Cynthia Dwork: The Mathematics of Privacy

Explore the mathematics of privacy in this 40-minute lecture by Cynthia Dwork, presented by the International Mathematical Union. Delve into fundamental concepts such as the Law of Information Reconstruction and Privacy Preserving Data Analysis. Examine the principles of Differential Privacy, including its properties, the Laplace Mechanism, and the Privacy Loss Random Variable. Investigate advanced topics like the Advanced Composition Theorem, Gaussian Mechanism, and Concentrated Differential Privacy. Learn about Privacy Amplification via Subsampling and optimized private gradient descent techniques. Engage with creative privacy accounting thought experiments and explore the concept of amplification by secrecy of the journey. Conclude by addressing challenges and crucial definitions in the field of privacy mathematics.

Intro
Fundamental Law of Info Reconstruction • Overly accurate" estimates of too many" statistics is
Statistics 'Feel Private
Privacy Preserving Data Analysis
Differential Privacy M gives e-differential privacy if for all pairs of adjacent data
Some Properties of Differential Privacy
The Laplace Mechanism
The Privacy Loss Random Variable
Advanced Composition Theorem • Recall privacy loss is sometimes negative -- there is cancellation
Gaussian Mechanism
Concentrated Differential Privacy
Privacy Amplification via Subsampling
(6,8)-DP Projected Gradient Descent
Optimized Private Gradient Descent
Creative Privacy Accounting Thought Experiment: Consider two steps of Noisy-SGD with fixed sample order
Amplification by Secrecy of the Journey
Challenge
Crucial Definition
"Shift" Calculus