# Differential Privacy on Finite Computers

arXiv: https://arxiv.org/abs/1709.05396 · HTML: https://mlsanity.com/paper/1709.05396/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Sep 2017.

## Built on by (most cited first, 8 of 8)

- [Private Convex Optimization via Exponential Mechanism](https://mlsanity.com/paper/2203.00263/) (2022)
- [Privacy Amplification via Compression: Achieving the Optimal Privacy-Accuracy-Communication Trade-off in Distributed Mean Estimation](https://mlsanity.com/paper/2304.01541/) (2023)
- [Fairness, Integrity, and Privacy in a Scalable Blockchain-based Federated Learning System](https://mlsanity.com/paper/2111.06290/) (2021)
- [Position: Certified Robustness Does Not (Yet) Imply Model Security](https://mlsanity.com/paper/2506.13024/) (2025)
- [Sparse Private LASSO Logistic Regression](https://mlsanity.com/paper/2304.12429/) (2023)
- [The Correlated Gaussian Sparse Histogram Mechanism](https://mlsanity.com/paper/2412.10357/) (2024)
- [Lumberjack: Better Differentially Private Random Forests through Heavy Hitter Detection in Trees](https://mlsanity.com/paper/2605.22756/) (2026)
- [Dithered Gaussian Mechanism for Randomness-Efficient Differential Privacy](https://mlsanity.com/paper/2607.06320/) (2026)

## Abstract (arXiv)

We consider the problem of designing and analyzing differentially private algorithms that can be implemented on em discrete models of computation in em strict polynomial time, motivated by known attacks on floating point implementations of real-arithmetic differentially private algorithms (Mironov, CCS 2012) and the potential for timing attacks on expected polynomial-time algorithms. As a case study, we examine the basic problem of approximating the histogram of a categorical dataset over a possibly large data universe X. The classic Laplace Mechanism (Dwork, McSherry, Nissim, Smith, TCC 2006 and J. Privacy & Confidentiality 2017) does not satisfy our requirements, as it is based on real arithmetic, and natural discrete analogues, such as the Geometric Mechanism (Ghosh, Roughgarden, Sundarajan, STOC 2009 and SICOMP 2012), take time at least linear in |X|, which can be exponential in the bit length of the input. In this paper, we provide strict polynomial-time discrete algorithms for approximate histograms whose simultaneous accuracy (the maximum error over all bins) matches that of the Laplace Mechanism up to constant factors, while retaining the same (pure) differential privacy guarantee. One of our algorithms produces a sparse histogram as output. Its "per-bin accuracy" (the error on individual bins) is worse than that of the Laplace Mechanism by a factor of log|X|, but we prove a lower bound showing that this is necessary for any algorithm that produces a sparse histogram. A second algorithm avoids this lower bound, and matches the per-bin accuracy of the Laplace Mechanism, by producing a compact and efficiently computable representation of a dense histogram, it is based on an (n+1)-wise independent implementation of an appropriately clamped version of the Discrete Geometric Mechanism.