In recent development of secure multi-party computation (MPC), pseudorandom correlations of subfield vector oblivious linear evaluation (sVOLE) type become popular due to their amazing applicability in multi-dimensional MPC protocols such as privacy-preserving biometric identification and privacy-preserving machine learning protocols. In this paper, we introduce a novel way of VOLE distribution in three-party and four-party honest majority settings with the aid of a trusted server. This new...

Private information retrieval (PIR) is a key component of many privacy-preserving systems. Although numerous PIR protocols have been proposed, designing a PIR scheme with communication overhead independent of the database size $N$ and computational cost practical for real-world applications remains a challenge. In this paper, we propose the NewtonPIR protocol, a communication efficient single-server PIR scheme. NewtonPIR can directly generate query values for the entire index without...

In 2023, Koshelev introduced an efficient method of subgroup membership testing for a list of non-pairing-friendly curves, using at most two small Tate pairings. In fact, this technique can also be applied to certain pairing-friendly curves, e.g., from the BLS and BW13 families. In this paper, we revisit Koshelev's method and propose simplified formulas for computing the two Tate pairings. Compared to the original formulas, ours reduce both the number of Miller's iterations and the storage...

We improve the performance of lattice-based cryptosystems Dilithium on Cortex-M3 with expensive multiplications. Our contribution is two-fold: (i) We generalize Barrett multiplication and show that the resulting shape-independent modular multiplication performs comparably to long multiplication on some platforms without special hardware when precomputation is free. We call a modular multiplication “shape-independent” if its correctness and efficiency depend only on the magnitude of moduli...

We examine the problem of finding small solutions to systems of modular multivariate polynomials. While the case of univariate polynomials has been well understood since Coppersmith's original 1996 work, multivariate systems typically rely on carefully crafted shift polynomials and significant manual analysis of the resulting Coppersmith lattice. In this work, we develop several algorithms that make such hand-crafted strategies obsolete. We first use the theory of Gröbner bases to develop an...

Homomorphically multiplying a plaintext matrix with a ciphertext matrix (PC-MM) is a central task for the private evaluation of transformers, commonly used for large language models. We provide several RLWE-based algorithms for PC-MM that consist of multiplications of plaintext matrices (PC-MM) and comparatively cheap pre-processing and post-processing steps: for small and large dimensions compared to the RLWE ring degree, and with and without precomputation. For the algorithms with...

We propose time-memory trade-off algorithms for evaluating look-up table (LUT) in both the leveled homomorphic encryption (LHE) and fully homomorphic encryption (FHE) modes in TFHE. For an arbitrary $n$-bit Boolean function, we reduce evaluation time by a factor of $O(n)$ at the expense of an additional memory of "only" $O(2^n)$ as a trade-off: The total asymptotic memory is also $O(2^n)$, which is the same as that of prior works. Our empirical results demonstrate that a $7.8 \times$ speedup...

Oblivious Transfer (OT) is at the heart of secure computation and is a foundation for many applications in cryptography. Over two decades of work have led to extremely efficient protocols for evaluating OT instances in the preprocessing model, through a paradigm called OT extension. A few OT instances generated in an offline phase can be used to perform many OTs in an online phase efficiently, i.e., with very low communication and computational overheads. Specifically, traditional OT...

Neural network inference as a service enables a cloud server to provide inference services to clients. To ensure the privacy of both the cloud server's model and the client's data, secure neural network inference is essential. Binarized neural networks (BNNs), which use binary weights and activations, are often employed to accelerate inference. However, achieving secure BNN inference with secure multi-party computation (MPC) is challenging because MPC protocols cannot directly operate on...

In this paper, we present three types of variations of the ALTEQ cryptosystem, a recent submission to the NIST's additional call for signatures. We name these Dangerous Variations of ALTEQ (DVA), as there is always a certain danger in stepping out of usual constructions, although we attempt to maintain heuristic security. First, we present DVA-GG (Graph Generalization), that can be seen as a more abstract point-of-view on the operations done in ALTEQ and encourages more research on the...

Asymmetric Password-Authenticated Key Exchange (aPAKE) protocols, particularly Strong aPAKE (saPAKE) have enjoyed significant attention, both from academia and industry, with the well-known OPAQUE protocol currently undergoing standardization. In (s)aPAKE, a client and a server collaboratively establish a high-entropy key, relying on a previously exchanged password for authentication. A main feature is its resilience against offline and precomputation (for saPAKE) attacks. OPAQUE, as well as...

Multi-scalar multiplication (MSM) is one of the core components of many zero-knowledge proof systems, and a primary performance bottleneck for proof generation in these schemes. One major strategy to accelerate MSM is utilizing precomputation. Several algorithms (e.g., Pippenger and BGMW) and their variants have been proposed in this direction. In this paper, we revisit the recent precomputation-based MSM calculation method proposed by Luo, Fu and Gong at CHES 2023 and generalize their...

Private Information Retrieval (PIR) permits clients to query data entries from a public database hosted on untrusted servers while preserving client privacy. Traditional PIR models suffer from high computation and/or bandwidth overhead due to linear database processing for privacy. Recently, Online-Offline PIR (OO-PIR) has been proposed to improve PIR practicality by precomputing query-independent materials to accelerate online access. While state-of-the-art OO-PIR schemes (e.g., S&P’24,...

Side-Channel Attacks target the recovery of key material in cryptographic implementations by measuring physical quantities such as power consumption during the execution of a program. Simple Power Attacks consist in deducing secret information from a trace using a single or a few samples, as opposed to differential attacks which require many traces. Software cryptographic implementations now all contain a data-independent execution path, but often do not consider variations in power...

Let $\star: G \times X \rightarrow X$ be the action of a group $G$ of size $N=|G|$ on a set $X$. Let $y = g \star x \in X$ be a group action dlog instance, where our goal is to compute the unknown group element $g \in G$ from the known set elements $x,y \in X$. The Galbraith-Hess-Smart (GHS) collision finding algorithm solves the group action dlog in $N^{\frac 1 2}$ steps with polynomial memory. We show that group action dlogs are suitable for precomputation attacks. More...

A distributed OPRF allows a client to evaluate a pseudorandom function on an input chosen by the client using a distributed key shared among multiple servers. This primitive ensures that the servers learn nothing about the input nor the output, and the client learns nothing about the key. We present a post-quantum OPRF in a distributed server setting, which can be computed in a single round of communication between a client and the servers. The only server-to-server communication occurs...

A multidimensional scalar multiplication ($d$-mul) consists of computing $[a_1]P_1+\cdots+[a_d]P_d$, where $d$ is an integer ($d\geq 2)$, $\alpha_1, \cdots, \alpha_d$ are scalars of size $l\in \mathbb{N}^*$ bits, $P_1, P_2, \cdots, P_d$ are points on an elliptic curve $E$. This operation ($d$-mul) is widely used in cryptography, especially in elliptic curve cryptographic algorithms. Several methods in the literature allow to compute the $d$-mul efficiently (e.g., the bucket...

We provide two improvements to Regev's quantum factoring algorithm (arXiv:2308.06572), addressing its space efficiency and its noise-tolerance. Our first contribution is to improve the quantum space efficiency of Regev's algorithm while keeping the circuit size the same. Our main result constructs a quantum factoring circuit using $O(n \log n)$ qubits and $O(n^{3/2} \log n)$ gates. We achieve the best of Shor and Regev (upto a logarithmic factor in the space complexity): on the one...

This article aims to speed up (the precomputation stage of) multi-scalar multiplication (MSM) on ordinary elliptic curves of $j$-invariant $0$ with respect to specific ``independent'' (a.k.a. ``basis'') points. For this purpose, so-called Mordell--Weil lattices (up to rank $8$) with large kissing numbers (up to $240$) are employed. In a nutshell, the new approach consists in obtaining more efficiently a considerable number (up to $240$) of certain elementary linear combinations of the...

We present new protocols for threshold Schnorr signatures that work in an asynchronous communication setting, providing robustness and optimal resilience. These protocols provide unprecedented performance in terms of communication and computational complexity. In terms of communication complexity, for each signature, a single party must transmit a few dozen group elements and scalars across the network (independent of the size of the signing committee). In terms of computational...

A number of supersingular isogeny based cryptographic protocols require the endomorphism ring of the initial elliptic curve to be either unknown or random in order to be secure. To instantiate these protocols, Basso et al. recently proposed a secure multiparty protocol that generates supersingular elliptic curves defined over $\mathbb{F}_{p^2}$ of unknown endomorphism ring as long as at least one party acts honestly. However, there are many protocols that specifically require curves defined...

Account Abstraction is a powerful feature that will transform today Web3 onboarding UX. This notes describes an EVM (Ethereum Virtual Machine) implementation of the well known secp256r1 and ed25519 curves optimized for the specificities of the EVM environment. Our optimizations rely on EVM dedicated XYZZ elliptic coordinates system, hacked precomputations, and assembly tricks to cut from more than 1M to 200K/62K (with or withoutprecomputations)

Randomness testing is one of the essential and easiest tools for evaluating cryptographic primitives. The faster we can test, the greater volume of data that can be tested. Thus a more detailed analysis is possible. This paper presents a range of observations made for a well-known frequency test for overlapping vectors in binary sequence testing. We have obtained precise chi-square statistic computed in $O \left(dt 2^{dt} \right)$ instead of $O\left( 2^{2dt}\right)$ time, without precomputed tables.

The Number Field Sieve and its variants are the best algorithms to solve the discrete logarithm problem in finite fields (except for the weak small characteristic case). The Factory variant accelerates the computation when several prime fields are targeted. This article adapts the Factory variant to non-prime finite fields of medium and large characteristic. A precomputation, solely dependent on an approximate finite field size and an extension degree, allows to efficiently compute...

The Number Theoretic Transform (NTT) is used to efficiently execute polynomial multiplication. It has become an important part of lattice-based post-quantum methods and the subsequent generation of standard cryptographic systems. However, implementing post-quantum schemes is challenging since they rely on intricate structures. This paper demonstrates how to develop a high-speed NTT multiplier highly optimized for FPGAs with few logical resources. We describe a novel architecture for NTT...

We propose and analyze a simple strategy for constructing 1-key constrained pseudorandom functions (CPRFs) from homomorphic secret sharing. In the process, we obtain the following contributions. First, we identify desirable properties for the underlying HSS scheme for our strategy to work. Second, we show that (most) recent existing HSS schemes satisfy these properties, leading to instantiations of CPRFs for various constraints and from various assumptions. Notably, we obtain the first...

The invertibility of a random function (IRF, in short) is an important problem and has wide applications in cryptography. For ex- ample, searching a preimage of Hash functions, recovering a key of block ciphers under the known-plaintext-attack model, solving discrete loga- rithms over a prime field with large prime, and so on, can be viewed as its instances. In this work we describe the invertibility of multiple random functions (IMRF, in short), which is a generalization of the IRF. In...

We investigate the relationship between the classical RSA and factoring problems when preprocessing is considered. In such a model, adversaries can use an unbounded amount of precomputation to produce an “advice” string to then use during the online phase, when a problem instance becomes known. Previous work (e.g., [Bernstein, Lange ASI- ACRYPT ’13]) has shown that preprocessing attacks significantly im- prove the runtime of the best-known factoring algorithms. Due to these improvements, we...

We propose the signature scheme Hawk, a concrete instantiation of proposals to use the Lattice Isomorphism Problem (LIP) as a foundation for cryptography that focuses on simplicity. This simplicity stems from LIP, which allows the use of lattices such as $\mathbb{Z}^n$ , leading to signature algorithms with no floats, no rejection sampling, and compact precomputed distributions. Such design features are desirable for constrained devices, and when computing signatures inside FHE or MPC. The...

Interactive oracle proofs (IOPs) are a generalization of probabilistically checkable proofs that can be used to construct succinct arguments. Improvements in the efficiency of IOPs lead to improvements in the efficiency of succinct arguments. Key efficiency goals include achieving provers that run in linear time and verifiers that run in sublinear time, where the time complexity is with respect to the arithmetic complexity of proved computations over a finite field $\mathbb{F}$. We...

The offline-online model is a leading paradigm for practical secure multi-party computation (MPC) protocol design that has successfully reduced the overhead for several prevalent privacy-preserving computation functionalities common to diverse application domains. However, the prohibitive overheads associated with secure comparison -- one of these vital functionalities -- often bottlenecks current and envisioned MPC solutions. Indeed, an efficient secure comparison solution has the potential...

We revisit and improve performance of arithmetic in the binary GLS254 curve by introducing the 2DT-GLS scalar multiplication algorithm. The algorithm includes theoretical and practice-oriented contributions of potential independent interest: (i) for the first time, a proof that the GLS scalar multiplication algorithm does not incur exceptions, such that faster incomplete formulas can be used; (ii) faster dedicated atomic formulas that alleviate the cost of precomputation; (iii) a table...

Protocols solving the Distributed Discrete Logarithm (DDLog) problem are a core component of many recent constructions of group-based homomorphic secret sharing schemes. On a high-level, these protocols enable two parties to transform multiplicative shares of a secret into additive share locally without any communication. Due to their important applications, various generic optimized DDLog protocols were proposed in the literature, culminating in the asymptotically optimal generic protocol...

Currently, public-key compression of supersingular isogeny Diffie-Hellman (SIDH) and its variant, supersingular isogeny key encapsulation (SIKE) involve pairing computation and discrete logarithm computation. Both of them require large storage for precomputation to accelerate the performance. In this paper, we propose a novel method to compute only three discrete logarithms instead of four, in exchange for computing a lookup table efficiently. We also suggest another alternative method to...

Two common variations of ECDSA signatures are additive key derivation and presignatures. Additive key derivation is a simple mechanism for deriving many subkeys from a single master key, and is already widely used in cryptocurrency applications with the Hierarchical Deterministic Wallet mechanism standardized in Bitcoin Improvement Proposal 32 (BIP32). Because of its linear nature, additive key derivation is also amenable to efficient implementation in the threshold setting. With...

At CRYPTO'19, Gohr built a bridge between deep learning and cryptanalysis. Based on deep neural networks, he trained neural distinguishers of Speck32/64 using a plaintext difference and single ciphertext pair. Compared with purely differential distinguishers, neural distinguishers successfully use features of the ciphertext pairs. Besides, with the help of neural distinguishers, he attacked 11-round Speck32/64 using Bayesian optimization. At EUROCRYPTO'21, Benamira proposed a detailed...

While the practicality of secure multi-party computation (MPC) has been extensively analyzed and improved over the past decade, we are hitting the limits of efficiency with the traditional approaches of representing the computed functionalities as generic arithmetic or Boolean circuits. This work follows the design principle of identifying and constructing fast and provably-secure MPC protocols to evaluate useful high-level algebraic abstractions; thus, improving the efficiency of all...

Many privacy preserving blockchain and e-voting systems are based on the modified ElGamal scheme that supports homomorphic addition of encrypted values. For practicality reasons though, decryption requires the use of precomputed discrete-log (dlog) lookup tables along with algorithms like Shanks's baby-step giant-step and Pollard's kangaroo. We extend the Shanks approach as it is the most commonly used method in practice due to its determinism and simplicity, by proposing a truncated lookup...

We introduce a new technique for indexing joins in encrypted SQL databases called partially precomputed joins which achieves lower leakage and bandwidth than those used in prior constructions. These techniques are incorporated into state-of-the-art structured encryption schemes for SQL data, yielding a hybrid indexing scheme with both partially and fully precomputed join indexes. We then introduce the idea of leakage-aware query planning by giving a heuristic that helps the client decide, at...

Multi-Server Private Information Retrieval (PIR) is a cryptographic protocol that allows a client to securely query a database entry from $n \geq 2$ servers of which less than $t$ can collude, s.t. the servers learn no information about the query. Highly efficient PIR could be used for large-scale applications like Compromised Credential Checking (C3) (USENIX Security'19), which allows users to check whether their credentials have been leaked in a data breach. However, state-of-the art PIR...

Due to its amazing speed and multiplicative properties the Legendre PRF recently finds widespread applications e.g. in Ethereum 2.0, multiparty computation and in the quantum-secure signature proposal LegRoast. However, its security is not yet extensively studied. The Legendre PRF computes for a key $k$ on input $x$ the Legendre symbol $L_k(x) = \left( \frac {x+k} {p} \right)$ in some finite field $\F_p$. As standard notion, PRF security is analysed by giving an attacker oracle access to...

The supersingular isogeny-based key encapsulation (SIKE) suite stands as an attractive post-quantum cryptosystem with its relatively small public keys. Public key sizes in SIKE can further be compressed by computing pairings and solving discrete logarithms in certain subgroups of finite fields. This comes at a cost of precomputing and storing large discrete logarithm tables. In this paper, we propose several techniques to optimize memory requirements in computing discrete logarithms in SIKE,...

Tradeoff attacks on symmetric ciphers can be considered as the generalization of the exhaustive search. Their main objective is reducing the time complexity by exploiting the memory after preparing very large tables at a cost of exhaustively searching all the space during the precomputation phase. It is possible to utilize data (plaintext/ciphertext pairs) in some cases like the internal state recovery attacks for stream ciphers to speed up further both online and offline phases. However,...

SIDH/SIKE-style protocols benefit from key compression to minimize their bandwidth requirements, but proposed key compression mechanisms rely on computing bilinear pairings. Pairing computation is a notoriously expensive operation, and, unsurprisingly, it is typically one of the main efficiency bottlenecks in SIDH key compression, incurring processing time penalties that are only mitigated at the cost of trade-offs with precomputed tables. We address this issue by describing how to compress...

Succinct non-interactive arguments (SNARGs) enable proofs of NP statements with very low communication. Recently, there has been significant work in both theory and practice on constructing SNARGs with very short proofs. Currently, the state-of-the-art in succinctness is due to Groth (Eurocrypt 2016) who constructed a SNARG from bilinear maps where the proof consists of just 3 group elements. In this work, we first construct a concretely-efficient designated-verifier (preprocessing) SNARG...

Authenticated dictionaries (ADs) are a key building block of many cryptographic systems, such as transparency logs, distributed file systems and cryptocurrencies. In this paper, we propose a new notion of cross-incremental proof (dis)aggregation for authenticated dictionaries, which enables aggregating multiple proofs with respect to different dictionaries into a single, succinct proof. Importantly, this aggregation can be done incrementally and can be later reversed via...

In most post-quantum signature protocols, the verification procedure leaks information about which signature is being verified, and/or which public key is being used to verify the signature, to timing and other side-channel attacks. In some applications, this information leak is a breach of user privacy or system security. One class of signature protocols, based on the parallel composition of many runs of one or more interactive cut-and-choose protocols, can be modified to enable...

We present MOTION, an efficient and generic open-source framework for mixed-protocol secure multi-party computation (MPC). MOTION is built in a user-friendly, modular, and extensible way, intended to be used as tool in MPC research and to increase adoption of MPC protocols in practice. Our framework incorporates several important engineering decisions such as full communication serialization, which enables MPC over arbitrary messaging interfaces and removes the need of owning network...

In this paper, we revisit the difference enumeration technique for LowMC and develop new algebraic techniques to achieve efficient key-recovery attacks. In the original difference enumeration attack framework, an inevitable step is to precompute and store a set of intermediate state differences for efficient checking via the binary search. Our first observation is that Bar-On et al.'s general algebraic technique developed for SPNs with partial nonlinear layers can be utilized to fulfill the...

In this work, we exhibit a hierarchy of polynomial time algorithms solving approximate variants of the Closest Vector Problem (CVP). Our first contribution is a heuristic algorithm achieving the same distance tradeoff as HSVP algorithms, namely $\approx \beta^{\frac{n}{2\beta}}\textrm{covol}(\Lambda)^{\frac{1}{n}}$ for a random lattice $\Lambda$ of rank $n$. Compared to the so-called Kannan's embedding technique, our algorithm allows using precomputations and can be used for...

Since the introduction of the ring-learning with errors problem, the number theoretic transform (NTT) based polynomial multiplication algorithm has been studied extensively. Due to its faster quasilinear time complexity, it has been the preferred choice of cryptographers to realize ring-learning with errors cryptographic schemes. Compared to NTT, Toom-Cook or Karatsuba based polynomial multiplication algorithms, though being known for a long time, still have a fledgling presence in the...

Isogeny-based cryptography is a kind of post-quantum cryptography whose security relies on the hardness of an isogeny problem over elliptic curves. In this paper, we study CSIDH, which is one of isogeny-based cryptography presented by Castryck et al. in Asiacrypt 2018. In CSIDH, the secret key is taken from an $L_\infty$-norm ball of integer vectors and the public key is generated by calculating the action of an ideal class corresponding to a secret key. For faster key exchange, it is...

Gaudry and Lubicz introduced the idea of Kummer line in 2009, and Karati and Sarkar proposed three Kummer lines over prime fields in 2017. In this work, we explore the problem of secure and efficient scalar multiplications on binary field using Kummer line and investigate the possibilities of speedups using Kummer line compared to Koblitz curves, binary Edwards curve and Weierstrass curves. We propose a binary Kummer line $\mathsf{BKL}251$ over binary field $\mathbb{F}_{2^{251}}$ where the...

Cryptosystems based on Learning with Errors or related problems are central topics in recent cryptographic research. One main witness to this is the NIST Post-Quantum Cryptography Standardization effort. Many submitted proposals rely on problems related to Learning with Errors. Such schemes often include the possibility of decryption errors with some very small probability. Some of them have a somewhat larger error probability in each coordinate, but use an error correcting code to get rid...

We initiate the study of threshold schemes based on the Hard Homogeneous Spaces (HHS) framework of Couveignes. Quantum-resistant HHS based on supersingular isogeny graphs have recently become usable thanks to the record class group precomputation performed for the signature scheme CSI-FiSh. Using the HHS equivalent of the technique of Shamir's secret sharing in the exponents, we adapt isogeny based schemes to the threshold setting. In particular we present threshold versions of the CSIDH...

The task of function inversion is central to cryptanalysis: breaking block ciphers, forging signatures, and cracking password hashes are all special cases of the function-inversion problem. In 1980, Hellman showed that it is possible to invert a random function $f\colon [N] \to [N]$ in time $T = \widetilde{O}(N^{2/3})$ given only $S = \widetilde{O}(N^{2/3})$ bits of precomputed advice about $f$. Hellman’s algorithm is the basis for the popular “Rainbow Tables” technique (Oechslin, 2003),...

Lightweight cryptography in computationally constrained devices is actively studied. In contrast to advances of lightweight blockcipher in the last decade, lightweight mode of operation is seemingly not so mature, yet it has large impact in performance. Therefore, there is a great demand for lightweight mode of operation, especially that for authenticated encryption with associated data (AEAD). Among many known properties of conventional modes of operation, the following four properties are...

Mobile messengers like WhatsApp perform contact discovery by uploading the user's entire address book to the service provider. This allows the service provider to determine which of the user's contacts are registered to the messaging service. However, such a procedure poses significant privacy risks and legal challenges. As we find, even messengers with privacy in mind currently do not deploy proper mechanisms to perform contact discovery privately. The most promising approaches addressing...

A framework is introduced for efficiently computing with encrypted data. We assume a semi-honest security model with two computing parties. Two different coding techniques are used with additively homomorphic encryption, such that many values can be put into one large encryption, and additions and multiplications can be performed on all values simultaneously. For more complicated operations such as comparisons and equality tests, bit-wise secret sharing is proposed as an additional technique...

We describe an algorithm to solve the approximate Shortest Vector Problem for lattices corresponding to ideals of the ring of integers of an arbitrary number field $K$. This algorithm has a pre-processing phase, whose run-time is exponential in $\log |\Delta|$ with $\Delta$ the discriminant of $K$. Importantly, this pre-processing phase depends only on $K$. The pre-processing phase outputs an advice, whose bit-size is no more than the run-time of the query phase. Given this advice, the query...

Hard learning problems are central topics in recent cryptographic research. Many cryptographic primitives relate their security to difficult problems in lattices, such as the shortest vector problem. Such schemes include the possibility of decryption errors with some very small probability. In this paper we propose and discuss a generic attack for secret key recovery based on generating decryption errors. In a standard PKC setting, the model first consists of a precomputation phase...

Oblivious linear evaluation (OLE) is a two party protocol that allows a receiver to compute an evaluation of a sender's private, degree $1$ polynomial, without letting the sender learn the evaluation point. OLE is a special case of oblivious polynomial evaluation (OPE) which was first introduced by Naor and Pinkas in 1999. In this article we utilise OLE for the purpose of computing multiplication in multi-party computation (MPC). MPC allows a set of $n$ mutually distrustful parties to...

We investigate the problem of securely outsourcing modular exponentiations to a single, malicious computational resource. We revisit recently proposed schemes using single server and analyse them against two fundamental security properties, namely privacy of inputs and verifiability of outputs. Interestingly, we observe that the chosen schemes do not appear to meet both the security properties. In fact we present a simple polynomial-time attack on each algorithm, allowing the malicious...

Cube-attack-like cryptanalysis on round-reduced Keccak was proposed by Dinur et al. at EUROCRYPT 2015. It recovers the key through two phases: the preprocessing phase for precomputing a look-up table and online phase for querying the output and getting the cube sum with which the right key can be retrieved by looking up the precomputed table. It was shown that such attacks are efficient specifically for Keccak-based constructions with small nonce or message block size. In this paper, we...

Standardization bodies such as NIST and ETSI are currently seeking quantum resistant alternatives to vulnerable RSA and elliptic curve-based public-key algorithms. In this context, we present Round5, a lattice-based cryptosystem providing a key encapsulation mechanism and a public-key encryption scheme. Round5 is based on the General Learning with Rounding problem, unifying non-ring and ring lattice rounding problems into one. Usage of rounding combined with a tight analysis leads to...

In the last decade, location information became easily obtainable using off-the-shelf mobile devices. This gave a momentum to developing Location Based Services (LBSs) such as location proximity detection, which can be used to find friends or taxis nearby. LBSs can, however, be easily misused to track users, which draws attention to the need of protecting privacy of these users. In this work, we address this issue by designing, implementing, and evaluating multiple algorithms for...

Sensitive data is often outsourced to cloud servers, with the server performing computation on the data. Computational correctness must be efficiently verifiable by a third party while the input data remains confidential. This paper introduces CHQS, a homomorphic signature scheme from bilinear groups fulfilling these requirements. CHQS is the first such scheme to be both context hiding and publicly verifiable for arithmetic circuits of degree two. It also achieves amortized efficiency: after...

PBKDF2 [27] is a well-known password-based key derivation function. In order to slow attackers down, PBKDF2 introduces CPU-intensive operations based on an iterated pseudorandom function (in our case HMAC-SHA-1). If we are able to speed up a SHA-1 or an HMAC implementation, we are able to speed up PBKDF2-HMAC-SHA-1. This means that a performance improvement might be exploited by regular users and attackers. Interestingly, FIPS 198-1 [31] suggests that it is possible to precompute first...

The provably secure Schnorr signature scheme is popular and efficient. However, each signature requires a fresh modular exponentiation, which is typically a costly operation. As the increased uptake in connected devices revives the interest in resource-constrained signature algorithms, we introduce a variant of Schnorr signatures that mutualises exponentiation efforts. Combined with precomputation techniques (which would not yield as interesting results for the original Schnorr algorithm),...

Cryptographic primitives that are secure against quantum computing are receiving growing attention with recent, steady advances in quantum computing and standardization initiatives in post-quantum cryptography by NIST and ETSI. Lattice-based cryptography is one of the families in post-quantum cryptography, demonstrating desirable features such as well-understood security, efficient performance, and versatility. In this work, we present Round2 that consists of a key-encapsulation mechanism...

We present Chameleon, a novel hybrid (mixed-protocol) framework for secure function evaluation (SFE) which enables two parties to jointly compute a function without disclosing their private inputs. Chameleon combines the best aspects of generic SFE protocols with the ones that are based upon additive secret sharing. In particular, the framework performs linear operations in the ring $\mathbb{Z}_{2^l}$ using additively secret shared values and nonlinear operations using Yao's Garbled Circuits...

This paper studies discrete-log algorithms that use preprocessing. In our model, an adversary may use a very large amount of precomputation to produce an "advice" string about a specific group (e.g., NIST P-256). In a subsequent online phase, the adversary's task is to use the preprocessed advice to quickly compute discrete logarithms in the group. Motivated by surprising recent preprocessing attacks on the discrete-log problem, we study the power and limits of such algorithms. In...

The cube attack is an important technique for the cryptanalysis of symmetric key primitives, especially for stream ciphers. Aiming at recovering some secret key bits, the adversary reconstructs a superpoly with the secret key bits involved, by summing over a set of the plaintexts/IV which is called a cube. Traditional cube attack only exploits linear/quadratic superpolies. Moreover, for a long time after its proposal, the size of the cubes has been largely confined to an experimental range,...

Aerial drones are becoming an integral part of application domains including but not limited to, military operations, package delivery, construction, monitoring and search/rescue operations. It is critical to ensure the cyber security of networked aerial drone systems in these applications. Standard cryptographic services can be deployed to provide basic security services; however, they have been shown to be inefficient in terms of energy and time consumption, especially for small aerial...

This paper suggests to use rounded Gaussians in place of dis- crete Gaussians in rejection-sampling-based lattice signature schemes like BLISS. We show that this distribution can efficiently be sampled from while additionally making it easy to sample in constant time, systematically avoiding recent timing-based side-channel attacks on lattice-based signatures. We show the effectiveness of the new sampler by applying it to BLISS, prove analogues of the security proofs for BLISS, and present...

The security models for Authenticated Key Exchange do not consider leakages on pre–computed ephemeral data before their use in sessions. We investigate the consequences of such leakages and point out damaging consequences. As an illustration, we show the HMQV–C protocol vulnerable to a Bilateral Unknown Key Share (BUKS) and an Unilateral Unknown Key Share (UUKS) Attack, when precomputed ephemeral public keys are leaked. We point out some shades in the seCK model in multi–certification...

Private set intersection (PSI) is a cryptographic technique that is applicable to many privacy-sensitive scenarios. For decades, researchers have been focusing on improving its efficiency in both communication and computation. However, most of the existing solutions are inefficient for an unequal number of inputs, which is common in conventional client-server settings. In this paper, we analyze and optimize the efficiency of existing PSI protocols to support precomputation so that they can...

This paper presents a series of Montgomery scalar multiplication algorithms on general short Weierstrass curves over odd characteristic fields, which need only 12 field multiplications plus 12 ~ 20 field additions per scalar bit using 8 ~ 10 field registers, thus significantly outperform the binary NAF method on average. Over binary fields, the Montgomery scalar multiplication algorithm which was presented at the first CHES workshop by L´opez and Dahab has been a favorite of ECC...

A cryptanalytic technique known as time-memory tradeoff (TMTO) was proposed by Hellman for finding the secret key of a block cipher. This technique allows sharing the effort of key search between the two extremes of exhaustively enumerating all keys versus listing all possible ciphertext mappings produced by a given plaintext (i.e. table lookups). The TMTO technique has also been used as an effective cryptanalytic approach for password hashing schemes (PHS). Increasing threat of password...

Several recent cryptographic constructions - including a public key encryption scheme, a fully homomorphic encryption scheme, and a candidate multilinear map construction - rely on the hardness of the short generator principal ideal problem (SG-PIP): given a $\mathbb{Z}$-basis of some principal (fractional) ideal in an algebraic number field that is guaranteed to have an exceptionally short generator with respect to the logarithmic embedding, find a shortest generator of the principal ideal....

Proof-of-work (PoW) schemes are cryptographic primitives with numerous applications, and in particular, they play a crucial role in maintaining consensus in cryptocurrency networks. Ideally, a cryptocurrency PoW scheme should have several desired properties, including efficient verification on one hand, and high memory consumption of the prover's algorithm on the other hand, making the scheme less attractive for implementation on dedicated hardware. At the USENIX Security Symposium 2016,...

The Border Gateway Protocol (BGP) computes routes between the organizational networks that make up today's Internet. Unfortunately, BGP suffers from deficiencies, including slow convergence, security problems, a lack of innovation, and the leakage of sensitive information about domains' routing preferences. To overcome some of these problems, we revisit the idea of centralizing and using secure multi-party computation (MPC) for interdomain routing which was proposed by Gupta et al. (ACM...

We propose new algorithms for constructing multidimensional differential addition chains and for performing multidimensional scalar point multiplication based on these chains. Our algorithms work in any dimension and offer some key efficiency and security features. In particular, our scalar point multiplication algorithm is uniform, it has high potential for constant time implementation, and it can be parallelized. It also allows trading speed for precomputation cost and storage...

Systems for verifiable outsourcing incur costs for a prover, a verifier, and precomputation; outsourcing makes sense when the combination of these costs is cheaper than not outsourcing. Yet, when prior works impose quantitative thresholds to analyze whether outsourcing is justified, they generally ignore prover costs. Verifiable ASICs (VA)---in which the prover is a custom chip---is the other way around: its cost calculations ignore precomputation. This paper describes a new VA system,...

NSEC5 is a proposed modification to DNSSEC that guarantees two security properties: (1) privacy against offline zone enumeration, and (2) integrity of zone contents, even if an adversary compromises the authoritative nameserver responsible for responding to DNS queries for the zone. In this work, we redesign NSEC5 in order to make it practical and performant. Our NSEC5 redesign features a new verifiable random function (VRF) based on elliptic curve cryptography (ECC), along with a...

In this work, we significantly improve the efficiency of non-malleable codes in the split state model, by constructing a code with codeword length $|s|+O(k)$, where $|s|$ is the length of the message, and $k$ is the security parameter. This is a substantial improvement over previous constructions, both asymptotically and concretely. Our construction relies on a new primitive which we define and study, called $\ell$-more extractable hash functions. This notion, which may be...

The hardness of discrete logarithm problem over finite fields is the foundation of many cryptographic protocols. When the characteristic of the finite field is medium or large, the state-of-art algorithms for solving the corresponding problem are the number field sieve and its variants. There are mainly three steps in such algorithms: polynomial selection, factor base logarithms computation, and individual logarithm computation. Note that the former two steps can be precomputed for fixed...

Nearly all verifiable e-voting schemes require trustworthy authorities to perform the tallying operations. An exception is the DRE-i system which removes this requirement by pre-computing all encrypted ballots before the election using random factors that will later cancel out and allow the public to verify the tally after the election. While the removal of tallying authorities significantly simplifies election management, the pre-computation of ballots necessitates secure ballot storage, as...

In this paper, we describe how to compute smallest monic polynomials that define a given number field $\mathbb K$. We make use of the one-to-one correspondence between monic defining polynomials of $\mathbb K$ and algebraic integers that generate $\mathbb K$. Thus, a smallest polynomial corresponds to a vector in the lattice of integers of $\mathbb K$ and this vector is short in some sense. The main idea is to consider weighted coordinates for the vectors of the lattice of integers of...

Password-based key derivation functions are of particular interest in cryptography because they (a) input a password/passphrase (which usually is short and lacks enough entropy) and derive a cryptographic key; (b) slow down brute force and dictionary attacks as much as possible. In PKCS#5 [17], RSA Laboratories described a password based key derivation function called PBKDF2 that has been widely adopted in many security related applications [6, 7, 11]. In order to slow down brute force...

Proofs of partial knowledge allow a prover to prove knowledge of witnesses for k out of n instances of NP languages. Cramer, Schoenmakers and Damg\aa rd [CDS94] provided an efficient construction of a 3-round public-coin witness-indistinguishable (k, n)-proof of partial knowledge for any NP language, by cleverly combining n executions of Sigma-protocols for that language. This transform assumes that all n instances are fully specified before the proof starts, and thus directly rules out the...

We introduce cMix, a new approach to anonymous communications. Through a precomputation, the core cMix protocol eliminates all expensive realtime public-key operations --- at the senders, recipients and mixnodes --- thereby decreasing real-time cryptographic latency and lowering computational costs for clients. The core real-time phase performs only a few fast modular multiplications. In these times of surveillance and extensive profiling there is a great need for an anonymous communication...

SQUARE is an iterated block cipher proposed by Daemen et.al. in FSE1997. Inspired by Bogdanov et.al.’s recent works [12], we first present an improved biclique attack, i.e. stat-based independent biclique attack on full rounds SQUARE in this paper. We construct a one round stat-based independent biclique for the initial round, and utilize matching with precomputation techniques to recover the whole key from the remaining rounds. The computing complexity of our attack is about $2^(126.17)$...

In security proofs of lattice based cryptography, bounding the closeness of two probability distributions is an important procedure. To measure the closeness, the Rényi divergence has been used instead of the classical statistical distance. Recent results have shown that the Rényi divergence offers security reductions with better parameters, e.g. smaller deviations for discrete Gaussian distributions. However, since previous analyses used a fixed order Rényi divergence, i.e., order two, they...

We propose the Synthetic Counter-in-Tweak (SCT) mode, which turns a tweakable block cipher into a nonce-based authenticated encryption scheme (with associated data). The SCT mode combines in a SIV-like manner a Wegman-Carter MAC inspired from PMAC for the authentication part and a new counter-like mode for the encryption part, with the unusual property that the counter is applied on the tweak input of the underlying tweakable block cipher rather than on the plaintext input. Unlike many...

The encryption mode of the Tweakable Block Cipher (TBC) of the SCREAM Authenticated Cipher is implemented in the MSP430 microcontroller. Assembly language versions of the TBC are prepared using both precomputed tweak keys and tweak keys computed “on-the-fly.” Both versions are compared against published results for the assembly language version of SCREAM on the ATMEL AVR microcontroller, and against the C reference implementation in terms of performance and size. The assembly language...

Modular exponentiation is core to today's main stream public key cryptographic systems. In this article, we generalize the classical fractional $w$NAF method for modular exponentiation -- the classical method uses a digit set of the form $\{1,3,\dots,m\}$ which is extended here to any set of odd integers of the form $\{1,d_2,\dots, d_n\}$. We give a formula for the average density of non-zero terms in this new representation and discuss its asymptotic behavior when those digits are randomly...

In this paper, we present a single round two-party {\em attribute-based authenticated key exchange} (ABAKE) protocol in the framework of ciphertext-policy attribute-based systems. Since pairing is a costly operation and the composite order groups must be very large to ensure security, we focus on pairing free protocols in prime order groups. The proposed protocol is pairing free, working in prime order group and having tight reduction to Strong Diffie Hellman (SDH) problem under the...

Higher-order side-channel attacks are able to break the security of cryptographic implementations even if they are protected with masking countermeasures. In this paper, we derive the best possible distinguishers (High-Order Optimal Distinguishers or HOOD) against masking schemes under the assumption that the attacker can profile. Our exact derivation admits simple approximate expressions for high and low noise and shows to which extent the optimal distinguishers reduce to known attacks in...

Precomputation techniques are useful to improve real-time performance of complex algorithms at the expense of extra memory, and extra preparatory computations. This practice is neglected especially in the embedded context where energy and memory space is limited. Instead, the embedded space favors the immediate reduction of energy and memory footprint. However, the embedded platforms of the future may be different from the traditional ones. Energy-harvesting sensor nodes may extract...