to solve using a SAT solver. We have formally verified both, our first- and second-order implementations of Ascon using CocoAlma for the first two rounds. Additionally, we have performed a leakage assessment using t-tests on all 12 rounds of the initial permutation. Finally, we provide a comparison of our second-order masked Ascon implementation with other results

The Rebound Attack and Subspace Distinguishers: Application to Whirlpool

We introduce the rebound attack as a variant of differential cryptanalysis on hash functions and apply it to the hash function Whirlpool, standardized by ISO/IEC. We give attacks on reduced variants of the Whirlpool hash function and the Whirlpool compression function. Next, we introduce the subspace problems as generalizations of near-collision resistance. Finally, we present distinguishers based on the rebound attack, that apply to the full compression function of Whirlpool and the underlying block cipher $W$