# Synthesizing Coupling Proofs of Differential Privacy

arXiv: https://arxiv.org/abs/1709.05361 · HTML: https://mlsanity.com/paper/1709.05361/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Sep 2017.

## Built on by (most cited first, 4 of 4)

- [Reproducibility in Learning](https://mlsanity.com/paper/2201.08430/) (2022)
- [The Hitchhiker's Guide to Efficient, End-to-End, and Tight DP Auditing](https://mlsanity.com/paper/2506.16666/) (2025)
- [Learning Differentially Private Mechanisms](https://mlsanity.com/paper/2101.00961/) (2021)
- [DPrivBench: Benchmarking LLMs' Reasoning for Differential Privacy](https://mlsanity.com/paper/2604.15851/) (2026)

## Abstract (arXiv)

Differential privacy has emerged as a promising probabilistic formulation of privacy, generating intense interest within academia and industry. We present a push-button, automated technique for verifying varepsilon-differential privacy of sophisticated randomized algorithms. We make several conceptual, algorithmic, and practical contributions: (i) Inspired by the recent advances on approximate couplings and randomness alignment, we present a new proof technique called coupling strategies, which casts differential privacy proofs as a winning strategy in a game where we have finite privacy resources to expend. (ii) To discover a winning strategy, we present a constraint-based formulation of the problem as a set of Horn modulo couplings (HMC) constraints, a novel combination of first-order Horn clauses and probabilistic constraints. (iii) We present a technique for solving HMC constraints by transforming probabilistic constraints into logical constraints with uninterpreted functions. (iv) Finally, we implement our technique in the FairSquare verifier and provide the first automated privacy proofs for a number of challenging algorithms from the differential privacy literature, including Report Noisy Max, the Exponential Mechanism, and the Sparse Vector Mechanism.