In this paper, we study preimage resistance of the SHA-3 standard. We propose a squeeze meet-in-the-middle attack as a new preimage attack method for the sponge functions. This attack combines the squeeze attack and meet-in-the-middle attack, and is implemented by internal differentials. We analyze the inverse operation of the SHA-3 round function, and develop a new target internal differential algorithm as well as a linearization technique for the Sbox in the backward phase. In addition, we...

Highly-optimized assembly is commonly used to achieve the best performance for popular cryptographic schemes such as the newly standardized ML-KEM and ML-DSA. The majority of implementations today rely on hand-optimized assembly for the core building blocks to achieve both security and performance. However, recent work by Abdulrahman et al. takes a new approach, writing a readable base assembly implementation first and leaving the bulk of the optimization work to a tool named SLOTHY based...

In modern cryptography, relatively few instantiations of foundational cryptographic primitives are used across most cryptographic protocols. For example, elliptic curve groups are typically instantiated using P-256, P-384, Curve25519, or Curve448, while block ciphers are commonly instantiated with AES, and hash functions with SHA-2, SHA-3, or SHAKE. This limited diversity raises concerns that an adversary with nation-state-level resources could perform a preprocessing attack, generating a...

In this paper we explain how we implemented the Secure Hash Algorithm-3 (SHA-3) family of functions in Lean 4, a functional programming language and theorem prover. We describe how we used several Lean facilities including type classes, dependent types, macros, and formal verification, and then refined the design to provide a simple one-shot and streaming API for hashing, and Extendable-output functions (XOFs), to reduce potential for misuse by users, and formally prove properties about the...

Authenticated encryption (AE) is a cryptographic mechanism that allows communicating parties to protect the confidentiality and integrity of messages exchanged over a public channel, provided they share a secret key. In this work, we present new AE schemes leveraging the SHA-3 standard functions SHAKE128 and SHAKE256, offering 128 and 256 bits of security strength, respectively, and their “Turbo” counterparts. They support session-based communication, where a ciphertext authenticates the...

With the standardization of NIST post-quantum cryptographic (PQC) schemes, optimizing these PQC schemes across various platforms presents significant research value. While most existing software implementation efforts have concentrated on ARM platforms, research on PQC implementations utilizing various RISC-V instruction set architectures (ISAs) remains limited. In light of this gap, this paper proposes comprehensive and efficient optimizations of Keccak, Kyber, and Dilithium on...

The SHA-3 standard consists of four cryptographic hash functions, called SHA3-224, SHA3-256, SHA3-384 and SHA3-512, and two extendable-output functions (XOFs), called SHAKE128 and SHAKE256. In this paper, we study the collision resistance of the SHA-3 instances. By analyzing the nonlinear layer, we introduce the concept of maximum difference density subspace, and develop a new target internal difference algorithm by probabilistic linearization. We also exploit new strategies for optimizing...

Quantum computers have the potential to solve hard problems that are nearly impossible to solve by classical computers, this has sparked a surge of research to apply quantum technology and algorithm against the cryptographic systems to evaluate for its quantum resistance. In the process of selecting post-quantum standards, NIST categorizes security levels based on the complexity that quantum computers would require to crack AES encryption (levels 1, 3 and 5) and SHA-2 or SHA-3 (levels 2 and...

Hardening microprocessors against side-channel attacks is a critical aspect of ensuring their security. A key step in this process is identifying and mitigating “leaky" hardware modules, which leak information during the execution of cryptographic algorithms. In this paper, we explore how different leakage detection methods, the Side-channel Vulnerability Factor (SVF) and the Test Vector Leakage Assessment (TVLA), contribute to hardening of microprocessors. We conduct experiments on two...

Sponge hashing is a widely used class of cryptographic hash algorithms which underlies the current international hash function standard SHA-3. In a nutshell, a sponge function takes as input a bit-stream of any length and processes it via a simple iterative procedure: it repeatedly feeds each block of the input into a so-called block function, and then produces a digest by once again iterating the block function on the final output bits. While much is known about the post-quantum security of...

Hashing algorithms are one-way functions that are used in cryptographic protocols as Pseudo Random Functions (PRF), to assess data integrity or to create a Hash-based Message Authentication Code (HMAC). In many cryptographic constructions, secret data is processed with hashing functions. In these cases, recovering the input given to the hashing algorithm allows retrieving secret data. In this paper, we investigate the application of Soft Analytical Side-Channel Attacks (SASCA), based on a...

Higher order differential properties constitute a very insightful tool at the hands of a cryptanalyst allowing for probing a cryptographic primitive from an algebraic perspective. In FSE 2017, Saha et al. reported SymSum (referred to as SymSum_Vec in this paper), a new distinguisher based on higher order vectorial Boolean derivatives of SHA-3, constituting one of the best distinguishers on the latest cryptographic hash standard. SymSum_Vec exploits the difference in the algebraic degree...

We introduce protocols for classical verification of quantum depth (CVQD). These protocols enable a classical verifier to differentiate between devices of varying quantum circuit depths, even in the presence of classical computation. The goal is to demonstrate that a classical verifier can reject a device with a quantum circuit depth of no more than $d$, even if the prover employs additional polynomial-time classical computation to deceive. Conversely, the verifier accepts a device with a...

Given a fixed-size block, cryptographic block functions gen- erate outputs by a sequence of bitwise operations. Block functions are widely used in the design of hash functions and stream ciphers. Their correct implementations hence are crucial to computer security. We pro- pose a method that leverages logic equivalence checking to verify assem- bly implementations of cryptographic block functions. Logic equivalence checking is a well-established technique from hardware verification....

Syndrome-based early epidemic warning plays a vital role in preventing and controlling unknown epidemic outbreaks. It monitors the frequency of each syndrome, issues a warning if some frequency is aberrant, identifies potential epidemic outbreaks, and alerts governments as early as possible. Existing systems adopt a cloud-assisted paradigm to achieve cross-facility statistics on the syndrome frequencies. However, in these systems, all symptom data would be directly leaked to the cloud, which...

The Boolean map $\chi_n \colon \mathbb{F}_2^n \to \mathbb{F}_2^n,\ x \mapsto y$ defined by $y_i = x_i + (x_{i+1}+1)x_{i+2}$ (where $i\in \mathbb{Z}/n\mathbb{Z}$) is used in various permutations that are part of cryptographic schemes, e.g., Keccak-f (the SHA-3-permutation), ASCON (the winner of the NIST Lightweight competition), Xoodoo, Rasta and Subterranean (2.0). In this paper, we study various algebraic properties of this map. We consider $\chi_n$ (through vectorial isomorphism) as a...

Authenticated encryption is a cryptographic mechanism that allows communicating parties to protect the confidentiality and integrity of message exchanged over a public channel, provided they share a secret key. Some applications require committing authenticated encryption schemes, a security notion that is not covered by the classical requirements of confidentiality and integrity given a secret key. An authenticated encryption (AE) scheme is committing in the strongest sense when it is...

Sponge paradigm, used in the design of SHA-3, is an alternative hashing technique to the popular Merkle-Damgård paradigm. We revisit the problem of finding $B$-block-long collisions in sponge hash functions in the auxiliary-input random permutation model, in which an attacker gets a piece of $S$-bit advice about the random permutation and makes $T$ (forward or inverse) oracle queries to the random permutation. Recently, significant progress has been made in the Merkle-Damgård setting and...

This note provides an update on Keccak performance on the ARMv7-M processors. Starting from the XKCP implementation, we have applied architecture-specific optimizations that have yielded a performance gain of up to 21% for the largest permutation instance.

Cryptographic hash functions are used inside many applications that critically rely on their resistance against cryptanalysis attacks and the correctness of their implementations. Nevertheless, vulnerabilities in cryptographic hash function implementations can remain unnoticed for more than a decade, as shown by the recent discovery of a buffer overflow in the implementation of SHA-3 in the eXtended Keccak Code Package (XKCP), impacting Python, PHP, and several other software projects. This...

Besides the U.S. NIST standard SHA-3(Keccak), another sponge-based primitive Ascon was selected as the NIST standard for lightweight applications, recently. Exploring the security against attacks on the sponge-based hash functions is very important. At EUROCRYPT 2023, Qin et al. introduced the MitM preimage attack framework and the automatic tools for Keccak, Ascon, and Xoodyak. In this paper, we extend Qin et al.'s MitM attack framework into collision attack and also develop various...

Cryptographic hash functions map data of arbitrary size to a fixed size digest, and are one of the most commonly used cryptographic objects. As it is infeasible to design an individual hash function for every input size, variable-input length hash functions are built by designing and bootstrapping a single fixed-input length function that looks sufficiently random. To prevent trivial preprocessing attacks, applications often require not just a single hash function but rather a family of...

This paper describes a vulnerability in several implementations of the Secure Hash Algorithm 3 (SHA-3) that have been released by its designers. The vulnerability has been present since the final-round update of Keccak was submitted to the National Institute of Standards and Technology (NIST) SHA-3 hash function competition in January 2011, and is present in the eXtended Keccak Code Package (XKCP) of the Keccak team. It affects all software projects that have integrated this code, such as...

In symmetric cryptography, block ciphers, stream ciphers and permutations often make use of a round function and many round functions consist of a linear and a non-linear layer. One that is often used is based on the cellular automaton that is denoted by $\chi$ as a Boolean map on bi-infinite sequences, $\mathbb{F}^{\mathbb{Z}}$. It is defined by $\sigma \mapsto \nu$ where each $\nu_i = \sigma_i + (\sigma_{i+1}+1)\sigma_{i+2}$. A map $\chi_n$ is a map that operatos on $n$-bit arrays...

Recently, linear structures and algebraic attacks have been widely used in preimage attacks on round-reduced Keccak. Inherited by pioneers' work, we make some improvements for 3-round Keccak-256 and 4-round Keccak[r=640, c=160]. For 3-round Keccak-256, we introduce a three-stage model to deal with the unsatisfied restrictions while bringing more degrees of freedom at the same time. Besides, we show that guessing values for different variables will result in different complexity of solving...

The random oracle methodology is central to the design of many practical cryptosystems. A common challenge faced in several systems is the need to have a random oracle that outputs from a structured distribution $\mathcal{D}$, even though most heuristic implementations such as SHA-3 are best suited for outputting bitstrings. Our work explores the problem of sampling from discrete Gaussian (and related) distributions in a manner that they can be programmed into random oracles. We...

Sponge hashing is a novel alternative to the popular Merkle-Damgård hashing design. The sponge construction has become increasingly popular in various applications, perhaps most notably, it underlies the SHA-3 hashing standard. Sponge hashing is parametrized by two numbers, $r$ and $c$ (bitrate and capacity, respectively), and by a fixed-size permutation on $r+c$ bits. In this work, we study the collision resistance of sponge hashing instantiated with a random permutation by adversaries with...

We introduce the notion of a universal random oracle. Analogously to a classical random oracle it idealizes hash functions as random functions. However, as opposed to a classical random oracle which is created freshly and independently for each adversary, the universal random oracle should provide security of a cryptographic protocol against all adversaries simultaneously. This should even hold if the adversary now depends on the random function. This reflects better the idea that the strong...

SHA-3 is considered to be one of the most secure standardized hash functions. It relies on the Keccak-f[1 600] permutation, which operates on an internal state of 1 600 bits, mostly represented as a 5×5×64-bit matrix. While software implementations process the state sequentially in chunks of typically 32 or 64 bits, the Keccak-f[1 600] permutation can benefit a lot from speedup through parallelization. This paper is the first to explore the full potential of parallelization of Keccak-f[1...

The Keccak sponge function family, designed by Bertoni et al. in 2007, was selected by the U.S. National Institute of Standards and Technology (NIST) in 2012 as the next generation of Secure Hash Algorithm (SHA-3). Due to its theoretical and practical importance, cryptanalysis against SHA-3 has attracted an increasing attention. To the best of our knowledge, the most powerful collision attack on SHA-3 up till now is the linearisation technique proposed by Jian Guo et al. However, that...

In this work, we focus on collision attacks against instances of SHA-3 hash family in both classical and quantum settings. Since the 5-round collision attacks on SHA3-256 and other variants proposed by Guo et al. at JoC~2020, no other essential progress has been published. With a thorough investigation, we identify that the challenges of extending such collision attacks on SHA-3 to more rounds lie in the inefficiency of differential trail search. To overcome this obstacle, we develop a...

SHA-3 is considered to be one of the most secure standardized hash functions. It relies on the Keccak-f[1,600] permutation, which operates on an internal state of 1,600 bits, mostly represented as a $5\times5\times64{-}bit$ matrix. While existing implementations process the state sequentially in chunks of typically 32 or 64 bits, the Keccak-f[1,600] permutation can benefit a lot from speedup through parallelization. This paper is the first to explore the full potential of parallelization of...

Performance in hardware has typically played a significant role in differentiating among leading candidates in cryptographic standardization efforts. Winners of two past NIST cryptographic contests (Rijndael in case of AES and Keccak in case of SHA-3) were ranked consistently among the two fastest candidates when implemented using FPGAs and ASICs. Hardware implementations of cryptographic operations may quite easily outperform software implementations for at least a subset of major...

In this paper we prove quantum indifferentiability of the sponge construction instantiated with random (invertible) permutations. With this result we bring the post-quantum security of the standardized SHA-3 hash function to the level matching its security against classical adversaries. To achieve our result, we generalize the compressed-oracle technique of Zhandry (Crypto'19) by defining and proving correctness of a compressed permutation oracle. We believe our technique will find...

FrodoKEM is a lattice-based key encapsulation mechanism, currently a semi-finalist in NIST’s post-quantum standardization effort. A condition for these candidates is to use NIST standards for sources of randomness (i.e., seed-expanding), and as such most candidates utilize SHAKE, an XOF defined in the SHA-3 standard. However, for many of the candidates, this module is a significant implementation bottleneck. Trivium is a lightweight, ISO standard stream cipher which performs well in hardware...

We provide a modified version of the Ligero sublinear zero knowledge proof system for arithmetic circuits provided by Ames et. al. (CCS ‘17). Our modification "BooLigero" tailors Ligero for use in Boolean circuits to achieve a significant improvement in proof size. Although the original Ligero system could be used for Boolean circuits, Ligero generally requires allocating an entire field element to represent a single bit on a wire in a Boolean circuit. In contrast, our system performs...

In this work we introduce Banquet, a digital signature scheme with post-quantum security, constructed using only symmetric-key primitives. The design is based on the MPC-in-head paradigm also used by Picnic (CCS 2017) and BBQ (SAC 2019). Like BBQ, Banquet uses only standardized primitives, namely AES and SHA-3, but signatures are more than 50% shorter, making them competitive with Picnic (which uses a non-standard block cipher to improve performance). The MPC protocol in Banquet uses a new...

Competitions are widely viewed as the safest way to select cryptographic algorithms. This paper surveys procedures that have been used in cryptographic competitions, and analyzes the extent to which those procedures reduce security risks.

This work presents a detailed study of the classical security of the post-quantum supersingular isogeny key encapsulation (SIKE) protocol using a realistic budget-based cost model that considers the actual computing and memory costs that are needed for cryptanalysis. In this effort, we design especially-tailored hardware accelerators for the time-critical multiplication and isogeny computations that we use to model an ASIC-powered instance of the van Oorschot-Wiener (vOW) parallel collision...

In this paper, we extend the protocol of classical verification of quantum computations (CVQC) recently proposed by Mahadev to make the verification efficient. Our result is obtained in the following three steps: - We show that parallel repetition of Mahadev's protocol has negligible soundness error. This gives the first constant round CVQC protocol with negligible soundness error. In this part, we only assume the quantum hardness of the learning with error (LWE) problem similar to...

Performance in hardware has typically played a major role in differentiating among leading candidates in cryptographic standardization efforts. Winners of two past NIST cryptographic contests (Rijndael in case of AES and Keccak in case of SHA-3) were ranked consistently among the two fastest candidates when implemented using FPGAs and ASICs. Hardware implementations of cryptographic operations may quite easily outperform software implementations for at least a subset of major performance...

Since Keccak was selected as the SHA-3 standard, more and more permutation-based primitives have been proposed. Different from block ciphers, there is no round key in the underlying permutation for permutation-based primitives. Therefore, there is a higher risk for a differential characteristic of the underlying permutation to become incompatible when considering the dependency of difference transitions over different rounds. However, in most of the MILP or SAT based models to search for...

Since its selection as the winner of the SHA-3 competition, Keccak, with all its variants, has found a large number of applications. It is, for instance, a common building block in schemes submitted to NIST's post-quantum cryptography project. In many of these applications, Keccak processes ephemeral secrets. In such a setting, side-channel adversaries are limited to a single observation, meaning that differential attacks are inherently prevented. If, however, such a single trace of Keccak...

Since Keccak was selected as the SHA-3 standard, both its hash mode and keyed mode have attracted lots of third-party cryptanalysis. Especially in recent years, there is progress in analyzing the collision resistance and preimage resistance of round-reduced Keccak. However, for the preimage attacks on round-reduced Keccak-384/512, we found that the linear relations leaked by the hash value are not well exploited when utilizing the current linear structures. To make full use of the...

In this paper we spot light on dedicated quantum collision attacks on concrete hash functions, which has not received much attention so far. In the classical setting, the generic complexity to find collisions of an $n$-bit hash function is $O(2^{n/2})$, thus classical collision attacks based on differential cryptanalysis such as rebound attacks build differential trails with probability higher than $2^{-n/2}$. By the same analogy, generic quantum algorithms such as the BHT algorithm find...

We show that many symmetric cryptography primitives would not be less safe with significantly fewer rounds. To support this claim, we review the cryptanalysis progress in the last 20 years, examine the reasons behind the current number of rounds, and analyze the risk of doing fewer rounds. Advocating a rational and scientific approach to round numbers selection, we propose revised number of rounds for AES, BLAKE2, ChaCha, and SHA-3, which offer more consistent security margins across...

We investigate multiple implementations of a hash-based digital signature scheme in software and hardware for a RISC-V processor. For this, different instantiations of XMSS by leveraging SHA-256 and SHA-3 are considered. Moreover, we propose various optimisations for accelerating the signature scheme on resource-constrained FPGAs. Compared to the pure software version, the implemented hardware accelerators for SHA-256 and SHA-3 achieve a significant speedup of 25x and 87x respectively for...

We present a high-assurance and high-speed implementation of the SHA-3 hash function. Our implementation is written in the Jasmin programming language, and is formally verified for functional correctness, provable security and timing attack resistance in the EasyCrypt proof assistant. Our implementation is the first to achieve simultaneously the four desirable properties (efficiency, correctness, provable security, and side-channel protection) for a non-trivial cryptographic...

Public key cryptography protocols, such as RSA and elliptic curve cryptography, will be rendered insecure by Shor’s algorithm when large-scale quantum computers are built. Cryptographers are working on quantum-resistant algorithms, and lattice-based cryptography has emerged as a prime candidate. However, high computational complexity of these algorithms makes it challenging to implement lattice-based protocols on low-power embedded devices. To address this challenge, we present Sapphire – a...

In this paper, we present new preimage attacks on KECCAK-384 and KECCAK-512 for 2, 3 and 4 rounds. The attacks are based on non-linear structures (structures that contain quadratic terms). These structures were studied by Guo et al. and Li et al. to give preimage attacks on round reduced KECCAK. We carefully construct non-linear structures such that the quadratic terms are not spread across the whole state. This allows us to create more linear equations between the variables and hash values,...

We present new preimage attacks on standard Keccak-224 and Keccak-256 that are reduced to 3 and 4 rounds. An allocating approach is used in the attacks, and the whole complexity is allocated to two stages, such that fewer constraints are considered and the complexity is lowered in each stage. Specifically, we are trying to find a 2-block preimage, instead of a 1-block one, for a given hash value, and the first and second message blocks are found in two stages, respectively. Both the...

The need for high-quality randomness in cryptography makes random-number generation one of its most fundamental tasks. A recent important line of work (initiated by Dodis et al., CCS ’13) focuses on the notion of *robustness* for *pseudorandom number generators (PRNGs) with inputs*—these are primitives that use various sources to accumulate sufficient entropy into a state, from which pseudorandom bits are extracted. Robustness ensures that PRNGs remain secure even under state compromise and...

At Real World Crypto 2017, Joan Daemen won the Levchin Prize and announced that he believed permutation-based crypto was the future of symmetric cryptography. At the same conference Mike Hamburg introduced Strobe, a symmetric protocol framework capable of protecting sessions as well as building symmetric cryptographic primitives for the single cost of Joan Daemen’s permutation Keccak. The next year, at Real World Crypto 2018 Trevor Perrin came to talk about the Noise protocol framework, a...

The KECCAK hash function is the winner of the SHA-3 competition (2008 -- 2012) and became the SHA-3 standard of NIST in 2015. In this paper, we focus on practical collision attacks against round-reduced SHA-3 and some KECCAK variants. Following the framework developed by Dinur et al. at FSE~2012 where 4-round collisions were found by combining 3-round differential trails and 1-round connectors, we extend the connectors to up to three rounds and hence achieve collision attacks for up to 6...

Internet-of-Things (IoT) applications often require constrained devices to be deployed in the field for several years, even decades. Protection of these tiny motes is crucial for end-to-end IoT security. Secure boot and attestation techniques are critical requirements in such devices which rely on public key Sign/Verify operations. In a not-so-distant future, quantum computers are expected to break traditional public key Sign/Verify functions (e.g. RSA and ECC signatures). Hash Based...

Message franking enables cryptographically verifiable reporting of abusive content in end-to-end encrypted messaging. Grubbs, Lu, and Ristenpart recently formalized the needed underlying primitive, what they call compactly committing authenticated encryption (AE), and analyzed the security of a number of approaches. But all known secure schemes are still slow compared to the fastest standard AE schemes. For this reason Facebook Messenger uses AES-GCM for franking of attachments such as...

In this paper, we present a cryptanalysis of round reduced Keccak-384 for 2 rounds. The best known preimage attack for this variant of Keccak has the time complexity $2^{129}$. In our analysis, we find a preimage in the time complexity of $2^{89}$ and almost same memory is required.

We show how to build distributed key generation and distributed decryption procedures for the LIMA Ring-LWE based post-quantum cryptosystem. Our protocols implement the CCA variants of distributed decryption and are actively secure (with abort) in the case of three parties and honest majority. Our protocols make use of a combination of problem specific MPC protocols, generic garbled circuit based MPC and generic Linear Secret Sharing based MPC. We also, as a by-product, report on the first...

Recently the CAESAR competition has announced several finalists among the submitted authenticated encryption algorithms, after an open selection process during the last 5 years. Applications using these algorithms are rapidly increasing today. Devices implementing these applications are enormously susceptible to physical attacks, which are able to retrieve secret data through side-channel information such as the power consumption or the electromagnetic radiations. In this work we present a...

The keyed sponge is a well-accepted method for message authentication. It processes data at a certain rate by sequential evaluation of an underlying permutation. If the key size $k$ is smaller than the rate, currently known bounds are tight, but if it exceeds the rate, state of the art only dictates security up to $2^{k/2}$. We take closer inspection at the key prediction security of the sponge and close the remaining gap in the existing security analysis: we confirm key security up to close...

We study instantiating the random permutation of the block-cipher mode of operation IAPM (Integrity-Aware Parallelizable Mode) with the public random permutation of Keccak, on which the draft standard SHA-3 is built. IAPM and the related mode OCB are single-pass highly parallelizable authenticated-encryption modes, and while they were originally proven secure in the private random permutation model, Kurosawa has shown that they are also secure in the public random permutation model assuming...

Keccak is the final winner of SHA-3 competition and it can be used as message authentic codes as well. The basic and balanced divide-and-conquer attacks on Keccak-MAC were proposed by Dinur et al. at Eurocrypt 2015. The idea of cube attacks is used in the two attacks to divide key bits into small portions. In this paper, by carefully analysing the mappings used in Keccak-MAC, it is found that some cube variables could divide key bits into smaller portions and so better divide-and-conquer...

Decision of whether a Boolean equation system has a solution is an NPC problem and finding a solution is NP hard. In this paper, we present a quantum algorithm to decide whether a Boolean equation system F has a solution and compute one if F does have solutions with any given success probability. The complexity of the algorithm is polynomial in the size of F and the condition number of F. As a consequence, we have achieved exponential speedup for solving sparse Boolean equation systems if...

In this paper, we propose a new MILP modeling to find better or even optimal choices of conditional cubes, under the general framework of conditional cube attacks. These choices generally find new or improved attacks against the keyed constructions based on Keccak permutation and its variants, including Keccak-MAC, KMAC, Keyak, and Ketje, in terms of attack complexities or the number of attacked rounds. Interestingly, conditional cube attacks were applied to round-reduced Keccak-MAC, but not...

In this paper, we give the first pre-image attack against 1- round KECCAK-512 hash function, which works for all variants of 1- round KECCAK. The attack gives a preimage of length less than 1024 bits by solving a system of 384 linear equations. We also give a collision attack against 1-round KECCAK using similar analysis.

Cryptographic hash functions are security-critical algorithms with many practical applications, notably in digital signatures. Developing an approach to test them can be particularly difficult, and bugs can remain unnoticed for many years. We revisit the NIST hash function competition, which was used to develop the SHA-3 standard, and apply a new testing strategy to all available reference implementations. Motivated by the cryptographic properties that a hash function should satisfy, we...

Keccak-based algorithms such as Secure Hash Algorithm-3 (SHA-3) will be widely used in crypto systems, and evaluating their security against different kinds of attacks is vitally important. This paper presents an efficient differential fault analysis (DFA) method on all four modes of SHA-3 to recover an entire internal state, which leads to message recovery in the regular hashing mode and key retrieval in the message authentication code (MAC) mode. We adopt relaxed fault models in this...

The Keccak hash function is the winner of the SHA-3 competition and became the SHA-3 standard of NIST in 2015. In this paper, we focus on practical collision attacks against round-reduced Keccak hash function, and two main results are achieved: the first practical collision attacks against 5-round Keccak-224 and an instance of 6-round Keccak collision challenge. Both improve the number of practically attacked rounds by one. These results are obtained by carefully studying the algebraic...

The efficient protection of security critical devices against side-channel analysis attacks is a fundamental need in the age of Internet of Things and ubiquitous computing. In this work, we introduce a configurable hardware design of Keccak (SHA-3) which can be tailored to fulfill the needs of a wide range of different applications. Our Keccak design is therefore equipped with generic side-channel protection capabilities. The design can thus be synthesized for any desired protection level by...

In this paper, we focus on collision attacks against Keccak hash function family and some of its variants. Following the framework developed by Dinur et al. at FSE~2012 where 4-round collisions were found by combining 3-round differential trails and 1-round connectors, we extend the connectors one round further hence achieve collision attacks for up to 5 rounds. The extension is possible thanks to the large degree of freedom of the wide internal state. By linearization of all S-boxes of the...

This paper presents an efficient algebraic fault analysis on all four modes of SHA-3 under relaxed fault models. This is the first work to apply algebraic techniques on fault analysis of SHA-3. Results show that algebraic fault analysis on SHA-3 is very efficient and effective due to the clear algebraic properties of Keccak operations. Comparing with previous work on differential fault analysis of SHA-3, algebraic fault analysis can identify the injected faults with much higher rates, and...

Truncation collision resistance is a simple non-interactive complexity assumption that seems very plausible for standard cryptographic hash functions like SHA-3. We describe how this assumption can be leveraged to obtain standard-model constructions of public-key cryptosystems that previously seemed to require a programmable random oracle. This includes the first constructions of identity-based key encapsulation mechanisms (ID-KEMs) and digital signatures over bilinear groups with full...

We investigate the cost of Grover's quantum search algorithm when used in the context of pre-image attacks on the SHA-2 and SHA-3 families of hash functions. Our cost model assumes that the attack is run on a surface code based fault-tolerant quantum computer. Our estimates rely on a time-area metric that costs the number of logical qubits times the depth of the circuit in units of surface code cycles. As a surface code cycle involves a significant classical processing stage, our cost...

Ever since Keccak won the SHA3 competition, sponge-based constructions are being suggested for many different applications, including pseudo-random number generators (PRNGs). Sponges are very desirable, being well studied, increasingly efficient to implement and simplistic in their design. The initial construction of a sponge-based PRNG (Bertoni et al. CHES 2010) based its security on the well known sponge indifferentiability proof in the random permutation model and provided no forward...

In this paper, we analyze the security of round-reduced versions of the Keccak hash function family. Based on the work pioneered by Aumasson and Meier, and Dinur et al., we formalize and develop a technique named linear structure, which allows linearization of the underlying permutation of Keccak for up to 3 rounds with large number of variable spaces. As a direct application, it extends the best zero-sum distinguishers by 2 rounds without increasing the complexities. We also apply linear...

BLAKE2 is a hash function introduced at ACNS 2013, which has been adopted in many constructions and applications. It is a successor to the SHA-3 finalist BLAKE, which received a significant amount of security analysis. Nevertheless, BLAKE2 introduces sufficient changes so that not all results from BLAKE carry over, meaning new analysis is necessary. To date, all known cryptanalysis done on BLAKE2 has focused on its underlying building blocks, with little focus placed on understanding...

The security analysis of Keccak, the winner of SHA-3, has attracted considerable interest. Recently, some attention has been paid to the analysis of keyed modes of Keccak sponge function. As a notable example, the most efficient key recovery attacks on Keccak-MAC and Keyak were reported at EUROCRYPT'15 where cube attacks and cubeattack- like cryptanalysis have been applied. In this paper, we develop a new type of cube distinguisher, the conditional cube tester, for Keccak sponge function. By...

We present KangarooTwelve, a fast and secure arbitrary output-length hash function aiming at a higher speed than the FIPS 202's SHA-3 and SHAKE functions. While sharing many features with SHAKE128, like the cryptographic primitive, the sponge construction, the eXtendable Output Function (XOF) and the 128-bit security strength, KangarooTwelve offers two major improvements over its standard counterpart. First it has a built-in parallel mode that efficiently exploits multi-core or SIMD...

The security of SHA-3 against different kinds of attacks are of vital importance for crypto systems with SHA-3 as the security engine. In this paper, we look into the differential fault analysis of SHA-3, and this is the first work to conquer SHA3-224 and SHA3-256 using differential fault analysis. Comparing with one existing related work, we relax the fault models and make them realistic for different implementation architectures. We analyze fault propagation in SHA-3 under such single-byte...

Discussions about the choice of a tree hash mode of operation for a standardization have recently been undertaken. It appears that a single tree mode cannot address adequately all possible uses and specifications of a system. In this paper, we review the tree modes which have been proposed, we discuss their problems and propose remedies. We make the reasonable assumption that communicating systems have different specifications and that software applications are of different types (securing...

As the new SHA-3 standard, the security and reliability of Keccak have attracted a lot of attentions. Previous works already show that both software and hardware implementations of Keccak have strong side-channel power (electromagnetic) leakages, and these leakages can be easily used by attackers to recover secret key bits. Meanwhile, Keccak is vulnerable to random errors and injected faults, which will cause errors in the computation results. In this paper, we introduce a scheme based on...

We study the problem of devising provably secure PRNGs with input based on the sponge paradigm. Such constructions are very appealing, as efficient software/hardware implementations of SHA-3 can easily be translated into a PRNG in a nearly black-box way. The only existing sponge-based construction, proposed by Bertoni et al. (CHES 2010), fails to achieve the security notion of robustness recently considered by Dodis et al. (CCS 2013), for two reasons: (1) The construction is deterministic,...

Recently, many efficient cryptographic hash function design strategies have been explored, not least because of the SHA-3 competition. These designs are, almost exclusively, geared towards high performance on long inputs. However, various applications exist where the performance on short (fixed length) inputs matters more. Such hash functions are the bottleneck in hash-based signature schemes like SPHINCS or XMSS, which is currently under standardization. Secure functions specifically...

In this document we present an introductory overview of the algorithms and design components underlying the Keccac cryptographic primitive and the Keyak encryption scheme for authenticated (session-supporting) encryption. This document aims to familiarize readers with the basic principles of authenticated encryption, the Sponge and Duplex constructions (full-state, keyed as well as regular versions), the permutation functions underlying Keccak and Keyak as well as Keyak v2's Motorist mode of...

In this paper, we investigate Keccak --- the cryptographic hash function adopted as the SHA-3 standard. We propose a malicious variant of the function, where new round constants are introduced. We show that for such the variant, collision and preimage attacks are possible. We also identify a class of weak keys for the malicious Keccak working in the MAC mode. Ideas presented in the paper were verified by implementing the attacks on the function with the 128-bit hash.

One of the crucial factors for enabling fast and secure computations in the Zettabyte era is the use of incremental cryptographic primitives. For files ranging from several megabytes up to hundreds of gigabytes, incremental cryptographic primitives offer speedup factors measured in multiple orders of magnitude. In this paper we define two incremental hash functions iSHAKE128 and iSHAKE256 based on the recent NIST proposal for SHA-3 Extendable-Output Functions SHAKE128 and SHAKE256. We give...

As the new SHA-3 standard, the side-channel security of Keccak has attracted a lot of attentions. Some works show that both software and hardware implementation of Keccak have strong side-channel leakages, and these leakages can be used easily by an attacker to recover secret key information. Secret sharing schemes are introduced to mask the leakages, while such schemes will incur large resource overhead. In this paper, we introduce another scheme based on the round rotation probability of...

The hash function Kupyna was recently published as the Ukrainian standard DSTU 7564:2014. It is structurally very similar to the SHA-3 finalist Grøstl, but differs in details of the round transformations. Most notably, some of the round constants are added with a modular addition, rather than bitwise xor. This change prevents a straightforward application of some recent attacks, in particular of the rebound attacks on the compression function of similar AES-like hash constructions. However,...

At CRYPTO 2012, Knellwolf and Khovratovich presented a differential formulation of advanced meet-in-the-middle techniques for preimage attacks on hash functions. They demonstrated the usefulness of their approach by significantly improving the previously best known attacks on SHA-1 from CRYPTO~2009, increasing the number of attacked rounds from a 48-round one-block pseudo-preimage without padding and a 48-round two-block preimage without padding to a 57-round one-block preimage without...

As Keccak has been selected as the new SHA-3 standard, Message Authentication Code (MAC) (MAC-Keccak) using a secret key will be widely used for integrity checking and authenticity assurance. Recent works have shown the feasibility of side-channel attacks against software implementations of MAC-Keccak to retrieve the key, with the security assessment of hardware implementations remaining an open problem. In this paper, we present a comprehensive and practical side-channel analysis of a...

In October 2012, the American National Institute of Standards and Technology (NIST) announced the selection of Keccak as the winner of the SHA-3 Cryptographic Hash Algorithm Competition [10,11]. This concluded an open competition that was remarkable both for its magnitude and the involvement of the cryptographic community. Public review is of paramount importance to increase the confidence in the new standard and to favor its quick adoption. The SHA-3 competition explicitly took this into...

We present a new definition of computationally binding commitment schemes in the quantum setting, which we call "collapse-binding". The definition applies to string commitments, composes in parallel, and works well with rewinding-based proofs. We give simple constructions of collapse-binding commitments in the random oracle model, giving evidence that they can be realized from hash functions like SHA-3. We evidence the usefulness of our definition by constructing three-round statistical...

AES-based functions have attracted of a lot of analysis in the recent years, mainly due to the SHA-3 hash function competition. In particular, the rebound attack allowed to break several proposals and many improvements/variants of this method have been published. Yet, it remained an open question whether it was possible to reach one more round with this type of technique compared to the state-of-the-art. In this article, we close this open problem by providing a further improvement over the...

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...

We prove (nearly) tight bounds on the concrete PRF-security of two constructions of message-authentication codes (MACs): (1) The truncated CBC-MAC construction, which operates as plain CBC-MAC (without prefix-free encoding of messages), but only returns a subset of the output bits. (2) The MAC derived from the sponge hash-function family by pre-pending a key to the message, which is the de-facto standard method for SHA-3-based message authentication. The tight analysis of keyed sponges is...

Keccak is the hash function selected by NIST as the new SHA-3 standard. Keccak is built on Sponge construction and it provides a new MAC function called MAC-Keccak. These new algorithms have raised questions with regards to side-channel leakage and analysis attacks of MAC-Keccak. So far there exists prior work on attacks of software implementations of MAC-Keccak, but there has been no comprehensive side-channel vulnerability assessment of its hardware implementation. In this paper we...

In this paper, we comprehensively study the resistance of keyed variants of SHA-3 (Keccak) against algebraic attacks. This analysis covers a wide range of key recovery, MAC forgery and other types of attacks, breaking up to 9 rounds (out of the full 24) of the Keccak internal permutation much faster than exhaustive search. Moreover, some of our attacks on the 6-round Keccak are completely practical and were verified on a desktop PC. Our methods combine cube attacks (an algebraic key recovery...

The notion of indifferentiability, which is a stronger version of the classic notion of indistinguishability, was introduced by Maurer, Renner, and Holenstein in 2003. Indifferentiability, among other things, gives us a way of ``securely replacing" a random oracle of one type by a random oracle of a different type. Most indifferentiability proofs in the literature are very complicated, which makes them difficult to verify and in some cases, has even resulted in them being erroneous. In this...

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...

In this paper we mount the cube attack on the Keccak sponge function. The cube attack, formally introduced in 2008, is an algebraic technique applicable to cryptographic primitives whose output can be described as a low-degree polynomial in the input. Our results show that 5- and 6-round Keccak sponge function is vulnerable to this technique. All the presented attacks have practical complexities and were verified on a desktop PC.