Hongchao Zhou

Efficient homomorphic encryption on integer vectors and its applications

Homomorphic encryption, aimed at enabling computation in the encrypted domain, is becoming important to a wide and growing range of applications, from cloud computing to distributed sensing. In recent years, a number of approaches to fully (or nearly fully) homomorphic encryption have been proposed, but to date the space and time complexity of the associated schemes has precluded their use in practice. In this work, we demonstrate that more practical homomorphic encryption schemes are possible when we require that not all encrypted computations be supported, but rather only those of interest to the target application. More specifically, we develop a homomorphic encryption scheme operating directly on integer vectors that supports three operations of fundamental interest in signal processing applications: addition, linear transformation, and weighted inner products. Moreover, when used in combination, these primitives allow us to efficiently and securely compute arbitrary polynomials. Some practically relevant examples of the computations supported by this framework are described, including feature extraction, recognition, classification, and data aggregation.

Layered schemes for large-alphabet secret key distribution

We discuss the design of practical codes for large-alphabet secret key distribution, motivated by the application of high-dimensional quantum key distribution. We introduce and study a simple scheme called layered scheme, which can be treated as a variant of coded modulation. The idea of layered schemes is to first split the observed large-alphabet symbols into bit layers, and to then encode all the bit layers either independently or jointly using binary codes. The channels that we are interested in are more general than the AWGN channels or Rayleigh fading channels studied in coded modulation. We present and compare different implementations of layered schemes, i.e., based on independent parallel encoding or joint encoding, and we investigate different approaches in how to map large-alphabet symbols into bit layers. Both theoretical analyses and simulation results show that layered schemes have good performances on q-ary channels such as uniform-error channels and limited-magnitude-error channels.

A simple class of efficient compression schemes supporting local access and editing

In this paper, we study the problem of compressing a collection of sequences of variable length that allows us to efficiently add, read, or edit an arbitrary sequence without decompressing the whole data. This problem has important applications in data servers, file-editing systems, and bioinformatics. We propose a novel and practical compression scheme, which shows that, by paying a small price in storage space (3% extra storage space in our examples), we can retrieve or edit a sequence (a few hundred bits) by accessing compressed bits close to the entropy of the sequence.

Adaptive pulse-position modulation for high-dimensional quantum key distribution

High-dimensional quantum key distribution (QKD) systems that exploit temporal correlation among entangled photons are of growing practical interest. In such systems, the observation time is typically partitioned into frames of fixed duration, with pulse-position modulation (PPM) coding used within each frame, via which a secret key is established between the parties. Such schemes can be very inefficient in their use of photons, since only a fraction of the frames can be used. As an alternative, we describe an efficient class of schemes with adaptive frame size whose performance can converge to the fundamental limit much more quickly. We analyze and compare the performances of both fixed and adaptive PPM schemes, taking into account photon transmission and detection losses. Further numerical results reveal the significant performance gain of adaptive PPM relative to fixed PPM.

High-dimensional time-energy entanglement-based quantum key distribution using dispersive optics

We implement a high-dimensional quantum key distribution protocol secure against collective attacks. We transform between conjugate measurement bases using group velocity dispersion. We obtain > 3 secure bits per photon coincidence.

Low-density random matrices for secret key extraction

Secret key extraction, the task of extracting a secret key from shared information that is partially known by an eavesdropper, has important applications in cryptography. Motivated by the requirements of high-speed quantum key distribution, we study secret-key extraction methods with simple and efficient hardware implementations, in particular, linear transformations based on low-density random matrices. We show that this method can achieve the information-theoretic upper bound (conditional Shannon entropy) on efficiency for a wide range of key-distribution systems. In addition, we introduce a numerical method that allows us to tightly estimate the quality of the generated secret key in the regime of finite block length, and use this method to demonstrate that low-density random matrices achieve very high performance for secret key extraction.

On-Off Keying Communication Over Optical Channels With Crosstalk

We investigate the fundamental limits of communication over optical on-off-keying channels with crosstalk, where a light pulse may span over multiple time slots or spatial pixels, and the receiver is equipped with single-photon detectors. First, we analyze achievable rates of communication over such channels, and observe that increasing transmission power (expected number of photons emitted per slot or pixel) does not necessarily lead to higher rates. Under simple but reasonable models, the highest rates are often achieved in a low-photon regime, with an average of 3 to 7 photons received in each slot or pixel. We further characterize the tradeoff between information rate and photon efficiency (in terms of the expected number of bits transmitted per photon) in the presence of crosstalk. Finally, we develop guidelines for slot length and pixel size selection for different application scenarios. Our analysis reveals that optimum optical-communication systems do not minimize the level of crosstalk.

On the Limits of Communication over Optical On-Off Keying Channels with Crosstalk

In this paper, we investigate the limits of communication over optical on-off-keying channels with 1-D or 2-D crosstalk, where photons are transferable between adjacent time slots or spatial pixels, and the receiver is equipped with single-photon detectors.We observe that high transmission power (measured by the expected number of photons emitted in each signal slot or pixel) may not lead to high information rate; the maximum capacity is typically achieved in a low-photon regime - with about expected 3 to 8 photons received in each signal slot or pixel. Furthermore, we study the selection of slot length for maximizing the channel bandwidth, as the slot length affects the crosstalk probability and hence the channel capacity. It reveals that optimum optical-communication systems do not minimize the level of crosstalk between slots or pixels.