arXiv subjects

Amin Sakzad

Publications and source records attributed to Amin Sakzad.

At least 19 recordsLinked to original sources

arXiv2026

On the Maximum Toroidal Distance Code for Lattice-Based Public-Key Cryptography

We propose a maximum toroidal distance (MTD) code for lattice-based public-key encryption (PKE). By formulating the encryption encoding problem as the selection of $2^\ell$ points in the discrete $\ell$-dimensional torus $\mathbb{Z}_q^\ell$, the proposed construction maximizes the minimum $L_2$-norm toroidal distance to reduce the decryption failure rate (DFR) in post-quantum schemes such as the NIST ML-KEM (Crystals-Kyber). For $\ell = 2$, we show that the MTD code is essentially a variant of the Minal code recently introduced at IACR CHES 2025. For $\ell = 4$, we present a construction based on the $D_4$ lattice that achieves the largest known toroidal distance, while for $\ell = 8$, the MTD code corresponds to $2E_8$ lattice points in $\mathbb{Z}_4^8$. Numerical evaluations under the Kyber setting show that the proposed codes outperform both Minal and maximum Lee-distance ($L_1$-norm) codes in DFR for $\ell > 2$, while matching Minal code performance for $\ell = 2$.

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arXiv2025

Compact Lattice-Coded (Multi-Recipient) Kyber without CLT Independence Assumption

This work presents a joint design of encoding and encryption procedures for public key encryptions (PKEs) and key encapsulation mechanism (KEMs) such as Kyber, without relying on the assumption of independent decoding noise components, achieving reductions in both communication overhead (CER) and decryption failure rate (DFR). Our design features two techniques: ciphertext packing and lattice packing. First, we extend the Peikert-Vaikuntanathan-Waters (PVW) method to Kyber: $\ell$ plaintexts are packed into a single ciphertext. This scheme is referred to as P$_\ell$-Kyber. We prove that the P$_\ell$-Kyber is IND-CCA secure under the M-LWE hardness assumption. We show that the decryption decoding noise entries across the $\ell$ plaintexts (also known as layers) are mutually independent. Second, we propose a cross-layer lattice encoding scheme for the P$_\ell$-Kyber, where every $\ell$ cross-layer information symbols are encoded to a lattice point. This way we obtain a \emph{coded} P$_\ell$-Kyber, where the decoding noise entries for each lattice point are mutually independent. Therefore, the DFR analysis does not require the assumption of independence among the decryption decoding noise entries. Both DFR and CER are greatly decreased thanks to ciphertext packing and lattice packing. We demonstrate that with $\ell=24$ and Leech lattice encoder, the proposed coded P$_\ell$-KYBER1024 achieves DFR $<2^{-281}$ and CER $ = 4.6$, i.e., a decrease of CER by $90\%$ compared to KYBER1024.

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arXiv2025

Joint Power and Bit Allocation for Precoded Massive MIMO Channels

This work addresses the joint optimization of power and bit allocation in precoded large-scale n x n MIMO systems with discrete input alphabets, specifically QAM constellations. We propose an adaptive QAM scheme that maintains a fixed gap to the Gaussian-input capacity for a given n. A key finding is that, under the proposed scheme, the mercury/waterfilling (MWF) solution reduces analytically to the classical water-filling (WF) policy. Furthermore, the adaptive QAM configuration can be precomputed under the large-system assumption, enabling the replacement of full SVD with truncated SVD and yielding substantial computational savings. To support practical deployment, we develop a bit-allocation algorithm that meets a target transmission data rate while minimizing the overall decoding error rate and preserving computational complexity at O(n log n). Simulation results confirm that the proposed truncated SVD precoding, paired with the joint power and bit allocation, achieves superior decoding performance relative to conventional approaches, while operating at significantly lower complexity.

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arXiv2024

Lattice-Based Vulnerabilities in Lee Metric Post-Quantum Cryptosystems

Post-quantum cryptography has gained attention due to the need for secure cryptographic systems in the face of quantum computing. Code-based and lattice-based cryptography are two prominent approaches, both heavily studied within the NIST standardization project. Code-based cryptography -- most prominently exemplified by the McEliece cryptosystem -- is based on the hardness of decoding random linear error-correcting codes. Despite the McEliece cryptosystem having been unbroken for several decades, it suffers from large key sizes, which has led to exploring variants using metrics than the Hamming metric, such as the Lee metric. This alternative metric may allow for smaller key sizes, but requires further analysis for potential vulnerabilities to lattice-based attack techniques. In this paper, we consider a generic Lee metric based McEliece type cryptosystem and evaluate its security against lattice-based attacks.

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arXiv2024

Semi-Compressed CRYSTALS-Kyber

In this paper, we investigate the communication overhead of the Kyber, which has recently been standardized by the National Institute of Standards and Technology (NIST). Given the same decryption failure rate (DFR) and security argument, we show it is feasible to reduce the communication overhead of the Kyber by 54%. The improvement is based on two technologies: ciphertext quantization and plaintext encoding. First, we prove that the Lloyd-Max quantization is optimal to minimize the decryption decoding noise. The original Kyber compression function is not optimal. Second, we propose an encoding scheme, which combines Pulse-Amplitude Modulation (PAM), Gray mapping, and a binary error correcting code. An explicit expression for the DFR is derived. The minimum possible communication overhead is also derived. Finally, we demonstrate that with the Lloyd-Max quantization, 8-PAM, Gray mapping, and a shortened binary BCH(768,638,13) code, the proposed scheme encapsulates 638 bits (e.g., 2.5 AES keys) in a single ciphertext.

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arXiv2024

CRYSTALS-Kyber With Lattice Quantizer

Module Learning with Errors (M-LWE) based key reconciliation mechanisms (KRM) can be viewed as quantizing an M-LWE sample according to a lattice codebook. This paper describes a generic M-LWE-based KRM framework, valid for any dimensional lattices and any modulus $q$ without a dither. Our main result is an explicit upper bound on the decryption failure rate (DFR) of M-LWE-based KRM. This bound allows us to construct optimal lattice quantizers to reduce the DFR and communication cost simultaneously. Moreover, we present a KRM scheme using the same security parameters $(q,k,η_1,η_2)$ as in Kyber. Compared with Kyber, the communication cost is reduced by up to $36.47\%$ and the DFR is reduced by a factor of up to $2^{99}$. The security arguments remain the same as Kyber.

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arXiv2024

Lattice Codes for CRYSTALS-Kyber

This paper describes a constant-time lattice encoder for the National Institute of Standards and Technology (NIST) recommended post-quantum encryption algorithm: Kyber. The first main contribution of this paper is to refine the analysis of Kyber decoding noise and prove that Kyber decoding noise can be bounded by a sphere. This result shows that the Kyber encoding problem is essentially a sphere packing in a hypercube. The original Kyber encoder uses the integer lattice for sphere packing purposes, which is far from optimal. Our second main contribution is to construct optimal lattice codes to ensure denser packing and a lower decryption failure rate (DFR). Given the same ciphertext size as the original Kyber, the proposed lattice encoder enjoys a larger decoding radius, and is able to encode much more information bits. This way we achieve a decrease of the communication cost by up to 32.6%, and a reduction of the DFR by a factor of up to 2^{85}. Given the same plaintext size as the original Kyber, e.g., 256 bits, we propose a bit-interleaved coded modulation (BICM) approach, which combines a BCH code and the proposed lattice encoder. The proposed BICM scheme significantly reduces the DFR of Kyber, thus enabling further compression of the ciphertext. Compared with the original Kyber encoder, the communication cost is reduced by 24.49%, while the DFR is decreased by a factor of 2^{39}. The proposed encoding scheme is a constant-time algorithm, thus resistant against the timing side-channel attacks.

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arXiv2023

ACE: A Consent-Embedded privacy-preserving search on genomic database

In this paper, we introduce ACE, a consent-embedded searchable encryption scheme. ACE enables dynamic consent management by supporting the physical deletion of associated data at the time of consent revocation. This ensures instant real deletion of data, aligning with privacy regulations and preserving individuals' rights. We evaluate ACE in the context of genomic databases, demonstrating its ability to perform the addition and deletion of genomic records and related information based on ID, which especially complies with the requirements of deleting information of a particular data owner. To formally prove that ACE is secure under non-adaptive attacks, we present two new definitions of forward and backward privacy. We also define a new hard problem, which we call D-ACE, that facilitates the proof of our theorem (we formally prove its hardness by a security reduction from DDH to D-ACE). We finally present implementation results to evaluate the performance of ACE.

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arXiv2023

SePEnTra: A secure and privacy-preserving energy trading mechanisms in transactive energy market

In this paper, we design and present a novel model called SePEnTra to ensure the security and privacy of energy data while sharing with other entities during energy trading to determine optimal price signals. Furthermore, the market operator can use this data to detect malicious activities of users in the later stage without violating privacy (e.g., deviation of actual energy generation/consumption from forecast beyond a threshold). We use two cryptographic primitives, additive secret sharing and Pedersen commitment, in SePEnTra. The performance of our model is evaluated theoretically and numerically. We compare the performance of SePEnTra with the same Transactive energy market (TEM) framework without security mechanisms. The result shows that even though using advanced cryptographic primitives in a large market framework, SePEnTra has very low computational complexity and communication overhead. Moreover, it is storage efficient for all parties.

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arXiv2022

Collaborative analysis of genomic data: vision and challenges

The cost of DNA sequencing has resulted in a surge of genetic data being utilised to improve scientific research, clinical procedures, and healthcare delivery in recent years. Since the human genome can uniquely identify an individual, this characteristic also raises security and privacy concerns. In order to balance the risks and benefits, governance mechanisms including regulatory and ethical controls have been established, which are prone to human errors and create hindrance for collaboration. Over the past decade, technological methods are also catching up that can support critical discoveries responsibly. In this paper, we explore regulations and ethical guidelines and propose our visions of secure/private genomic data storage/processing/sharing platforms. Then, we present some available techniques and a conceptual system model that can support our visions. Finally, we highlight the open issues that need further investigation.

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arXiv2021

PrivGenDB: Efficient and privacy-preserving query executions over encrypted SNP-Phenotype database

Searchable symmetric encryption (SSE) has been used to protect the confidentiality of genomic data while providing substring search and range queries on a sequence of genomic data, but it has not been studied for protecting single nucleotide polymorphism (SNP)-phenotype data. In this article, we propose a novel model, PrivGenDB, for securely storing and efficiently conducting different queries on genomic data outsourced to an honest-but-curious cloud server. To instantiate PrivGenDB, we use SSE to ensure confidentiality while conducting different types of queries on encrypted genomic data, phenotype and other information of individuals to help analysts/clinicians in their analysis/care. To the best of our knowledge, PrivGenDB construction is the first SSE-based approach ensuring the confidentiality of shared SNP-phenotype data through encryption while making the computation/query process efficient and scalable for biomedical research and care. Furthermore, it supports a variety of query types on genomic data, including count queries, Boolean queries, and k'-out-of-k match queries. Finally, the PrivGenDB model handles the dataset containing both genotype and phenotype, and it also supports storing and managing other metadata like gender and ethnicity privately. Computer evaluations on a dataset with 5,000 records and 1,000 SNPs demonstrate that a count/Boolean query and a k'-out-of-k match query over 40 SNPs take approximately 4.3s and 86.4μs, respectively, that outperforms the existing schemes.

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arXiv2021

Towards Practical Encrypted Network Traffic Pattern Matching for Secure Middleboxes

Network Function Virtualisation (NFV) advances the adoption of composable software middleboxes. Accordingly, cloud data centres become major NFV vendors for enterprise traffic processing. Due to the privacy concern of traffic redirection to the cloud, secure middlebox systems (e.g., BlindBox) draw much attention; they can process encrypted packets against encrypted rules directly. However, most of the existing systems supporting pattern matching based network functions require the enterprise gateway to tokenise packet payloads via sliding windows. Such tokenisation induces a considerable communication overhead, which can be over 100$\times$ to the packet size. To overcome this bottleneck, in this paper, we propose the first bandwidth-efficient encrypted pattern matching protocol for secure middleboxes. We resort to a primitive called symmetric hidden vector encryption (SHVE), and propose a variant of it, aka SHVE+, to achieve constant and moderate communication cost. To speed up, we devise encrypted filters to reduce the number of accesses to SHVE+ during matching highly. We formalise the security of our proposed protocol and conduct comprehensive evaluations over real-world rulesets and traffic dumps. The results show that our design can inspect a packet over 20k rules within 100 $μ$s. Compared to prior work, it brings a saving of $94\%$ in bandwidth consumption.

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arXiv2020

Comments on "Physical-layer cryptography through massive MIMO"

We present two attacks on two different versions of physical layer cryptography schemes based on massive multiple-input multiple-output (MIMO). Both cryptosystems employ a singular value decomposition (SVD) precoding technique. For the first one, we show that the eavesdropper (who knows its own channel and the channel between legitimate users) can decrypt the information data under the same condition as the legitimate receiver. We study the signal-to-noise advantage ratio for decoding by the legitimate user over the eavesdropper in a more generalized scheme when an arbitrary precoder at the transmitter is employed. On the negative side, we show that if the eavesdropper uses a number of receive antennas much larger than the number of legitimate user antennas, then there is no advantage, independent of the precoding scheme employed at the transmitter. On the positive side, for the case where the adversary is limited to have the same number of antennas as legitimate users, we give an $O\left(n^2\right)$ upper bound on the advantage and show that this bound can be approached using an inverse precoder. For the second cryptosystem, we show that the required security conditions prevent the legitimate user from decoding the plaintext uniquely.

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arXiv2019

Enabling Efficient Privacy-Assured Outlier Detection over Encrypted Incremental Datasets

Outlier detection is widely used in practice to track the anomaly on incremental datasets such as network traffic and system logs. However, these datasets often involve sensitive information, and sharing the data to third parties for anomaly detection raises privacy concerns. In this paper, we present a privacy-preserving outlier detection protocol (PPOD) for incremental datasets. The protocol decomposes the outlier detection algorithm into several phases and recognises the necessary cryptographic operations in each phase. It realises several cryptographic modules via efficient and interchangeable protocols to support the above cryptographic operations and composes them in the overall protocol to enable outlier detection over encrypted datasets. To support efficient updates, it integrates the sliding window model to periodically evict the expired data in order to maintain a constant update time. We build a prototype of PPOD and systematically evaluates the cryptographic modules and the overall protocols under various parameter settings. Our results show that PPOD can handle encrypted incremental datasets with a moderate computation and communication cost.

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arXiv2019

Steepest Gradient-Based Orthogonal Precoder For Integer-Forcing MIMO

In this paper, we develop an orthogonal precoding scheme for integer-forcing (IF) linear receivers using the steepest gradient algorithm. Although this scheme can be viewed as a special case of the unitary precoded integer-forcing (UPIF), it has two major advantages. First, the orthogonal precoding outperforms its unitary counterpart in terms of achievable rate, outage probability, and error rate. We verify this advantage via theoretical and numerical analyses. Second, it exhibits lower complexity as the dimension of orthogonal matrices is half that of unitary matrices in the real-valued domain. For finding ``good'' orthogonal precoder matrices, we propose an efficient algorithm based on the steepest gradient algorithm that exploits the geometrical properties of orthogonal matrices as a Lie group. The proposed algorithm has low complexity and can be easily applied to an arbitrary MIMO configuration. We also confirm numerically that the proposed orthogonal precoding outperforms UPIF type II in some scenarios and the X-precoder in high-order QAM schemes, e.g., $64$- and $256$-QAM.

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arXiv2018

A Neural Network Lattice Decoding Algorithm

Neural network decoding algorithms are recently introduced by Nachmani et al. to decode high-density parity-check (HDPC) codes. In contrast with iterative decoding algorithms such as sum-product or min-sum algorithms in which the weight of each edge is set to $1$, in the neural network decoding algorithms, the weight of every edge depends on its impact in the transmitted codeword. In this paper, we provide a novel \emph{feed-forward neural network lattice decoding algorithm} suitable to decode lattices constructed based on Construction A, whose underlying codes have HDPC matrices. We first establish the concept of feed-forward neural network for HDPC codes and improve their decoding algorithms compared to Nachmani et al. We then apply our proposed decoder for a Construction A lattice with HDPC underlying code, for which the well-known iterative decoding algorithms show poor performances. The main advantage of our proposed algorithm is that instead of assigning and training weights for all edges, which turns out to be time-consuming especially for high-density parity-check matrices, we concentrate on edges which are present in most of $4$-cycles and removing them gives a girth-$6$ Tanner graph. This approach, by slight modifications using updated LLRs instead of initial ones, simultaneously accelerates the training process and improves the error performance of our proposed decoding algorithm.

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arXiv2018

Full-Diversity Space-Time Block Codes for Integer-Forcing Linear Receivers

In multiple-input multiple-output (MIMO) fading channels, the design criterion for full-diversity space-time block codes (STBCs) is primarily determined by the decoding method at the receiver. Although constructions of STBCs have predominantly matched the maximum-likelihood (ML) decoder, design criteria and constructions of full-diversity STBCs have also been reported for low-complexity linear receivers. A new receiver architecture called Integer-Forcing (IF) linear receiver has been proposed to MIMO channels by Zhan et al. which showed promising results for the high-rate V-BLAST encoding scheme. In this paper, we address the design of full-diversity STBCs for IF linear receivers. In particular, we are interested in characterizing the structure of STBCs that provide full-diversity with the IF receiver. Along that direction, we derive an upper bound on the probability of decoding error, and show that STBCs that satisfy the restricted non-vanishing singular value (RNVS) property provide full-diversity for the IF receiver. Furthermore, we prove that all known STBCs with the non-vanishing determinant property provide full-diversity with IF receivers, as they guarantee the RNVS property. By using the formulation of RNVS property, we also prove the existence of a full-diversity STBC outside the class of perfect STBCs, thereby adding significant insights compared to the existing works on STBCs with IF decoding. Finally, we present extensive simulation results to demonstrate that linear designs with RNVS property provide full-diversity for IF receiver.

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arXiv2017

Integer-Forcing Linear Receivers: A Design Criterion for Full-Diversity STBCs

In multiple-input multiple-output (MIMO) fading channels, the design criterion for full-diversity space-time block codes (STBCs) is primarily determined by the decoding method at the receiver. Although constructions of STBCs have predominantly matched the maximum-likelihood (ML) decoder, design criteria and constructions of full-diversity STBCs have also been reported for low-complexity linear receivers. A new receiver architecture called Integer-Forcing (IF) linear receiver has been proposed to MIMO channels by Zhan et al. which showed promising results for the high-rate V-BLAST encoding scheme. In this work we address the design of full-diversity STBCs for IF linear receivers. We derive an upper bound on the probability of decoding error, and show that STBCs that satisfy the non-vanishing singular value (NVS) property provide full-diversity for the IF receiver. We also present simulation results to demonstrate that linear designs with NVS property provide full diversity for IF receiver. As a special case of our analysis on STBCs, we present an upper bound on the error probability for the V-BLAST architecture presented by Zhan \emph{et al.}, and demonstrate that the IF linear receivers provide full receive diversity. Our results supplement the existing outage probability based results for the IF receiver.

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