Bilinear Compressive Security

2025-10-17

AI Summary

Traditional compressive sensing (CS)-based secure transmission suffers from vulnerability to known-plaintext attacks, as a fixed measurement matrix enables full recovery of the $n$-column secret key $Q$ using only $n$ observations. To address this, we propose a bilinear compressive security mechanism: at the transmitter, the measurement matrix is convolved with a complex-valued random filter, and decryption employs a blind deconvolution framework. This design raises the minimum number of observations required for key recovery to $Omega(max(n, (n/s)^2))$, where $s$ denotes signal sparsity—rendering the scheme theoretically unbreakable when $s = 1$. Crucially, the method preserves low computational complexity while substantially enhancing resilience against known-plaintext attacks. Its efficiency and robustness make it particularly suitable for resource-constrained IoT secure communication scenarios.

Technology Category

• Machine Learning: Privacy
• Computer Vision: Adversarial Attacks & Robustness
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Security and Privacy: Large-scale security measurements
• Responsible Web: Measurement, analysis, and circumvention of Web censorship
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

Beyond its widespread application in signal and image processing, emph{compressed sensing} principles have been greatly applied to secure information transmission (often termed 'compressive security'). In this scenario, the measurement matrix $Q$ acts as a one time pad encryption key (in complex number domain) which can achieve perfect information-theoretic security together with other benefits such as reduced complexity and energy efficiency particularly useful in IoT. However, unless the matrix is changed for every message it is vulnerable towards known plain text attacks: only $n$ observations suffices to recover a key $Q$ with $n$ columns. In this paper, we invent and analyze a new method (termed 'Bilinear Compressive Security (BCS)') addressing these shortcomings: In addition to the linear encoding of the message $x$ with a matrix $Q$, the sender convolves the resulting vector with a randomly generated filter $h$. Assuming that $h$ and $x$ are sparse, the receiver can then recover $x$ without knowledge of $h$ from $y=h*Qx$ through blind deconvolution. We study a rather idealized known plaintext attack for recovering $Q$ from repeated observations of $y$'s for different, known $x_k$, with varying and unknown $h$ ,giving Eve a number of advantages not present in practice. Our main result for BCS states that under a weak symmetry condition on the filter $h$, recovering $Q$ will require extensive sampling from transmissions of $Ωleft(maxleft(n,(n/s)^2 ight) ight)$ messages $x_k$ if they are $s$-sparse. Remarkably, with $s=1$ it is impossible to recover the key. In this way, the scheme is much safer than standard compressed sensing even though our assumptions are much in favor towards a potential attacker.

Problem

• Enhancing security against known plaintext attacks in compressed sensing
• Introducing bilinear encoding with random filters for key protection
• Increasing required message samples for key recovery under sparse conditions

Innovation

• Bilinear encoding combines matrix multiplication and convolution
• Blind deconvolution enables message recovery without filter knowledge
• Sparse inputs require extensive sampling for key recovery