The impossible differential (ID) attack is crucial for analyzing the strength of block ciphers. The critical aspect of this technique is to identify IDs, and the researchers introduced several methods to detect them. Recently, the researchers extended the mixed-integer linear programming (MILP) approach by partitioning the input and output differences to identify IDs. The researchers proposed techniques to determine the representative set and partition table of a set over any nonlinear...

Bitcoin, while being the most prominent blockchain with the largest market capitalization, suffers from scalability and throughput limitations that impede the development of ecosystem projects like Bitcoin Decentralized Finance (BTCFi). Recent advancements in BitVM propose a promising Layer 2 (L2) solution to enhance Bitcoin's scalability by enabling complex computations off-chain with on-chain verification. However, Bitcoin's constrained programming environment—characterized by its...

One of the most popular techniques to prove adaptive security of identity-based encryptions (IBE) and verifiable random functions (VRF) is the partitioning technique. Currently, there are only two methods to relate the adversary's advantage and runtime $(\epsilon, {\sf T})$ to those of the reduction's ($\epsilon_{\sf proof}, {\sf T}_{\sf proof}$) using this technique: One originates to Waters (Eurocrypt 2005) who introduced the famous artificial abort step to prove his IBE, achieving...

This paper deals with reducing the secret key computation time of small scale variants of the AES cipher using algebraic cryptanalysis, which is accelerated by data mining methods. This work is based on the known plaintext attack and aims to speed up the calculation of the secret key by processing the polynomial equations extracted from plaintext-ciphertext pairs. Specifically, we propose to transform the overdefined system of polynomial equations over GF(2) into a new system so that the...

Attribute-based encryption (ABE) is a generalization of public-key encryption that enables fine-grained access control to encrypted data. In (ciphertext-policy) ABE, a central trusted authority issues decryption keys for attributes $x$ to users. In turn, ciphertexts are associated with a decryption policy $\mathcal{P}$. Decryption succeeds and recovers the encrypted message whenever $\mathcal{P}(x) = 1$. Recently, Hohenberger, Lu, Waters, and Wu (Eurocrypt 2023) introduced the notion of...

To introduce a post-quantum-secure encryption scheme specifically for use in flight-computers, we used avionics’ module-isolation methods to wrap a recent encryption standard (HPKE – Hybrid Public Key Encryption) within a software partition. This solution proposes an upgrade to HPKE, using quantum-resistant ciphers (Kyber/ML-KEM and Dilithium/ML-DSA) redundantly alongside well-established ciphers, to achieve post-quantum security. Because cryptographic technology can suddenly become...

Storage of sensitive multi-dimensional arrays must be secure and efficient in storage and processing time. Searchable encryption allows one to trade between security and efficiency. Searchable encryption design focuses on building indexes, overlooking the crucial aspect of record retrieval. Gui et al. (PoPETS 2023) showed that understanding the security and efficiency of record retrieval is critical to understand the overall system. A common technique for improving security is partitioning...

The Advanced Encryption Standard (AES) is one of the most commonly used and analyzed encryption algorithms. In this work, we present new combinations of some prominent attacks on AES, achieving new records in data requirements among attacks, utilizing only $2^4$ and $2^{16}$ chosen plaintexts (CP) for 6-round and 7-round AES-192/256 respectively. One of our attacks is a combination of a meet-in-the-middle (MiTM) attack with a square attack mounted on 6-round AES-192/256 while ...

Fault injection attacks are a serious threat to system security, enabling attackers to bypass protection mechanisms or access sensitive information. To evaluate the robustness of CPU-based systems against these attacks, it is essential to analyze the consequences of the fault propagation resulting from the complex interplay between the software and the processor. However, current formal methodologies combining hardware and software face scalability issues due to the monolithic approach...

The problem of Broadcast Encryption (BE) consists in broadcasting an encrypted message to a large number of users or receiving devices in such a way that the emitter of the message can control which of the users can or cannot decrypt it. Since the early 1990's, the design of BE schemes has received significant interest and many different concepts were proposed. A major breakthrough was achieved by Naor, Naor and Lotspiech (CRYPTO 2001) by partitioning cleverly the set of authorized...

Driven by the open problem raised by Hofheinz and Kiltz (Journal of Cryptology, 2012), we study the formalization of lattice-based programmable hash function (PHF), and give three types of concrete constructions by using several techniques such as a novel combination of cover-free sets and lattice trapdoors. Under the Inhomogeneous Small Integer Solution (ISIS) assumption, we show that any (non-trivial) lattice-based PHF is a collision-resistant hash function, which gives a direct...

Differential-Linear (DL) cryptanalysis is a well known cryptanalytic technique that combines differential and linear cryptanalysis. Over the years, multiple techniques were proposed to increase its strength and applicability. Two relatively recent ones are: The partitioning technique by Leurent and the use of neutral bits adapted by Beierle et al. to DL cryptanalysis. In this paper we compare these techniques and discuss the possibility of using them together to achieve the best possible...

The differential-linear attack is one of the most effective attacks against ARX ciphers. However, two technical problems are preventing it from being more effective and having more applications: (1) there is no efficient method to search for good differential-linear approximations. Existing methods either have many constraints or are currently inefficient. (2) partitioning technique has great potential to reduce the time complexity of the key-recovery attack, but there is no general tool to...

Existing proofs of adaptive security (e.g., in settings in which decryption keys are adaptively revealed) often rely on guessing arguments. Such guessing arguments can be simple (and, e.g., just involve guessing which keys are revealed), or more complex "partitioning'' arguments. Since guessing directly and negatively impacts the loss of the corresponding security reduction, this leads to black-box lower bounds for a number of cryptographic scenarios that involve adaptive security. In...

Mobile contact discovery is a convenience feature of messengers such as WhatsApp or Telegram that helps users to identify which of their existing contacts are registered with the service. Unfortunately, the contact discovery implementation of many popular messengers massively violates the users' privacy as demonstrated by Hagen et al. (NDSS '21, ACM TOPS '23). Unbalanced private set intersection (PSI) protocols are a promising cryptographic solution to realize mobile private contact...

In SAC’14, Biham and Carmeli presented a novel attack on DES, involving a variation of Partitioning Cryptanalysis. This was further extended in ToSC’18 by Biham and Perle into the Conditional Linear Cryptanalysis in the context of Feistel ciphers. In this work, we formalize this cryptanalytic technique for block ciphers in general and derive several properties. This conditional approximation is then used to approximate the inv : GF(2^8) → GF(2^8) : x → x^254 function which forms the...

We show how to obfuscate pseudo-deterministic quantum circuits in the classical oracle model, assuming the quantum hardness of learning with errors. Given the classical description of a quantum circuit $Q$, our obfuscator outputs a quantum state $\ket{\widetilde{Q}}$ that can be used to evaluate $Q$ repeatedly on arbitrary inputs. Instantiating the classical oracle using any candidate post-quantum indistinguishability obfuscator gives us the first candidate construction of...

We introduce flexible password-based encryption (FPBE), an extension of traditional password-based encryption designed to meet the operational and security needs of contemporary applications like end-to-end secure cloud storage. Operationally, FPBE supports nonces, associated data and salt reuse. Security-wise, it strengthens the usual privacy requirement, and, most importantly, adds an authenticity requirement, crucial because end-to-end security must protect against a malicious server. We...

Re-randomizable Replayable CCA-secure public key encryption (Rand-RCCA PKE) schemes guarantee security against chosen-ciphertext attacks while ensuring the useful property of re-randomizable ciphertexts. We introduce the notion of multi-user and multi-ciphertext Rand-RCCA PKE and we give the first construction of such a PKE scheme with an almost tight security reduction to a standard assumption. Our construction is structure preserving and can be instantiated over Type-1 pairing groups....

In this paper we present several analyses on ChaCha, a software stream cipher. First, we consider a divide-and-conquer approach on the secret key bits by partitioning them. The partitions are based on multiple input-output differentials to obtain a significantly improved attack on 6-round ChaCha256 with a complexity of 2^{99.48}. It is 2^{40} times faster than the currently best known attack. Note that, this is the first time an attack could be mounted on reduced round ChaCha with a...

Randomized cache architectures have proven to significantly increase the complexity of contention-based cache side channel attacks and therefore pre\-sent an important building block for side channel secure microarchitectures. By randomizing the address-to-cache-index mapping, attackers can no longer trivially construct minimal eviction sets which are fundamental for contention-based cache attacks. At the same time, randomized caches maintain the flexibility of traditional...

Secure multiparty computation (MPC) has been proposed to allow multiple mutually distrustful data owners to jointly train machine learning (ML) models on their combined data. However, by design, MPC protocols faithfully compute the training functionality, which the adversarial ML community has shown to leak private information and can be tampered with in poisoning attacks. In this work, we argue that model ensembles, implemented in our framework called SafeNet, are a highly MPC-amenable way...

Digital ledger technologies supporting smart contracts usually does not ensure any privacy for user transactions or state. Most solutions to this problem either use private network setups, centralized parties, hardware enclaves, or cryptographic primitives, which are novel, complex, and computationally expensive. This paper looks into an alternative way of implementing smart contracts. Our construction of a protocol for smart contracts employs an overlay protocol design pattern for...

In a ring-signature-based anonymous cryptocurrency, signers of a transaction are hidden among a set of potential signers, called a ring, whose size is much smaller than the number of all users. The ring-membership relations specified by the sets of transactions thus induce bipartite transaction graphs, whose distribution is in turn induced by the ring sampler underlying the cryptocurrency. Since efficient graph analysis could be performed on transaction graphs to potentially deanonymise...

In this paper, we formulate a new framework of cryptanalysis called rotational-linear attack on ARX ciphers. We firstly build an efficient distinguisher for the cipher $ E$ consisted of the rotational attack and the linear attack together with some intermediate variables. Then a key recovery technique is introduced with which we can recover some bits of the last whitening key in the related-key scenario. To decrease data complexity of our attack, we also apply a new method, called bit...

In this work, we show how weak key forgeries against polynomial hash based Authenticated Encryption (AE) schemes, such as AES-GCM, can be leveraged to launch partitioning oracle attacks. Partitioning oracle attacks were recently introduced by Len et al. (Usenix'21) as a new class of decryption error oracle which, conceptually, takes a ciphertext as input and outputs whether or not the decryption key belongs to some known subset of keys. Partitioning oracle attacks allow an adversary to query...

For Key Encapsulation Mechanism (KEM) deployed in a multi-user setting, an adversary may corrupt some users to learn their secret keys, and obtain some encapsulated keys due to careless key managements of users. To resist such attacks, we formalize Enhanced security against Chosen Plaintext/Ciphertext Attack (ECPA/ECCA), which ask the pseudorandomness of unrevealed encapsulated keys under uncorrupted users. This enhanced security for KEM serves well for the security of a class of...

We construct more efficient cryptosystems with provable security against adaptive attacks, based on simple and natural hardness assumptions in the standard model. Concretely, we describe: - An adaptively-secure variant of the efficient, selectively-secure LWE-based identity-based encryption (IBE) scheme of Agrawal, Boneh, and Boyen (EUROCRYPT 2010). In comparison to the previously most efficient such scheme by Yamada (CRYPTO 2017) we achieve smaller lattice parameters and shorter public...

$P_4$-free graphs-- also known as cographs, complement-reducible graphs, or hereditary Dacey graphs--have been well studied in graph theory. Motivated by computer science and information theory applications, our work encodes (flat) joint probability distributions and Boolean functions as bipartite graphs and studies bipartite $P_4$-free graphs. For these applications, the graph properties of edge partitioning and covering a bipartite graph using the minimum number of these graphs are...

A ring signature scheme allows the signer to sign on behalf of an ad hoc set of users, called a ring. The verifier can be convinced that a ring member signs, but cannot point to the exact signer. Ring signatures have become increasingly important today with their deployment in anonymous cryptocurrencies. Conventionally, it is implicitly assumed that all ring members are equally likely to be the signer. This assumption is generally false in reality, leading to various practical and...

In this paper we introduce partitioning oracles, a new class of decryption error oracles which, conceptually, take a ciphertext as input and output whether the decryption key belongs to some known subset of keys. We introduce the first partitioning oracles which arise when encryption schemes are not committing with respect to their keys. We detail novel adaptive chosen ciphertext attacks that exploit partitioning oracles to efficiently recover passwords and de-anonymize anonymous...

Secret sharing enables a dealer to split a secret into a set of shares, in such a way that certain authorized subsets of share holders can reconstruct the secret, whereas all unauthorized subsets cannot. Non-malleable secret sharing (Goyal and Kumar, STOC 2018) additionally requires that, even if the shares have been tampered with, the reconstructed secret is either the original or a completely unrelated one. In this work, we construct non-malleable secret sharing tolerating $p$-time {\em...

Quasi-adaptive non-interactive zero-knowledge proof (QA-NIZK) systems and structure-preserving signature (SPS) schemes are two powerful tools for constructing practical pairing-based cryptographic schemes. Their efficiency directly affects the efficiency of the derived ad- vanced protocols. We construct more efficient QA-NIZK and SPS schemes with tight security reductions. Our QA-NIZK scheme is the first one that achieves both tight simulation soundness and constant proof size (in terms of...

We show how to construct structure-preserving signatures (SPS) and unbounded quasi-adaptive non-interactive zero-knowledge (USS QA-NIZK) proofs with a tight security reduction to simple assumptions, being the first with a security loss of $\mathcal{O}(1)$. Specifically, we present a SPS scheme which is more efficient than existing tightly secure SPS schemes and from an efficiency point of view is even comparable with other non-tight SPS schemes. In contrast to existing work, however, we only...

CRAFT is a lightweight block cipher, designed to provide efficient protection against differential fault attacks. It is a tweakable cipher that includes 32 rounds to produce a ciphertext from a 64-bit plaintext using a 128-bit key and 64-bit public tweak. In this paper, compared to the designers' analysis, we provide a more detailed analysis of CRAFT against differential and zero-correlation cryptanalysis, aiming to provide better distinguishers for the reduced rounds of the cipher. Our...

We study leakage-resilient continuously non-malleable secret sharing, as recently introduced by Faonio and Venturi (CRYPTO 2019). In this setting, an attacker can continuously tamper and leak from a target secret sharing of some message, with the goal of producing a modified set of shares that reconstructs to a message related to the originally shared value. Our contributions are two fold. -- In the plain model, assuming one-to-one one-way functions, we show how to obtain...

A verifiable random function (VRF) is a pseudorandom function, where outputs can be publicly verified. That is, given an output value together with a proof, one can check that the function was indeed correctly evaluated on the corresponding input. At the same time, the output of the function is computationally indistinguishable from random for all non-queried inputs. We present the first construction of a VRF which meets the following properties at once: It supports an exponential-sized...

We present a construction of an adaptively single-key secure constrained PRF (CPRF) for $\mathbf{NC}^1$ assuming the existence of indistinguishability obfuscation (IO) and the subgroup hiding assumption over a (pairing-free) composite order group. This is the first construction of such a CPRF in the standard model without relying on a complexity leveraging argument. To achieve this, we first introduce the notion of partitionable CPRF, which is a CPRF accommodated with partitioning...

Frit is a cryptographic 384-bit permutation recently proposed by Simon et al. and follows a novel design approach for built-in countermeasures against fault attacks. We analyze the cryptanalytic security of Frit in different use-cases and propose attacks on the full-round primitive. We show that the inverse Frit$^{-1}$ of Frit is significantly weaker than Frit from an algebraic perspective, despite the better diffusion of the inverse of the used mixing functions: Its round function has an...

In this paper we study cryptanalysis with non-linear polynomials cf. Eurocrypt’95 (adapted to Feistel ciphers at Crypto 2004). Previously researchers had serious difficulties in making such attacks work. Even though this is less general than a general space partitioning attack (FSE’97), a polynomial algebraic approach has enormous advantages. Properties are more intelligible and algebraic computational methods can be applied in order to discover or construct the suitable properties. In this...

In (STOC, 2008), Gentry, Peikert, and Vaikuntanathan proposed the first identity-based encryption (GPV-IBE) scheme based on a post-quantum assumption, namely, the learning with errors (LWE) assumption. Since their proof was only made in the random oracle model (ROM) instead of the quantum random oracle model (QROM), it remained unclear whether the scheme was truly post-quantum or not. In (CRYPTO, 2012), Zhandry developed new techniques to be used in the QROM and proved the security of...

Software side channel attacks have become a serious concern with the recent rash of attacks on speculative processor architectures. Most attacks that have been demonstrated exploit the cache tag state as their exfiltration channel. While many existing defense mechanisms that can be implemented solely in software have been proposed, these mechanisms appear to patch specific attacks, and can be circumvented. In this paper, we propose minimal modifications to hardware to defend against a broad...

We introduce a new cryptographic primitive called signatures with flexible public key (SFPK). We divide the key space into equivalence classes induced by a relation $\mathcal{R}$. A signer can efficiently change his or her key pair to a different representatives of the same class, but without a trapdoor it is hard to distinguish if two public keys are related. Our primitive is motivated by structure-preserving signatures on equivalence classes (SPSEQ), where the partitioning is done on the...

Structure Preserving Signatures (SPS) allow the signatures and the messages signed to be further encrypted while retaining the ability to be proven valid under zero-knowledge. In particular, SPS are tailored to have structure suitable for Groth-Sahai NIZK proofs. More precisely, the messages, signatures, and verification keys are required to be elements of groups that support efficient bilinear-pairings (bilinear groups), and the signature verification consists of just evaluating one or more...

In structure-preserving cryptography, every building block shares the same bilinear groups. These groups must be generated for a specific, a prior fixed security level, and thus it is vital that the security reduction of all involved building blocks is as tight as possible. In this work, we present the first generic construction of structure-preserving signature schemes whose reduction cost is independent of the number of signing queries. Its chosen-message security is almost tightly reduced...

A Degenerate Grouping Power Attack (DGPA) is a type of Partitioning Power Analysis (PPA) used to extract secret keys from the power sidechannel signal of an encryption algorithm running on a device along with some known and varying information such as the associated plaintext or ciphertext associated with each encryption. The DGPA is applied to SIMON and SPECK implementations on MSP430, PIC16F, and Spartan 6 platforms in this work. While keys are successfully recovered from unprotected...

In this paper, we focus on the constructions of adaptively secure identity-based encryption (IBE) from lattices and verifiable random function (VRF) with large input spaces. Existing constructions of these primitives suffer from low efficiency, whereas their counterparts with weaker guarantees (IBEs with selective security and VRFs with small input spaces) are reasonably efficient. We try to fill these gaps by developing new partitioning techniques that can be performed with compact...

We describe new cryptanalytic attacks on the candidate branching program obfuscator proposed by Garg, Gentry, Halevi, Raykova, Sahai and Waters (GGHRSW) using the GGH13 graded encoding, and its variant using the GGH15 graded encoding as specified by Gentry, Gorbunov and Halevi. All our attacks require very specific structure of the branching programs being obfuscated, which in particular must have some input-partitioning property. Common to all our attacks are techniques to extract...

In this paper, we present new adaptively secure identity-based encryption (IBE) schemes. One of the distinguishing property of the schemes is that it achieves shorter public parameters than previous schemes. Both of our schemes follow the general framework presented in the recent IBE scheme of Yamada (Eurocrypt 2016), employed with novel techniques tailored to meet the underlying algebraic structure to overcome the difficulties arising in our specific setting. Specifically, we obtain the...

Driven by the open problem raised by Hofheinz and Kiltz (Journal of Cryptology, 2012), we study the formalization of lattice-based programmable hash function (PHF), and give two types of constructions by using several techniques such as a novel combination of cover-free sets and lattice trapdoors. Under the Inhomogeneous Small Integer Solution (ISIS) assumption, we show that any (non-trivial) lattice-based PHF is collision-resistant, which gives a direct application of this new primitive. We...

We present a new strategy for partitioning proofs, and use it to obtain new tightly secure encryption schemes. Specifically, we provide the following two conceptual contributions: - A new strategy for tight security reductions that leads to compact public keys and ciphertexts. - A relaxed definition of non-interactive proof systems for non-linear (``OR-type'') languages. Our definition is strong enough to act as a central tool in our new strategy to obtain tight security, and is achievable...

We introduce a new technique for tight security proofs called work factor partitioning. Using this technique in a modified version of the framework of Döttling and Schröder (CRYPTO 2015), we obtain the first generic construction of tightly-secure pseudorandom functions (PRFs) from PRFs with small domain. By instantiating the small-domain PRFs with the Naor-Reingold function (FOCS 1997) or its generalization by Lewko and Waters (ACM CCS 2009), this yields the first fully-secure PRFs whose...

In this work we study the security of Chaskey, a recent lightweight MAC designed by Mouha et al., currently being considered for standardisation by ISO/IEC and ITU-T. Chaskey uses an ARX structure very similar to SipHash. We present the first cryptanalysis of Chaskey in the single user setting, with a differential-linear attack against 6 and 7 rounds, hinting that the full version of Chaskey with 8 rounds has a rather small security margin. In response to these attacks, a 12-round...

Given the increasing adoption of Bitcoin, the number of transactions and the block sizes within the system are only expected to increase. To sustain its correct operation in spite of its ever-increasing use, Bitcoin implements a number of necessary optimizations and scalability measures. These measures limit the amount of information broadcast in the system to the minimum necessary. In this paper, we show that current scalability measures adopted by Bitcoin come at odds with the security of...

The protection of cryptographic implementations against higher-order attacks has risen to an important topic in the side-channel community after the advent of enhanced measurement equipment that enables the capture of millions of power traces in reasonably short time. However, the preprocessing of multi-million traces for such an attack is still challenging, in particular when in the case of (multivariate) higher-order attacks all traces need to be parsed at least two times. Even worse,...

We describe a new technique for conducting ``partitioning arguments''. Partitioning arguments are a popular way to prove the security of a cryptographic scheme. For instance, to prove the security of a signature scheme, a partitioning argument could divide the set of messages into ``signable'' messages for which a signature can be simulated during the proof, and ``unsignable'' ones for which any signature would allow to solve a computational problem. During the security proof, we would then...

Biclique attack, is a new cryptanalytic technique which brings new tools from the area of hash functions to the area of block cipher cryptanalysis. Till now, this technique is the only one able to analyze the full-round AES cipher in a single key scenario. In this paper, we introduce non-isomorphic biclique attack, a modified version of the original biclique attack. In this attack we obtain isomorphic groups of bicliques, each group contains several non-isomorphic bicliques of different...

Finding the key of symmetric cipher takes computing common zero of polynomials, which define ideal and corresponding variety, usually considered over algebraically closed field. The solution is the point of the variety over prime field; it is defined by a sum of the polynomial ideal and the field ideal that defines prime field. Some authors use partitioning of this sum and reducing syzygies of polynomial ideal modulo field ideal. We generalize this method and consider polynomial ideal as a...

We present a novel approach for solving systems of polynomial equations via graph partitioning. The concept of a variable-sharing graph of a system of polynomial equations is defined. If such graph is disconnected, then the corresponding system of equations can be split into smaller ones that can be solved individually. This can provide a significant speed-up in computing the solution to the system, but is unlikely to occur either randomly or in applications. However, by deleting a certain...

We present a novel approach for solving systems of polynomial equations via graph partitioning. The concept of a variable-sharing graph of a system of polynomial equations is defined. If such graph is disconnected, then the system of equations is actually two separate systems that can be solved individually. This can provide a significant speed-up in computing the solution to the system, but is unlikely to occur either randomly or in applications. However, by deleting a small number of...

Very recently, a new software side-channel attack, called Branch Prediction Analysis (BPA) attack, has been discovered and also demonstrated to be practically feasible on popular commodity PC platforms. While the above recent attack still had the flavor of a classical timing attack against RSA, where one uses many execution-time measurements under the same key in order to statistically amplify some small but key-dependent timing differences, we dramatically improve upon the former result. We...

This paper presents a new software side-channel attack - enabled by the branch prediction capability common to all modern high-performance CPUs. The penalty payed (extra clock cycles) for a mispredicted branch can be used for cryptanalysis of cryptographic primitives that employ a data-dependent program flow. Analogous to the recently described cache-based side-channel attacks our attacks also allow an unprivileged process to attack other processes running in parallel on the same processor,...

We describe several software side-channel attacks based on inter-process leakage through the state of the CPU's memory cache. This leakage reveals memory access patterns, which can be used for cryptanalysis of cryptographic primitives that employ data-dependent table lookups. The attacks allow an unprivileged process to attack other processes running in parallel on the same processor, despite partitioning methods such as memory protection, sandboxing and virtualization. Some of our methods...

We develop a couple of new methods to reduce transmission overheads in broadcast encryption. The methods are based on the idea of assigning {\it one key per each partition using one-way key chains} after partitioning the users. One method adopts {\it skipping chains} on partitions containing up to $p$ revoked users and the other adopts {\it cascade chains} on partitions with layer structure. The scheme using the former reduces the transmission overhead down to $\frac r{p+1}$ asymptotically...