Coded computing has emerged as a key framework for addressing the impact of stragglers in distributed computation. While polynomial functions often admit exact recovery under existing coded computing schemes, non-polynomial functions require approximate reconstruction from a finite number of evaluations, posing significant challenges. Consequently, interpolation-based methods for non-polynomial coded computing have gained attention, with Berrut approximated coded computing emerging as a state-of-the-art approach. However, due to the global support of Berrut interpolants, the reconstruction accuracy degrades significantly as the number of stragglers increases. To address this challenge, we propose a coded computing framework based on cubic B-spline interpolation. In our approach, server-side function evaluations are reconstructed at the master using B-splines, exploiting their local support and smoothness properties to enhance stability and accuracy. We provide a systematic methodology for integrating B-spline interpolation into coded computing and derive theoretical bounds on approximation error for certain class of smooth functions. Our analysis demonstrates that the error bounds of our approach exhibit a faster decay with respect to the number of workers compared to the Berrut-based method. Experimental results also confirm that our method offers improved accuracy over Berrut-based methods for various smooth non-polynomial functions.

Coded computing is a reliable and fault-tolerant mechanism for implementing large computing tasks over a distributed set of worker nodes. While a majority of coded computing frameworks address accurate computation of the target functions, they are restricted to computing multivariate polynomial functions. To generalize these computing platforms to non-polynomial target functions, Jahani-Nezhad and Maddah-Ali recently proposed Berrut Approximated Coded computing (BACC), which was proven fault-tolerant against stragglers albiet with tolerable approximation errors on the target functions. Despite these benefits, there is no formal study on the security of BACC against worker nodes which report erroneous computations. To fill this research gap, we use a coding-theoretic approach to propose Secure Berrut Approximated Coded Computing (SBACC), which is resilient to stragglers and also robust to the presence of such untrusted worker nodes. One of the highlights of SBACC is the new choice of evaluation points for distributed computation which makes the well-known Discrete Cosine Transform (DCT) codes amenable to error detection and correction. To validate the new choice of evaluation points, first, we derive bounds on the accuracy of SBACC in the absence of untrusted worker nodes. Subsequently, to handle the presence of untrusted worker nodes, we derive bounds on the accuracy of SBACC and show that interesting optimization problems can be formulated to study the trade-off between the error correcting capability of the DCT codes and the accuracy of the target computation.

Secure federated learning enables collaborative model training across decentralized users while preserving data privacy. A key component is secure aggregation, which keeps individual updates hidden from both the server and users, while also defending against Byzantine users who corrupt the aggregation. To this end, Jinhyun So et al. recently developed a Byzantine-resilient secure aggregation scheme using a secret-sharing strategy over finite-field arithmetic. However, such an approach can suffer from numerical errors and overflows when applied to real-valued model updates, motivating the need for secure aggregation methods that operate directly over the real domain.We propose FORTA, a Byzantine-resilient secure aggregation framework that operates entirely in the real domain. FORTA leverages Discrete Fourier Transform (DFT) codes for privacy and employs Krum-based outlier detection for robustness. While DFT decoder is error-free under infinite precision, finite precision introduces numerical perturbations that can distort distance estimates and allow malicious updates to evade detection. To address this, FORTA refines Krum using feedback from DFT decoder, improving the selection of trustworthy updates. Theoretical analysis and experiments show that our modification of Krum offers improved robustness and more accurate aggregation than standard Krum.

Coded blockchains have acquired prominence in the recent past as a promising approach to slash the storage costs as well as to facilitate scalability. Within this class, Luby Transform (LT) coded blockchains are an appealing choice for scalability in heterogeneous networks owing to the availability of a wide range of low-complexity LT decoders. While these architectures have been studied from the aspects of storage savings and scalability, not much is known in terms of their security vulnerabilities. Pointing at this research gap, in this work, we present novel denial-of-service (DoS) threats on LT coded blockchains that target nodes with specific decoding capabilities, thereby preventing them from joining the network. Our proposed threats are non-oblivious in nature, wherein adversaries gain access to the archived blocks, and choose to execute their threat on a subset of them based on underlying coding scheme. We show that our optimized threats can achieve the same level of damage as that of blind attacks, however, with limited amount of resources. This is the first work of its kind that opens up new questions on designing coded blockchains to jointly provide storage savings, scalability and resilience to optimized threats.

Analog Lagrange Coded Computing (ALCC) is a recently proposed coded computing paradigm wherein certain computations over analog datasets can be efficiently performed using distributed worker nodes through floating point implementation. While ALCC is known to preserve privacy of data from the workers, it is not resilient to adversarial workers that return erroneous computation results. Pointing at this security vulnerability, we focus on securing ALCC from a wide range of non-colluding and colluding adversarial workers. As a foundational step, we make use of error-correction algorithms for Discrete Fourier Transform (DFT) codes to build novel algorithms to nullify the erroneous computations returned from the adversaries. Furthermore, when such a robust ALCC is implemented in practical settings, we show that the presence of precision errors in the system can be exploited by the adversaries to propose novel colluding attacks to degrade the computation accuracy. As the main takeaway, we prove a counter-intuitive result that not all the adversaries should inject noise in their computations in order to optimally degrade the accuracy of the ALCC framework. This is the first work of its kind to address the vulnerability of ALCC against colluding adversaries.

Reactive injection attacks are a class of security threats in wireless networks wherein adversaries opportunistically inject spoofing packets in the frequency band of a client thereby forcing the base-station to deploy impersonation-detection methods. Towards circumventing such threats, we implement secret-key based physical-layer signalling methods at the clients which allow the base-stations to deploy machine learning (ML) models on their in-phase and quadrature samples at the baseband for attack detection. Using Adalm Pluto based software defined radios to implement the secret-key based signalling methods, we show that robust ML models can be designed at the base-stations. However, we also point out that, in practice, insufficient availability of training datasets at the base-stations can make these methods ineffective. Thus, we use a federated learning framework in the backhaul network, wherein a group of base-stations that need to protect their clients against reactive injection threats collaborate to refine their ML models by ensuring privacy on their datasets. Using a network of XBee devices to implement the backhaul network, experimental results on our federated learning setup shows significant enhancements in the detection accuracy, thus presenting wireless security as an excellent use-case for federated learning in 6G networks and beyond.

Denial-of-Service (DoS) threats pose a major challenge to the idea of physical-layer key generation as the underlying wireless channels for key extraction are usually public. Identifying this vulnerability, we study the effect of DoS threats on relay-assisted key generation, and show that a reactive jamming attack on the distribution phase of relay-assisted key generation can forbid the nodes from extracting secret keys. To circumvent this problem, we propose a self-sustainable key generation model, wherein a frequency-hopping based distribution phase is employed to evade the jamming attack even though the participating nodes do not share prior credentials. A salient feature of the idea is to carve out a few bits from the key generation phase and subsequently use them to pick a frequency band at random for the broadcast phase. Interesting resource-allocation problems are formulated on how to extract maximum number of secret bits while also being able to evade the jamming attack with high probability. Tractable low-complexity solutions are also provided to the resource-allocation problems, along with insights on the feasibility of their implementation in practice.

Low-latency provenance embedding methods have received traction in wireless networks for their ability to track the footprint of information flow. One such known method is based on Bloom filters wherein the nodes that forward the packets appropriately choose a certain number of hash functions to embed their signatures in a shared space in the packet. Although Bloom filter methods can achieve the required accuracy level in provenance recovery, they are known to incur higher processing delay since higher number of hash functions are needed to meet the accuracy level. Motivated by this behaviour, we identify a regime of delay-constraints within which new provenance embedding methods must be proposed as Bloom filter methods are no longer applicable. To fill this research gap, we present network-coded edge embedding (NCEE) protocols that facilitate low-latency routing of packets in wireless network applications. First, we show that the problem of designing provenance recovery methods for the NCEE protocol is equivalent to the celebrated problem of compressed sensing, however, with additional constraints of path formation on the solution. Subsequently, we present a family of path-aware orthogonal matching pursuit algorithms that jointly incorporates the sparsity and path constraints. Through extensive simulation results, we show that our algorithms enjoy low-complexity implementation, and also improve the path recovery performance when compared to path-agnostic counterparts.

It is well known that physical-layer key generation methods enable wireless devices to harvest symmetric keys by accessing the randomness offered by the wireless channels. Although two-user key generation is well understood, group secret-key (GSK) generation, wherein more than two nodes in a network generate secret-keys, still poses open problems. Recently, Manish Rao et al., have proposed the Algebraic Symmetrically Quantized GSK (A-SQGSK) protocol for a network of three nodes wherein the nodes share quantized versions of the channel realizations over algebraic rings, and then harvest a GSK. Although A-SQGSK protocol guarantees confidentiality of common randomness to an eavesdropper, we observe that the key-rate of the protocol is poor since only one channel in the network is used to harvest GSK. Identifying this limitation, in this paper, we propose an opportunistic selection method wherein more than one wireless channel is used to harvest GSKs without compromising the confidentiality feature, thereby resulting in remarkable improvements in the key-rate. Furthermore, we also propose a log-likelihood ratio (LLR) generation method for the common randomness observed at various nodes, so that the soft-values are applied to execute LDPC codes based reconciliation to reduce the bit mismatches among the nodes.

In physical-layer Group Secret-Key (GSK) generation, multiple nodes of a wireless network synthesize symmetric keys by observing a subset of their channel realizations, referred to as the common source of randomness (CSR). Unlike the case of two-user key generation, exchanging pilot symbols within the coherence-block is not sufficient to arrive at a CSR. In addition, some nodes must act as facilitators by broadcasting linear combinations of the channel realizations within the coherence-block, thereby giving rise to low-latency requirement for sharing the CSR. To assist the latency constraint, practical radio devices are forced to quantize the linear combination of channel realizations directly to finite complex constellations before broadcasting them to the other nodes. First, we show that this direct quantization at the facilitator results in asymmetric noise levels at the nodes, which in turn impacts the overall key-rate.Identifying the above issue, we propose a practical GSK generation protocol, referred to as Algebraic Symmetrically Quantized GSK (A-SQGSK) protocol, in a network of three nodes. In the proposed protocol, due to quantization of symbols at the facilitator, the other two nodes also quantize their channel realizations, and use them appropriately over algebraic rings to generate the keys. Under special conditions, we analytically show that the A-SQGSK protocol provides higher key-rate than the baselines, and also prove that the proposed protocol incurs zero leakage to an external eavesdropper. We also use extensive simulation results to demonstrate the benefits of the proposed protocol at different regimes of signal-to-noise-ratios.

In this paper, we address physical-layer key generation between two unmanned aerial vehicles (UAVs) in flight, which are hindered by a dominant line-of-sight component (LOS) in their wireless channel. Although strong LOS component yields better error-performance in data transmission, it is well known that limited randomness in the channel variation will render the underlying physical-layer key generation algorithms ineffective. Pointing at this disadvantage, we explore a relay-based secret-key generation technique between the two UAVs, wherein a ground- stationed relay assists the two UAVs to witness a common source of randomness with higher entropy than their direct channel. We propose the Relay- Assisted Selective Inversion (RASI) protocol, which selectively offers common randomness from either of the channels from the relay to the two UAVs. To showcase the benefits of the RASI protocol, we first obtain theoretical lower bounds on the differential entropy of the common source of randomness, and subsequently employ a practical key-generation algorithm to synthesize the digital keys. We show that RASI can help the two UAVs to generate keys with higher key-rate than using the direct channel only. Finally, we also show that RASI outperforms an existing state-of-the-art relay-based method in terms of key-rate and computational complexity at the UAVs, while marginally losing to the latter in communication- overhead.

Constructions of lattices are known to have a strong connection to the study of classical linear codes over F2; one such celebrated construction is that of Barnes-Wall (BW) lattices over ℤ[i], with i = √-1, wherein weighted sum of nested Reed-Muller codes over powers of the base 1 + i leads to the famous multi-level construction of BW lattices. Although these constructions facilitate simple encoding and decoding of information bits, the resulting codewords need to be mapped onto their representatives in order to reduce the average energy of the lattice code. Drawing inspirations from the case of BW lattices, in this work, we address a general question of how to arrive at representatives of the codewords of a lattice code over ℤ[θ], where θ is a quadratic integer, that is generated via a multi-level construction over linear codes over Fq, for q > 2. In particular, we introduce a novel shaping function τ : ℤ[θ] → ℤ[θ] on the components of lattice codewords, and prove that the natural constellation of lattices from multi-level constructions can be rearranged into a multi-dimensional cube or parallelepiped under such a map. We demonstrate numerically that our mapping results in a reduction of the average energy of lattice constellations. Our proposed mapping has applications in communications, particularly in encoding and decoding of lattice codes from multi-level constructions over q-ary linear codes.

In this work, we study the problem of storing reliably an archive of versioned data. Specifically, we focus on systems where the differences (deltas) between subsequent versions rather than the whole objects are stored - a typical model for storing versioned data. For reliability, we propose erasure encoding techniques that exploit the sparsity of information in the deltas while storing them reliably in a distributed back-end storage system, resulting in improved I/O read performance to retrieve the whole versioned archive. Along with the basic techniques, we propose a few optimization heuristics, and evaluate the techniques' efficacy analytically and with numerical simulations.

A wiretap channel models a communication channel between a legitimate sender Alice and a legitimate receiver Bob in the presence of an eavesdropper Eve. Confidentiality between Alice and Bob is obtained using wiretap codes, which exploit the difference between the channels to Bob and to Eve. This paper discusses a first implementation of wiretap lattice codes using USRP (Universal Software Radio Peripheral), which focuses on the channel between Alice and Eve. Benefits of coset encoding for Eve's confusion are observed, using different lattice codes in small dimensions, and varying the position of the eavesdropper.