Quasi-cyclic moderate-density parity check (QC-MDPC) code-based encryption schemes under iterative decoders offer highly-competitive performance in the quantum-resistant space of cryptography, but the decoding-failure rate (DFR) of these algorithms are not well-understood. The DFR decreases extremely rapidly as the ratio of code-length to error-bits increases, then decreases much more slowly in regimes known as the waterfall and error-floor, respectively. This work establishes three,...

For a finite field $\mathbb{F}$ of size $n$, the (patched) inverse permutation $\operatorname{INV}: \mathbb{F} \to \mathbb{F}$ computes the inverse of $x$ over $\mathbb{F}$ when $x\neq 0$ and outputs $0$ when $x=0$, and the $\operatorname{ARK}_K$ (for AddRoundKey) permutation adds a fixed constant $K$ to its input, i.e., $$\operatorname{INV}(x) = x^{n-2} \hspace{.1in} \mbox{and} \hspace{.1in} \operatorname{ARK}_K(x) = x + K \;.$$ We study the process of alternately applying the...

The zeta function $\zeta(z)=\sum_{n=1}^{\infty} \frac{1}{n^z}$ is convergent for $\text{Re}(z)>1$, and the eta function $\eta(z)=\sum_{n=1}^{\infty}\frac{(-1)^{n-1}}{n^z}$ is convergent for $\text{Re}(z)>0$. The eta function and the analytic continuation of zeta function have the same zeros in the critical strip $0<\text{Re}(z)<1$, owing to that $\eta(z)=\left(1-2^{1-z}\right)\zeta(z)$. In this paper, we present the new experimental evidences which show that for any $a\in (0, 1),...

The zeta function $\zeta(z)=\sum_{n=1}^{\infty} \frac{1}{n^z}$ is convergent only for $\text{Re}(z)>1$. To test its zeros, one needs to use the Riemann-Siegel function $Z(t)$. If $Z(t_1)$ and $Z(t_2)$ have opposite signs, $Z(t)$ vanishes between $t_1$ and $t_2$, and $\zeta(z)$ has a zero on the critical line between $\frac{1}{2}+it_1$ and $\frac{1}{2}+it_2$. This method is non-polynomial time, because it has to compute the sum $\sum_{n\leq...

Amid the landscape of confidential computing, where security and privacy reign supreme, PRIVATON emerges as a pioneering and practical solution to safeguard sensitive data and computations. A verifiable proof of computation model, with one of its variant built upon the dual sandbox strategy, PRIVATON combines Trusted Execution Environment (TEE) technologies with WebAssembly (WASM) runtime environments to establish an ecosystem for privacy-preserving computations. This approach involves fine...

The best lattice reduction algorithm known in theory for approximating the Shortest Vector Problem (SVP) over lattices is the slide reduction algorithm (STOC '08 & CRYPTO '20). In this paper, we first improve the running time analysis of computing slide-reduced bases based on potential functions. This analysis applies to a generic slide reduction algorithm that includes (natural variants of) slide reduction and block-Rankin reduction (ANTS '14). We then present a rigorous dynamic analysis...

Deep learning is very efficient at breaking masked implementations even when the attacker does not assume knowledge of the masks. However, recent works pointed out a significant challenge: overcoming the initial learning plateau. This paper discusses the advantages of multi-task learning to break through the initial plateau consistently. We investigate different ways of applying multi-task learning against masked AES implementations (via the ASCAD-r, ASCAD-v2, and CHESCTF-2023 datasets)...

The efficiency of the profiling side-channel analysis can be significantly improved with machine learning techniques. Although powerful, a fundamental machine learning limitation of being data-hungry received little attention in the side-channel community. In practice, the maximum number of leakage traces that evaluators/attackers can obtain is constrained by the scheme requirements or the limited accessibility of the target. Even worse, various countermeasures in modern devices increase the...

As the prevalence of quantum computing is growing in leaps and bounds over the past few years, there is an ever-growing need to analyze the symmetric-key ciphers against the upcoming threat. Indeed, we have seen a number of research works dedicated to this. Our work delves into this aspect of block ciphers, with respect to the SPECK family and LowMC family. The SPECK family received two quantum analysis till date (Jang et al., Applied Sciences, 2020; Anand et al., Indocrypt, 2020). We...

In this paper, we present the quantum implementation and analysis of the recently proposed block cipher, DEFAULT. DEFAULT is consisted of two components, namely DEFAULT-LAYER and DEFAULT-CORE. Two instances of DEFAULT-LAYER is used before and after DEFAULT-CORE (the so-called `sandwich construction'). We discuss about the the various choices made to keep the cost for the basic quantum circuit and that of the Grover's oracle search, and compare it with the levels of quantum security...

Current side-channel evaluation methodologies exhibit a gap between inefficient tools offering strong theoretical guarantees and efficient tools only offering heuristic (sometimes case-specific) guarantees. Profiled attacks based on the empirical leakage distribution correspond to the first category. Bronchain et al. showed at Crypto 2019 that they allow bounding the worst-case security level of an implementation, but the bounds become loose as the leakage dimensionality increases. Template...

In this paper we present our solution to the CHES Challenge 2020, the task of which it was to break masked hardware respective software implementations of the lightweight cipher Clyde by means of side-channel analysis. We target the secret cipher state after processing of the first $S$-box layer. Using the provided trace data we obtain a strongly biased posterior distribution for the secret-shared cipher state at the targeted point; this enables us to see exploitable biases even before...

While the convergence of Artificial Intelligence (AI) techniques with improved information technology systems ensured enormous benefits to the Internet of Vehicles (IoVs) systems, it also introduced an increased amount of security and privacy threats. To ensure the security of IoVs data, privacy preservation methodologies have gained significant attention in the literature. However, these strategies also need specific adjustments and modifications to cope with the advances in IoVs design....

In this work, we characterize online linear extractors. In other words, given a matrix $A \in \mathbb{F}_2^{n \times n}$, we study the convergence of the iterated process $\mathbf{S} \leftarrow A\mathbf{S} \oplus \mathbf{X} $, where $\mathbf{X} \sim D$ is repeatedly sampled independently from some fixed (but unknown) distribution $D$ with (min)-entropy at least $k$. Here, we think of $\mathbf{S} \in \{0,1\}^n$ as the state of an online extractor, and $\mathbf{X} \in \{0,1\}^n$ as its...

\textit{Privacy} and \textit{Byzantine-robustness} are two major concerns of federated learning (FL), but mitigating both threats simultaneously is highly challenging: privacy-preserving strategies prohibit access to individual model updates to avoid leakage, while Byzantine-robust methods require access for comprehensive mathematical analysis. Besides, most Byzantine-robust methods only work in the \textit{honest-majority} setting. We present $\mathsf{FLOD}$, a novel oblivious defender for...

While it is well known that the sawtooth function has a point-wise convergent Fourier series, the rate of convergence is not the best possible for the application of approximating the mod function in small intervals around multiples of the modulus. We show a different sine series, such that the sine series of order n has error O(epsilon^(2n+1)) for approximating the mod function in epsilon-sized intervals around multiples of the modulus. Moreover, the resulting polynomial, after Taylor...

Iterative methods are a standard technique in many areas of scientific computing. The key idea is that a function is applied repeatedly until the resulting sequence converges to the correct answer. When applying such methods in a secure computation methodology (for example using MPC, FHE, or SGX) one either needs to perform enough steps to ensure convergence irrespective of the input data, or one needs to perform a convergence test within the algorithm, and this itself leads to a leakage of...

Various Artificial Intelligence (AI) techniques are combined with classic side-channel methods to improve the efficiency of attacks. Among them, Genetic Algorithms based Correlation Power Analysis (GA-CPA) is proposed to launch attacks on hardware cryptosystems to extract the secret key efficiently. However, the convergence rate is unsatisfactory due to two problems: individuals of the initial population generally have low fitnesses, and the mutation operation is hard to generate...

In this work we apply the dynamical systems analysis of Hanrot et al. (CRYPTO'11) to a class of lattice block reduction algorithms that includes (natural variants of) slide reduction and block-Rankin reduction. This implies sharper bounds on the polynomial running times (in the query model) for these algorithms and opens the door to faster practical variants of slide reduction. We give heuristic arguments showing that such variants can indeed speed up slide reduction significantly in...

The deep learning-based side-channel analysis represents a powerful and easy to deploy option for profiled side-channel attacks. A detailed tuning phase is often required to reach a good performance where one first needs to select relevant hyperparameters and then tune them. A common selection for the tuning phase are hyperparameters connected with the neural network architecture, while those influencing the training process are less explored. In this work, we concentrate on the optimizer...

The side-channel community recently investigated a new approach, based on deep learning, to significantly improve profiled attacks against embedded systems. Compared to template attacks, deep learning techniques can deal with protected implementations, such as masking or desynchronization, without substantial pre-processing. However, important issues are still open. One challenging problem is to adapt the methods classically used in the machine learning field (e.g. loss function, performance...

The classical heuristic complexity of the Number Field Sieve (NFS) is the solution of an optimization problem that involves an unknown function, usually noted $o(1)$ and called $\xi(N)$ throughout this paper, which tends to zero as the entry $N$ grows. The aim of this paper is to find optimal asymptotic choices of the parameters of NFS as $N$ grows, in order to minimize its heuristic asymptotic computational cost. This amounts to minimizing a function of the parameters of NFS bound together...

A novel Nakamoto-like consensus was proposed by Tang et al. (ACISP 2019) to speed up the convergence (block finality) rate by determining a weight of a block in the blockchain by a tunable potential function of the block hash. However, the convergence of the scheme was evaluated only in an experimental way and a sudden utilization of another blockchain was not clearly explained. This article asymptotically analyses the convergence of Nakamoto-like consensus of Tang et al. by proposing a...

The Holy Grail of a decentralised stablecoin is achieved on rigorous mathematical frameworks, obtaining multiple advantageous proofs: stability, convergence, truthfulness, faithfulness, and malicious-security. These properties could only be attained by the novel and interdisciplinary combination of previously unrelated fields: model predictive control, deep learning, alternating direction method of multipliers (consensus-ADMM), mechanism design, secure multi-party computation, and...

Sampling from the lattice Gaussian distribution has emerged as an important problem in coding, decoding and cryptography. In this paper, the classic Metropolis-Hastings (MH) algorithm in Markov chain Monte Carlo (MCMC) methods is adopted for lattice Gaussian sampling. Two MH-based algorithms are proposed, which overcome the limitation of Klein's algorithm. The first one, referred to as the independent Metropolis-Hastings-Klein (MHK) algorithm, establishes a Markov chain via an independent...

Sampling from the lattice Gaussian distribution plays an important role in various research fields. In this paper, the Markov chain Monte Carlo (MCMC)-based sampling technique is advanced in several fronts. Firstly, the spectral gap for the independent Metropolis-Hastings-Klein (MHK) algorithm is derived, which is then extended to Peikert's algorithm and rejection sampling; we show that independent MHK exhibits faster convergence. Then, the performance of bounded distance decoding using MCMC...

As an append-only distributed database, blockchain is utilized in a vast variety of applications including the cryptocurrency and Internet-of-Things (IoT). The existing blockchain solutions have downsides in communication and storage efficiency, convergence to centralization, and consistency problems. In this paper, we propose LightChain, which is the first blockchain architecture that operates over a Distributed Hash Table (DHT) of participating peers. LightChain is a permissionless...

Correlation power analysis (CPA) is widely used in side-channel attacks on cryptographic devices. Its efficiency mostly depends on the noise produced by the devices. For parallel implementations, the power consumption during the S-box operation contains information of the whole intermediate state. When one S-box is analyzed by CPA, the others are regarded as noise. Apparently, the information of the remained S-boxes not only is wasted, but also increases the complexity of analysis. If two or...

How to train a machine learning model while keeping the data private and secure? We present CodedPrivateML, a fast and scalable approach to this critical problem. CodedPrivateML keeps both the data and the model information-theoretically private, while allowing efficient parallelization of training across distributed workers. We characterize CodedPrivateML's privacy threshold and prove its convergence for logistic (and linear) regression. Furthermore, via experiments over Amazon EC2, we...

Leakage certification aims at guaranteeing that the statistical models used in side-channel security evaluations are close to the true statistical distribution of the leakages, hence can be used to approximate a worst-case security level. Previous works in this direction were only qualitative: for a given amount of measurements available to an evaluation laboratory, they rated a model as "good enough" if the model assumption errors (i.e., the errors due to an incorrect choice of model...

Belief propagation, or the sum-product algorithm, is a powerful and well known method for inference on probabilistic graphical models, which has been proposed for the specific use in side channel analysis by Veyrat-Charvillon et al. We define a novel metric to capture the importance of variable nodes in factor graphs, we propose two improvements to the sum-product algorithm for the specific use case in side channel analysis, and we explicitly define and examine different ways of combining...

The presented work continues the line of recent distributed computing community efforts dedicated to the theoretical aspects of blockchains. This paper is the first to specify blockchains as a composition of abstract data types all together with a hierarchy of consistency criteria that formally characterizes the histories admissible for distributed programs that use them. Our work is based on an original oracle-based construction that, along with new consistency definitions, captures the...

In this paper we describe symbolic side-channel analysis techniques for detecting and quantifying information leakage, given in terms of Shannon and Min Entropy. Measuring the precise leakage is challenging due to the randomness and noise often present in program executions and side-channel observations. We account for this noise by introducing additional (symbolic) program inputs which are interpreted probabilistically, using symbolic execution with parameterized model counting. We also...

Most algorithms for hard lattice problems are based on the principle of rank reduction: to solve a problem in a $d$-dimensional lattice, one first solves one or more problem instances in a sublattice of rank $d - 1$, and then uses this information to find a solution to the original problem. Existing lattice sieving methods, however, tackle lattice problems such as the shortest vector problem (SVP) directly, and work with the full-rank lattice from the start. Lattice sieving further seems to...

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 privacy-preserving protocols for computing linear regression models, in the setting where the training dataset is vertically distributed among several parties. Our main contribution is a hybrid multi-party computation protocol that combines Yao's garbled circuits with tailored protocols for computing inner products. Like many machine learning tasks, building a linear regression model involves solving a system of linear equations. We conduct a comprehensive evaluation and...

The "blockchain" distributed ledger pioneered by Bitcoin is effective at preventing double-spending, but inherently attracts (1) "user cartels" and (2) incompressible delays, as a result of linear verification and a winner-takes-all incentive lottery. We propose to forgo the blocks and chain entirely, and build a truly distributed ledger system based on a lean graph of cross-verifying transactions, which now become the main and only objects in the system. A fully distributed consensus...

The accuracy and the fast convergence of a leakage model are both essential components for the efficiency of side-channel analysis. Thus for efficient leakage estimation an evaluator is requested to pick a Probability Density Function (PDF) that constitutes the optimal trade-off between both aspects. In the case of parametric estimation, Gaussian templates are a common choice due to their fast convergence, given that the actual leakages follow a Gaussian distribution (as in the case of an...

Lattice-based cryptography became a hot-topic in the past years because it seems to be quantum immune, i.e., resistant to attacks operated with quantum computers. The security of lattice-based cryptosystems is determined by the hardness of certain lattice problems, such as the Shortest Vector Problem (SVP). Thus, it is of prime importance to study how efficiently SVP-solvers can be implemented. This paper presents a parallel shared-memory implementation of the GaussSieve algorithm, a well...

Enumeration algorithms are the best currently known methods to solve lattice problems, both in theory (within the class of polynomial space algorithms), and in practice (where they are routinely used to evaluate the concrete security of lattice cryptography). However, there is an uncomfortable gap between our theoretical understanding and practical performance of lattice point enumeration algorithms. The algorithms typically used in practice have worst-case asymptotic running time...

Given a linear code $C$, one can define the $d$-th power of $C$ as the span of all componentwise products of $d$ elements of $C$. A power of $C$ may quickly fill the whole space. Our purpose is to answer the following question: does the square of a code ``typically'' fill the whole space? We give a positive answer, for codes of dimension $k$ and length roughly $\frac{1}{2}k^2$ or smaller. Moreover, the convergence speed is exponential if the difference $k(k+1)/2-n$ is at least linear in...

Well-designed initialisation and keystream generation processes for stream ciphers should ensure that each key-IV pair generates a distinct keystream. In this paper, we analyse some ciphers where this does not happen due to state convergence occurring either during initialisation, keystream generation or both. We show how state convergence occurs in each case and identify two mechanisms which can cause state convergence.

We investigate False Positive (FP) accusation probabilities for q-ary Tardos codes in the Restricted Digit Model. We employ a computation method recently introduced by us, to which we refer as Convolution and Series Expansion (CSE). We present a comparison of several collusion attacks on q-ary codes: majority voting, minority voting, Interleaving, $\tilde\mu$-minimizing and Random Symbol (the q-ary equivalent of the Coin Flip strategy). The comparison is made by looking at the FP rate at...

This paper presents an analysis of the stream cipher Mixer, a bit-based cipher with structural components similar to the well-known Grain cipher and the LILI family of keystream generators. Mixer uses a 128-bit key and 64-bit IV to initialise a 217-bit internal state. The analysis is focused on the initialisation function of Mixer and shows that there exist multiple key-IV pairs which, after initialisation, produce the same initial state, and consequently will generate the same keystream....

With the wide use of online social networks (OSNs), the problem of data privacy has attracted much attention. Several approaches have been proposed to address this issue. One of privacy management approaches for OSN leverages a key management technique to enable a user to simply post encrypted contents so that only users who can satisfy the associate security policy can derive the key to access the data. However, the key management policies of existing schemes may grant access to...

In Backes&Kopf(2008), the authors introduced an important new information theoretic numerical measure for assessing a system's resistance to unknown-message side-channel attacks and computed a formula for the limit of the numerical values defined by this measure as the number of side-channel observations tends to infinity. Here, we present corresponding quantitative (exponential) bounds that yield an actual rate-of-convergence for this limit, something not given in Backes&Kopf(2008). Such...

Visual secret sharing scheme (VSSS) is a secret sharing method which decodes the secret by using the contrast ability of the human visual system. Autostereogram is a single two dimensional (2D) image which becomes a virtual three dimensional (3D) image when viewed with proper eye convergence or divergence. Combing the two technologies via human vision, this paper presents a new visual secret sharing scheme called (k, n)-VSSS with autostereogram. In the scheme, each of the shares is an...