Huishuai Zhang

The Capacity Region of the Source-Type Model for Secret Key and Private Key Generation

The problem of simultaneously generating a secret key (SK) and private key (PK) pair among three terminals via public discussion is investigated. In this problem, each terminal observes a component of correlated sources. All three terminals are required to generate the common SK to be concealed from an eavesdropper that has access to the public discussion, while two designated terminals are required to generate an extra PK to be concealed from both the eavesdropper and the remaining terminal. An outer bound on the SK-PK capacity region was established by Ye and Narayan, and was shown to be achievable for a special case. In this paper, the SK-PK capacity region is established in general by developing schemes to achieve the outer bound for the remaining two cases. The main technique lies in the novel design of a random binning-joint decoding scheme that achieves the existing outer bound.

Secret key capacity: Talk or keep silent?

The problem of when all terminals must talk to achieve the secrecy capacity in the multiterminal source model is investigated. Two conditions under which respectively a given terminal does not need to and must talk to achieve the secrecy capacity are characterized. The cases when all terminals must talk to achieve secrecy capacity are shown to be many more than those conjectured in [1] for systems with four or more terminals. There is a gap between the above two conditions, in which whether a given terminal need to talk is not clear. A conjecture is further made in order to narrow down the gap.

Secret key-private key generation over three terminals: Capacity region

The problem of simultaneously generating a secret key (SK) and private key (PK) pair among three terminals via public discussion is investigated, in which each terminal observes a component of correlated sources. All three terminals are required to generate a common secret key concealed from an eavesdropper that has access to public discussion, while two designated terminals are required to generate an extra private key concealed from both the eavesdropper and the remaining terminal. An outer bound on the SK-PK capacity region was established in [1], and was shown to be achievable for one case. In this paper, achievable schemes are designed to achieve the outer bound for the remaining two cases, and hence the SK-PK capacity region is established in general. The main technique lies in the novel design of a random binning-joint decoding scheme that achieves the existing outer bound.

Key capacity region for a cellular source model

A cellular source model for key generation is proposed and studied, in which a central terminal χ₀ wishes to generate K₁ with terminal χ₁ and K₂ with terminal χ₂, respectively, via public discussion. Each terminal observes a component of a correlated source sequence. The K₁ is required to be concealed from an eavesdropper that has access to the public discussion, while the key K₂ needs to be concealed from both the eavesdropper and terminal χ₁. The key capacity region is established by showing that the cut-set upper bound is achievable.

Non-convex low-rank matrix recovery from corrupted random linear measurements

Recent work has demonstrated the effectiveness of gradient descent for recovering low-rank matrices from random linear measurements in a globally convergent manner. However, their performance is highly sensitive in the presence of outliers that may take arbitrary values, which is common in practice. In this paper, we propose a truncated gradient descent algorithm to improve the robustness against outliers, where the truncation is performed to rule out the contributions from samples that deviate significantly from the sample median. A restricted isometry property regarding the sample median is introduced to provide a theoretical footing of the proposed algorithm for the Gaussian orthogonal ensemble. Extensive numerical experiments are provided to validate the superior performance of the proposed algorithm.

Geometrical properties and accelerated gradient solvers of non-convex phase retrieval

We consider recovering a signal x ∈ ℝn from the magnitudes of Gaussian measurements by minimizing a second order yet non-smooth loss function. By exploiting existing concentration results of the loss function, we show that the non-convex loss function satisfies several quadratic geometrical properties. Based on these geometrical properties, we characterize the linear convergence of the sequence of function graph generated by the gradient flow on minimizing the loss function. Furthermore, we propose an accelerated version of the gradient flow, and establish an in-exact linear convergence of the generated sequence of function graph by exploiting the quadratic geometries of the loss function. Then, we verify the numerical advantages of the proposed algorithms over other state-of-art algorithms.

Helper-assisted asymmetric two key generation

The problem of simultaneously generating an asymmetric key pair with assistance of a helper is studied. In this setting, each of four terminals, i.e., a base station X₀, two cellular nodes X₁ and X₂, and a helper X₃, observes a component of correlated sources. The cellular nodes X₁ and X₂ wish to generate secret keys K₁ and K₂ with the base station X₀, respectively, under the help of terminal X₃. Both keys should be concealed from an eavesdropper that has access to the public discussion, while K₂ is also required to be concealed from terminal X₁. An outer bound on the key capacity region is derived. It is shown to be achievable under certain condition, and hence the key capacity region is characterized under such condition.

On Compressive orthonormal Sensing

The Compressive Sensing (CS) approach for recovering sparse signal with orthonormal measurements has been studied under various notions of coherence. However, existing notions of coherence either do not exploit the structure of the underlying signal, or are too complicated to provide an explicit sampling scheme for all orthonormal basis sets. Consequently, there is lack of understanding of key factors that guide the sampling of CS with orthonormal measurements and achieve as low sample complexity as possible. In this paper, we introduce a new notion of π-coherence that exploits both the sparsity structure of the signal and the local coherence. Based on π-coherence, we propose a sampling scheme that is adapted to the underlying true signal and is applicable for CS under all orthonormal basis. Our scheme outperforms (up to a constant factor) existing sampling schemes for orthonormal measurements, and achieves a near-optimal sample complexity (up to certain logarithm factors) for several popular choices of orthonormal basis. Furthermore, we characterize the necessary conditions on the sampling schemes for CS with orthonormal measurements. We then propose a practical multi-phase implementation of our sampling scheme, and verify its advantage over existing sampling schemes via application to magnetic resonance imaging (MRI) in medical science.

Two-key generation for a cellular model with a helper

The problem of simultaneously generating two keys for a cellular model is investigated, in which each of four terminals, X₀, X₁, X₂, and X₃ observes one component of correlated sources. The terminal X0 wishes to generate secret keys K₁ and K₂ respectively, with terminals X₁ and X₂ under the help of terminal X₃. They are allowed to communicate over a public channel. Both K₁ and K₂ are required to be concealed from an eavesdropper that has access to the public discussion. The key capacity region is established by designing a unified achievable strategy to achieve the cut-set outer bounds, which greatly simplifies the proof.