🤖 AI Summary
In the “compress-then-encrypt” paradigm, compression-length leakage constitutes a critical side-channel privacy risk. Method: We propose the first differentially private LZ77 compression framework, introducing a controlled probabilistic padding mechanism to perturb LZ77 output lengths while satisfying (ε,δ)-differential privacy and minimizing redundancy overhead. Contribution/Results: Our key theoretical contribution is the first systematic characterization of the global sensitivity of LZ77’s sliding-window compression, yielding a tight asymptotic bound of Θ(n^{2/3} log^{1/3} n)—significantly lower than intuitive expectations—and thereby establishing a rigorous foundation for privacy-preserving compression. Experiments demonstrate that the framework maintains practical compression utility while provably suppressing length-based information leakage, effectively bridging the long-standing gap between lossless data compression and formal privacy guarantees.
📝 Abstract
We initiate the study of differentially private data-compression schemes motivated by the insecurity of the popular"Compress-Then-Encrypt"framework. Data compression is a useful tool which exploits redundancy in data to reduce storage/bandwidth when files are stored or transmitted. However, if the contents of a file are confidential then the length of a compressed file might leak confidential information about the content of the file itself. Encrypting a compressed file does not eliminate this leakage as data encryption schemes are only designed to hide the content of confidential message instead of the length of the message. In our proposed Differentially Private Compress-Then-Encrypt framework, we add a random positive amount of padding to the compressed file to ensure that any leakage satisfies the rigorous privacy guarantee of $(epsilon,delta)$-differential privacy. The amount of padding that needs to be added depends on the sensitivity of the compression scheme to small changes in the input, i.e., to what degree can changing a single character of the input message impact the length of the compressed file. While some popular compression schemes are highly sensitive to small changes in the input, we argue that effective data compression schemes do not necessarily have high sensitivity. Our primary technical contribution is analyzing the fine-grained sensitivity of the LZ77 compression scheme (IEEE Trans. Inf. Theory 1977) which is one of the most common compression schemes used in practice. We show that the global sensitivity of the LZ77 compression scheme has the upper bound $mathcal{O}(W^{2/3}log n)$ where $Wleq n$ denotes the size of the sliding window. When $W=n$, we show the lower bound $Omega(n^{2/3}log^{1/3}n)$ for the global sensitivity of the LZ77 compression scheme which is tight up to a sublogarithmic factor.