Threshold-Computation-in-the-Head (TCitH) and VOLE-in-the-Head (VOLEitH), two recent developments of the MPC-in-the-Head (MPCitH) paradigm, have significantly improved the performance of digital signature schemes. This work embeds the restricted decoding problem within these frameworks: we propose a structurally simple modeling that achieves competitive signature sizes. Specifically, by instantiating the restricted decoding problem with the same hardness assumption underlying CROSS, we reduce sizes by more than a factor of two compared to the NIST submission. Moreover, we observe that ternary full-weight decoding, closely related to the hardness assumption underlying WAVE, is a restricted decoding problem. Using ternary full-weight decoding, we obtain signature sizes comparable to the smallest MPCitH-based candidates in the NIST competition.

The weighted-Hamming metric generalizes the Hamming metric by assigning different weights to blocks of coordinates. It is well-suited for applications such as coding over independent parallel channels, each of which has a different level of importance or noise. From a coding-theoretic perspective, the actual error-correction capability of a code under this metric can exceed half its minimum distance. In this work, we establish direct bounds on this capability, tightening those obtained via minimum-distance arguments. We also propose a flexible code construction based on generalized concatenation and show that these codes can be efficiently decoded up to a lower bound on the error-correction capability.

Phased Burst Errors (PBEs) are bursts of errors occurring at one or more known locations. The correction of PBEs is a classical topic in coding theory, with prominent applications such as the design of array codes for memory systems or distributed storage. We propose a general yet finegrained approach to this problem, accounting not only for the number of bursts but also the error structure in each burst. By modeling PBEs as an error set in an adversarial channel, we investigate bounds on the maximal size of codes that can correct them. The PBE-correction capability of generalized concatenated codes is analyzed, and asymptotically good PBE-correcting codes are constructed, recovering a classical construction in a specific problem instance.

Abstract We study the hardness of the Syndrome Decoding problem, the base of most code-based cryptographic schemes, such as Classic McEliece, in the presence of side-channel information. We use ChipWhisperer equipment to perform a template attack on Classic McEliece running on an ARM Cortex-M4, and accurately classify the Hamming weights of consecutive 32-bit blocks of the secret error vector $$\textbf{e}\in {{\mathbb {F}}}_2^n$$ e ∈ F 2 n . With these weights at hand, we optimize Information Set Decoding algorithms. Technically, we demonstrate how to speed up information set decoding via a dimension reduction, additional parity-check equations, and an improved information set search, all derived from the Hamming-weight information. Consequently, using our template attack, we can practically recover an error vector $$\textbf{e}\in {{\mathbb {F}}}_2^n$$ e ∈ F 2 n in dimension $$n=2197$$ n = 2197 in a matter of seconds. Without side-channel information, such an instance has a complexity of around 88 bit. We also estimate how our template attack affects the security of the proposed McEliece parameter sets. Roughly speaking, even an error-prone leak of our Hamming weight information leads for $$n=3488$$ n = 3488 to a security drop of 89 bits.

Independent parallel q-ary symmetric channels are a suitable transmission model for several applications. The weighted-Hamming metric is tailored to this setting and enables optimal decoding performance. We show that some weighted-Hamming-metric codes exhibit the unusual property that all errors beyond half the minimum distance can be corrected. Nevertheless, a tight relation between the error-correction capability of a code and its minimum distance can be established. Generalizing their Hamming-metric counterparts, upper and lower bounds on the cardinality of a code with a given weighted-Hamming distance are obtained. Finally, we propose a simple code construction with optimal minimum distance for specific parameters.

This paper proposes a novel shift-sum decoding method for non-binary cyclic codes, which only requires finite field operations but yields advanced decoding performance. Using the cyclically different minimum-weight dual codewords (MWDCs) and their proper shifts, a frequency matrix can be obtained as a reliability metric for identifying the error positions and magnitudes. By analyzing the statistical distributions of the matrix entries, the rationale for the shift-sum decoding’s advanced error-correction capability is revealed. Based on this decoding method, a hard-decision iterative shift-sum (HISS) decoding algorithm is first proposed. It can correct errors beyond half of the code’s minimum Hamming distance. By further utilizing the reliability information obtained from the channel, a soft-decision iterative shift-sum (SISS) decoding algorithm is then proposed to improve the decoding performance. Both the HISS and the SISS algorithms are realized only with polynomial multiplications and numerical comparisons, which are hardware-friendly. To further improve the error-correction performance, the HISS and SISS algorithms can be integrated in a Chase decoding mechanism for handling the test-vectors. Simulation results on Reed-Solomon (RS) and non-binary BCH (NB-BCH) codes show that the proposed algorithms yield a competent decoding and complexity performances in comparison with the existing decoding algorithms.

Several recently proposed code-based cryptosystems base their security on a slightly generalized version of the classical (syndrome) decoding problem. Namely, in the so-called restricted (syndrome) decoding problem, the error values stem from a restricted set. In this paper, we propose new generic decoders, that are inspired by subset sum solvers and tailored to the new setting. The introduced algorithms take the restricted structure of the error set into account in order to utilize the representation technique efficiently. This leads to a considerable decrease in the security levels of recently published code-based cryptosystems.

Properties of random codes endowed with the cover metric are considered. We prove the NP-hardness of the decoding problem and then provide a generic decoder, following the information set decoding idea from Prange’s algorithm in the Hamming metric. Despite the cover metric lying between the Hamming and the rank metric, the complexity analysis of the algorithm reveals a significant difference between the metrics.

Information set decoding is a method for soft-decision decoding of general linear binary codes. Its performance can be improved by reprocessing multiple bases. Different methods for choosing the bases are known. We present a novel method for basis selection using probability analysis. The sequence of bases is determined which maximizes the decoding performance. We present a method for approximating this sequence by updating the error probabilities of the received symbols and give an efficient implementation. Furthermore, we show that the concept of updating bit error probabilities can be extended from information set decoding to box and match decoding. Simulation results confirm the efficiency of the proposed decoders compared with regular information set decoding and other multibasis algorithms.

The binary primitive BCH codes are cyclic and are constructed by choosing a subset of the cyclotomic cosets. Which subset is chosen determines the dimension, the minimum distance and the weight distribution of the BCH code. We construct possible BCH codes and determine their coderate, true minimum distance and the non-equivalent codes. A particular choice of cyclotomic cosets gives BCH codes which are, extended by one bit, equivalent to Reed-Muller codes, which is a known result from the sixties. We show that BCH codes have possibly better parameters than Reed-Muller codes, which are related in recent publications to polar codes. We study the decoding performance of these different BCH codes using information set decoding based on minimal weight codewords of the dual code. We show that information set decoding is possible even in case of a channel without reliability information since the decoding algorithm inherently calculates reliability information. Different BCH codes of the same rate are compared and different decoding performances and complexity are observed. Some examples of hard decision decoding of BCH codes have the same decoding performance as maximum likelihood decoding. All presented decoding methods can possibly be extended to include reliability information of a Gaussian channel for soft decision decoding. We show simulation results for soft decision list information set decoding and compare the performance to other methods.

This paper proposes a novel shift-sum decoding scheme for non-binary cyclic codes. Using minimum-weight dual codewords and their cyclic shifts, a reliability measure can be yielded as an indicator for the error position and the error magnitude. Based on this shift-sum decoding concept, a harddecision iterative decoding algorithm is proposed, which can correct errors beyond half of the code’s minimum Hamming distance. By utilizing reliability information from the channel, a soft-decision iterative decoding algorithm is further introduced to improve the decoding performance. These two shift-sum based iterative decoding algorithms are realized with polynomial multiplication and integer (or real number) comparisons, which are hardware-friendly. Simulation results on Reed-Solomon codes and non-binary BCH codes show the decoding potential of the proposed algorithms.

Trial-and-error learning is a universal strategy for establishing which actions are beneficial or harmful in new environments. However, learning stimulus-response associations solely via trial-and-error is often suboptimal, as in many settings dependencies among stimuli and responses can be exploited to increase learning efficiency. Previous studies have shown that in settings featuring such dependencies, humans typically engage high-level cognitive processes and employ advanced learning strategies to improve their learning efficiency. Here we analyze in detail the initial learning phase of a sample of human subjects (N = 85) performing a trial-and-error learning task with deterministic feedback and hidden stimulus-response dependencies. Using computational modeling, we find that the standard Q-learning model cannot sufficiently explain human learning strategies in this setting. Instead, newly introduced deterministic response models, which are theoretically optimal and transform stimulus sequences unambiguously into response sequences, provide the best explanation for 50.6% of the subjects. Most of the remaining subjects either show a tendency towards generic optimal learning (21.2%) or at least partially exploit stimulus-response dependencies (22.3%), while a few subjects (5.9%) show no clear preference for any of the employed models. After the initial learning phase, asymptotic learning performance during the subsequent practice phase is best explained by the standard Q-learning model. Our results show that human learning strategies in the presented trial-and-error learning task go beyond merely associating stimuli and responses via incremental reinforcement. Specifically during initial learning, high-level cognitive processes support sophisticated learning strategies that increase learning efficiency while keeping memory demands and computational efforts bounded. The good asymptotic fit of the Q-learning model indicates that these cognitive processes are successively replaced by the formation of stimulus-response associations over the course of learning.

In simple perceptual decisions the brain has to identify a stimulus based on noisy sensory samples from the stimulus. Basic statistical considerations state that the reliability of the stimulus information, i.e., the amount of noise in the samples, should be taken into account when the decision is made. However, for perceptual decision making experiments it has been questioned whether the brain indeed uses the reliability for making decisions when confronted with unpredictable changes in stimulus reliability. We here show that even the basic drift diffusion model, which has frequently been used to explain experimental findings in perceptual decision making, implicitly relies on estimates of stimulus reliability. We then show that only those variants of the drift diffusion model which allow stimulus-specific reliabilities are consistent with neurophysiological findings. Our analysis suggests that the brain estimates the reliability of the stimulus on a short time scale of at most a few hundred milliseconds.

Even for simple perceptual decisions, the mechanisms that the brain employs are still under debate. Although current consensus states that the brain accumulates evidence extracted from noisy sensory information, open questions remain about how this simple model relates to other perceptual phenomena such as flexibility in decisions, decision-dependent modulation of sensory gain, or confidence about a decision. We propose a novel approach of how perceptual decisions are made by combining two influential formalisms into a new model. Specifically, we embed an attractor model of decision making into a probabilistic framework that models decision making as Bayesian inference. We show that the new model can explain decision making behaviour by fitting it to experimental data. In addition, the new model combines for the first time three important features: First, the model can update decisions in response to switches in the underlying stimulus. Second, the probabilistic formulation accounts for top-down effects that may explain recent experimental findings of decision-related gain modulation of sensory neurons. Finally, the model computes an explicit measure of confidence which we relate to recent experimental evidence for confidence computations in perceptual decision tasks.

The olfactory information that is received by the insect brain is encoded in the form of spatiotemporal patterns in the projection neurons of the antennal lobe. These dense and overlapping patterns are transformed into a sparse code in Kenyon cells in the mushroom body. Although it is clear that this sparse code is the basis for rapid categorization of odors, it is yet unclear how the sparse code in Kenyon cells is computed and what information it represents. Here we show that this computation can be modeled by sequential firing rate patterns using Lotka-Volterra equations and Bayesian online inference. This new model can be understood as an 'intelligent coincidence detector', which robustly and dynamically encodes the presence of specific odor features. We found that the model is able to qualitatively reproduce experimentally observed activity in both the projection neurons and the Kenyon cells. In particular, the model explains mechanistically how sparse activity in the Kenyon cells arises from the dense code in the projection neurons. The odor classification performance of the model proved to be robust against noise and time jitter in the observed input sequences. As in recent experimental results, we found that recognition of an odor happened very early during stimulus presentation in the model. Critically, by using the model, we found surprising but simple computational explanations for several experimental phenomena.

Reinforcement learning in the high-dimensional, continuous spaces typical in robotics, remains a challenging problem. To overcome this challenge, a popular approach has been to use demonstrations to find an appropriate initialisation of the policy in an attempt to reduce the number of iterations needed to find a solution. Here, we present an alternative way to incorporate prior knowledge from demonstrations of individual postures into learning, by extracting the inherent problem structure to find an efficient state representation. In particular, we use probabilistic, nonlinear dimensionality reduction to capture latent constraints present in the data. By learning policies in the learnt latent space, we are able to solve the planning problem in a reduced space that automatically satisfies task constraints. As shown in our experiments, this reduces the exploration needed and greatly accelerates the learning. We demonstrate our approach for learning a bimanual reaching task on the 19-DOF KHR-1HV humanoid.

We introduce a method based on support vector machines which can detect opening and closing actions of the human thumb, index finger, and other fingers recorded via surface EMG only. The method is shown to be robust across sessions and can be used independently of the position of the arm. With these stability criteria, the method is ideally suited for the control of active prosthesis with a high number of active degrees of freedom. The method is successfully demonstrated on a robotic four-finger hand, and can be used to grasp objects