arXiv subjects

Rafael G. L. D'Oliveira

Publications and source records attributed to Rafael G. L. D'Oliveira.

At least 19 recordsLinked to original sources

arXiv2026

Low-Rank Masking for Single-Server Matrix Multiplication

We study the statistical privacy of outsourcing matrix multiplication over a finite field ${\mathbb F_q}$ to a single server using additive masks of rank at most $r$. For independent uniform $n\times n$ inputs, we show that uniform \emph{rank-ball masks} and products of independent uniform factors give maximal-correlation secrecy of at most $q^{-r}$ against the complete server view, with $O(n^2r)$ field operations for encoding and decoding. This secrecy captures how effectively the server is prevented from estimating functions of the inputs. We prove an asymptotically matching lower bound of this secrecy measure for $r=o(n)$, showing that both sampling methods are asymptotically optimal among input-independent additive masks of rank at most $r$, even when secret invertible transformations are allowed. We also characterize the posterior distribution for uniform rank-ball masks under arbitrary joint input distributions and prove approximate individual security for rows and columns under independent uniform inputs. Finally, we show that every input-independent additive mask of rank at most $r=o(n)$ requires $δ\to1$ in entry-level $(\varepsilon,δ)$-differential privacy for fixed field size $q$ and bounded $\varepsilon$.

cs.IT↗

arXiv2026

Function Tables for Secure Distributed Matrix Multiplication

We introduce function tables, an entrywise representation of the coefficient functions that appear in the worker responses of a secure distributed matrix multiplication (SDMM) scheme. We work under the outer-product partition, with $K$ row blocks, $L$ column blocks, and privacy against any $T$ colluding workers, in the general model of linear encoding and linear decoding. In this representation, privacy is a rank condition on the data and mask coefficients, and decodability is linear independence of the desired entries modulo the nuisance space. Degree tables, cyclic-addition tables, and algebraic-geometry constructions are the special cases obtained by restricting the coefficient functions to a structured family; we impose no such restriction, so our converses bind every linear scheme. For $T=1$, we determine the exact optimum over every finite field $\mathbb{F}_q$: it is $KL+K+L$ when $q\geq3$, and $KL+K+L+1$ over $\mathbb{F}_2$, where the identity $z^2=z$ forces one more worker. For arbitrary $T$, we prove $N\geq KL+K+L$ and $N\geq\max\{K,L\}+T$ with no MDS hypothesis on the masks; the first is stronger than the previously known bound $KL+\max\{K,L\}+2T-1$ whenever $\min\{K,L\}\geq2T$. We then reduce field feasibility exactly to MDS existence: a scheme exists over $\mathbb{F}_q$ if and only if an $[\max\{K,L\}+T,T]$ linear MDS code does, and whenever it does, a Cartesian construction attains $N=(K+T)(L+T)$ over that same field. For $T=2$ this makes $q\geq\max\{K,L\}+1$ necessary and sufficient, and we give a projective-line construction with $N=KL+K+L+2$ whenever $KL+K+L$ divides $q-1$; for $K,L\geq2$ it matches the best known worker count while requiring only an element of order $KL+K+L$.

cs.IT↗

arXiv2026

Improved Degree Tables for Secure Distributed Matrix Multiplication

In secure distributed matrix multiplication, a user wishes to compute the product of two matrices with the assistance of servers, in such a way that any $T$ colluding servers learn nothing about either matrix. Degree tables are a combinatorial tool for constructing polynomial codes for this problem and underlie several state-of-the-art schemes, including $\mathsf{GASP}_r$, $\mathsf{GASP}_{r,s}$, and $\mathsf{DOG}_{r,s}$. We introduce a periodic-gap framework for constructing degree tables that contains these three families as special cases and leads to two new constructions, $\mathsf{SHIFT}_{r,s}$ and $\mathsf{COVER}_r$. We determine their exact recovery thresholds and show that, in many cases, they outperform the current state of the art. We also prove a new lower bound on the recovery threshold of ordinary integer degree tables. In the balanced case, in which the partitioning parameters and the security parameter are equal, we sharpen this bound to match $\mathsf{SHIFT}_{r,s}$ up to lower-order terms, showing that it is asymptotically optimal among degree-table constructions.

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arXiv2025

Optimal Computational Secret Sharing

In $(t, n)$-threshold secret sharing, a secret $S$ is distributed among $n$ participants such that any subset of size $t$ can recover $S$, while any subset of size $t-1$ or fewer learns nothing about it. For information-theoretic secret sharing, it is known that the share size must be at least as large as the secret, i.e., $|S|$. When computational security is employed using cryptographic encryption with a secret key $K$, previous work has shown that the share size can be reduced to $\tfrac{|S|}{t} + |K|$. In this paper, we present a construction achieving a share size of $\tfrac{|S| + |K|}{t}$. Furthermore, we prove that, under reasonable assumptions on the encryption scheme -- namely, the non-compressibility of pseudorandom encryption and the non-redundancy of the secret key -- this share size is optimal.

cs.IT↗

arXiv2025

Compressed Private Aggregation for Scalable and Robust Federated Learning over Massive Networks

Federated learning (FL) is an emerging paradigm that allows a central server to train machine learning models using remote users' data. Despite its growing popularity, FL faces challenges in preserving the privacy of local datasets, its sensitivity to poisoning attacks by malicious users, and its communication overhead. The latter is additionally considerably dominant in large-scale networks. These limitations are often individually mitigated by local differential privacy (LDP) mechanisms, robust aggregation, compression, and user selection techniques, which typically come at the cost of accuracy. In this work, we present compressed private aggregation (CPA), that allows massive deployments to simultaneously communicate at extremely low bit rates while achieving privacy, anonymity, and resilience to malicious users. CPA randomizes a codebook for compressing the data into a few bits using nested lattice quantizers, while ensuring anonymity and robustness, with a subsequent perturbation to hold LDP. The proposed CPA is proven to result in FL convergence in the same asymptotic rate as FL without privacy, compression, and robustness considerations, while satisfying both anonymity and LDP requirements. These analytical properties are empirically confirmed in a numerical study, where we demonstrate the performance gains of CPA compared with separate mechanisms for compression and privacy for training different image classification models, as well as its robustness in mitigating the harmful effects of malicious users.

cs.CR↗

arXiv2025

An Efficient Hybrid Key Exchange Mechanism

We present \textsc{CHOKE}, a novel code-based hybrid key-encapsulation mechanism (KEM) designed to securely and efficiently transmit multiple session keys simultaneously. By encoding $n$ independent session keys with an individually secure linear code and encapsulating each resulting coded symbol using a separate KEM, \textsc{CHOKE} achieves computational individual security -- each key remains secure as long as at least one underlying KEM remains unbroken. Compared to traditional serial or combiner-based hybrid schemes, \textsc{CHOKE} reduces computational and communication costs by an $n$-fold factor. Furthermore, we show that the communication cost of our construction is optimal under the requirement that each KEM must be used at least once.

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arXiv2025

Cryptanalysis via Machine Learning Based Information Theoretic Metrics

The fields of machine learning (ML) and cryptanalysis share an interestingly common objective of creating a function, based on a given set of inputs and outputs. However, the approaches and methods in doing so vary vastly between the two fields. In this paper, we explore integrating the knowledge from the ML domain to provide empirical evaluations of cryptosystems. Particularly, we utilize information theoretic metrics to perform ML-based distribution estimation. We propose two novel applications of ML algorithms that can be applied in a known plaintext setting to perform cryptanalysis on any cryptosystem. We use mutual information neural estimation to calculate a cryptosystem's mutual information leakage, and a binary cross entropy classification to model an indistinguishability under chosen plaintext attack (CPA). These algorithms can be readily applied in an audit setting to evaluate the robustness of a cryptosystem and the results can provide a useful empirical bound. We evaluate the efficacy of our methodologies by empirically analyzing several encryption schemes. Furthermore, we extend the analysis to novel network coding-based cryptosystems and provide other use cases for our algorithms. We show that our classification model correctly identifies the encryption schemes that are not IND-CPA secure, such as DES, RSA, and AES ECB, with high accuracy. It also identifies the faults in CPA-secure cryptosystems with faulty parameters, such a reduced counter version of AES-CTR. We also conclude that with our algorithms, in most cases a smaller-sized neural network using less computing power can identify vulnerabilities in cryptosystems, providing a quick check of the sanity of the cryptosystem and help to decide whether to spend more resources to deploy larger networks that are able to break the cryptosystem.

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arXiv2024

A Monotone Circuit Construction for Individually-Secure Multi-Secret Sharing

In this work, we introduce a new technique for taking a single-secret sharing scheme with a general access structure and transforming it into an individually secure multi-secret sharing scheme where every secret has the same general access structure. To increase the information rate, we consider Individual Security which guarantees zero mutual information with each secret individually, for any unauthorized subsets. Our approach involves identifying which shares of the single-secret sharing scheme can be replaced by linear combinations of messages. When $m-1$ shares are replaced, our scheme obtains an information rate of $m/|S|$, where $S$ is the set of shares. This provides an improvement over the information rate of $1/|S|$ in the original single-secret sharing scheme.

cs.IT↗

arXiv2024

Secure Distributed Matrix Multiplication with Precomputation

We consider the problem of secure distributed matrix multiplication in which a user wishes to compute the product of two matrices with the assistance of honest but curious servers. We show how to construct polynomial schemes for the outer product partitioning which take advantage of the user's ability to precompute, and provide bounds for our technique. We show that precomputation allows for a reduction in the order of the time complexity for the cases where the number of colluding servers is a fixed percentage of the number of servers. Furthermore, with precomputation, any percentage (less than 100%) of collusions can be tolerated, compared to the upper limit of 50% for the case without precomputation.

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arXiv2024

Leveraging AES Padding: dBs for Nothing and FEC for Free in IoT Systems

The Internet of Things (IoT) represents a significant advancement in digital technology, with its rapidly growing network of interconnected devices. This expansion, however, brings forth critical challenges in data security and reliability, especially under the threat of increasing cyber vulnerabilities. Addressing the security concerns, the Advanced Encryption Standard (AES) is commonly employed for secure encryption in IoT systems. Our study explores an innovative use of AES, by repurposing AES padding bits for error correction and thus introducing a dual-functional method that seamlessly integrates error-correcting capabilities into the standard encryption process. The integration of the state-of-the-art Guessing Random Additive Noise Decoder (GRAND) in the receiver's architecture facilitates the joint decoding and decryption process. This strategic approach not only preserves the existing structure of the transmitter but also significantly enhances communication reliability in noisy environments, achieving a notable over 3 dB gain in Block Error Rate (BLER). Remarkably, this enhanced performance comes with a minimal power overhead at the receiver - less than 15% compared to the traditional decryption-only process, underscoring the efficiency of our hardware design for IoT applications. This paper discusses a comprehensive analysis of our approach, particularly in energy efficiency and system performance, presenting a novel and practical solution for reliable IoT communications.

cs.ET↗

arXiv2024

Error Correction Capabilities of Non-Linear Cryptographic Hash Functions

Linear hashes are known to possess error-correcting capabilities. However, in most applications, non-linear hashes with pseudorandom outputs are utilized instead. It has also been established that classical non-systematic random codes, both linear and non-linear, are capacity achieving in the asymptotic regime. Thus, it is reasonable to expect that non-linear hashes might also exhibit good error-correcting capabilities. In this paper, we show this to be the case. Our proof is based on techniques from multiple access channels. As a consequence, we show that Systematic Random Non-Linear Codes (S-RNLC) are capacity achieving in the asymptotic regime. We validate our results by comparing the performance of the Secure Hash Algorithm (SHA) with that of Systematic Random Linear Codes (SRLC) and S-RNLC, demonstrating that SHA performs equally.

cs.IT↗

arXiv2024

Generalized Rainbow Differential Privacy

We study a new framework for designing differentially private (DP) mechanisms via randomized graph colorings, called rainbow differential privacy. In this framework, datasets are nodes in a graph, and two neighboring datasets are connected by an edge. Each dataset in the graph has a preferential ordering for the possible outputs of the mechanism, and these orderings are called rainbows. Different rainbows partition the graph of connected datasets into different regions. We show that if a DP mechanism at the boundary of such regions is fixed and it behaves identically for all same-rainbow boundary datasets, then a unique optimal $(ε,δ)$-DP mechanism exists (as long as the boundary condition is valid) and can be expressed in closed-form. Our proof technique is based on an interesting relationship between dominance ordering and DP, which applies to any finite number of colors and for $(ε,δ)$-DP, improving upon previous results that only apply to at most three colors and for $ε$-DP. We justify the homogeneous boundary condition assumption by giving an example with non-homogeneous boundary condition, for which there exists no optimal DP mechanism.

cs.CR↗

arXiv2023

Optimal Binary Differential Privacy via Graphs

We present the notion of \emph{reasonable utility} for binary mechanisms, which applies to all utility functions in the literature. This notion induces a partial ordering on the performance of all binary differentially private (DP) mechanisms. DP mechanisms that are maximal elements of this ordering are optimal DP mechanisms for every reasonable utility. By looking at differential privacy as a randomized graph coloring, we characterize these optimal DP in terms of their behavior on a certain subset of the boundary datasets we call a boundary hitting set. In the process of establishing our results, we also introduce a useful notion that generalizes DP conditions for binary-valued queries, which we coin as suitable pairs. Suitable pairs abstract away the algebraic roles of $\varepsilon,δ$ in the DP framework, making the derivations and understanding of our proofs simpler. Additionally, the notion of a suitable pair can potentially capture privacy conditions in frameworks other than DP and may be of independent interest.

cs.IT↗

arXiv2023

CRYPTO-MINE: Cryptanalysis via Mutual Information Neural Estimation

The use of Mutual Information (MI) as a measure to evaluate the efficiency of cryptosystems has an extensive history. However, estimating MI between unknown random variables in a high-dimensional space is challenging. Recent advances in machine learning have enabled progress in estimating MI using neural networks. This work presents a novel application of MI estimation in the field of cryptography. We propose applying this methodology directly to estimate the MI between plaintext and ciphertext in a chosen plaintext attack. The leaked information, if any, from the encryption could potentially be exploited by adversaries to compromise the computational security of the cryptosystem. We evaluate the efficiency of our approach by empirically analyzing multiple encryption schemes and baseline approaches. Furthermore, we extend the analysis to novel network coding-based cryptosystems that provide individual secrecy and study the relationship between information leakage and input distribution.

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arXiv2023

CERMET: Coding for Energy Reduction with Multiple Encryption Techniques -- $It's\ easy\ being\ green$

This paper presents CERMET, an energy-efficient hardware architecture designed for hardware-constrained cryptosystems. CERMET employs a base cryptosystem in conjunction with network coding to provide both information-theoretic and computational security while reducing energy consumption per bit. This paper introduces the hardware architecture for the system and explores various optimizations to enhance its performance. The universality of the approach is demonstrated by designing the architecture to accommodate both asymmetric and symmetric cryptosystems. The analysis reveals that the benefits of this proposed approach are multifold, reducing energy per bit and area without compromising security or throughput. The optimized hardware architectures can achieve below 1 pJ/bit operations for AES-256. Furthermore, for a public key cryptosystem based on Elliptic Curve Cryptography (ECC), a remarkable 14.6X reduction in energy per bit and a 9.3X reduction in area are observed, bringing it to less than 1 nJ/bit.

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arXiv2023

A Non-Asymptotic Analysis of Mismatched Guesswork

The problem of mismatched guesswork considers the additional cost incurred by using a guessing function which is optimal for a distribution $q$ when the random variable to be guessed is actually distributed according to a different distribution $p$. This problem has been well-studied from an asymptotic perspective, but there has been little work on quantifying the difference in guesswork between optimal and suboptimal strategies for a finite number of symbols. In this non-asymptotic regime, we consider a definition for mismatched guesswork which we show is equivalent to a variant of the Kendall tau permutation distance applied to optimal guessing functions for the mismatched distributions. We use this formulation to bound the cost of guesswork under mismatch given a bound on the total variation distance between the two distributions.

cs.IT↗

arXiv2023

PEOPL: Characterizing Privately Encoded Open Datasets with Public Labels

Allowing organizations to share their data for training of machine learning (ML) models without unintended information leakage is an open problem in practice. A promising technique for this still-open problem is to train models on the encoded data. Our approach, called Privately Encoded Open Datasets with Public Labels (PEOPL), uses a certain class of randomly constructed transforms to encode sensitive data. Organizations publish their randomly encoded data and associated raw labels for ML training, where training is done without knowledge of the encoding realization. We investigate several important aspects of this problem: We introduce information-theoretic scores for privacy and utility, which quantify the average performance of an unfaithful user (e.g., adversary) and a faithful user (e.g., model developer) that have access to the published encoded data. We then theoretically characterize primitives in building families of encoding schemes that motivate the use of random deep neural networks. Empirically, we compare the performance of our randomized encoding scheme and a linear scheme to a suite of computational attacks, and we also show that our scheme achieves competitive prediction accuracy to raw-sample baselines. Moreover, we demonstrate that multiple institutions, using independent random encoders, can collaborate to train improved ML models.

cs.LG↗

arXiv2022

AES as Error Correction: Cryptosystems for Reliable Communication

In this paper, we show that the Advanced Encryption Standard (AES) cryptosystem can be used as an error-correcting code to obtain reliability over noisy communication and data systems. Moreover, we characterize a family of computational cryptosystems that can potentially be used as well performing error correcting codes. In particular, we show that simple padding followed by a cryptosystem with uniform or pseudo-uniform outputs can approach the error-correcting performance of random codes. We empirically contrast the performance of the proposed approach using AES as error correction with that of Random Linear Codes and CA-Polar codes and show that in practical scenarios, they achieve almost the same performance. Finally, we present a modified counter mode of operation, named input plaintext counter mode, in order to utilize AES for multiple blocks while retaining its error correcting capabilities.

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