The Gradient
The Gradient: Perspectives on AI
Kristin Lauter: Private AI, Homomorphic Encryption, and AI for Cryptography

Kristin Lauter: Private AI, Homomorphic Encryption, and AI for Cryptography

On developing cryptographic protocols, their mathematical foundations and real-world implementation, Private AI, and AI for cryptography.

Episode 129

I spoke with Kristin Lauter about:

  • Elliptic curve cryptography and homomorphic encryption

  • Standardizing cryptographic protocols

  • Machine Learning on encrypted data

  • Attacking post-quantum cryptography with AI

Enjoy—and let me know what you think!

Kristin is Senior Director of FAIR Labs North America (2022—present), based in Seattle. Her current research areas are AI4Crypto and Private AI. She joined FAIR (Facebook AI Research) in 2021, after 22 years at Microsoft Research (MSR). At MSR she was Partner Research Manager on the senior leadership team of MSR Redmond. Before joining Microsoft in 1999, she was Hildebrandt Assistant Professor of Mathematics at the University of Michigan (1996-1999). She is an Affiliate Professor of Mathematics at the University of Washington (2008—present). She received all her advanced degrees from the University of Chicago, BA (1990), MS (1991), PhD (1996) in Mathematics. She is best known for her work on Elliptic Curve Cryptography, Supersingular Isogeny Graphs in Cryptography, Homomorphic Encryption (, Private AI, and AI4Crypto. She served as President of the Association for Women in Mathematics from 2015-2017 and on the Council of the American Mathematical Society from 2014-2017.

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  • (00:00) Intro

  • (01:10) Llama 3 and encrypted data — where do we want to be?

  • (04:20) Tradeoffs: individual privacy vs. aggregated value in e.g. social media forums

    • (07:48) Kristin’s shift in views on privacy

  • (09:40) Earlier work on elliptic curve cryptography — applications and theory

    • (10:50) Inspirations from algebra, number theory, and algebraic geometry

    • (15:40) On algebra vs. analysis and on clear thinking

  • (18:38) Elliptic curve cryptography and security, algorithms and concrete running time

  • (21:31) Cryptographic protocols and setting standards

  • (26:36) Supersingular isogeny graphs (and higher-dimensional supersingular isogeny graphs)

  • (32:26) Hard problems for cryptography and finding new problems

  • (36:42) Guaranteeing security for cryptographic protocols and mathematical foundations

  • (40:15) Private AI: Crypto-Nets / running neural nets on homomorphically encrypted data

    • (42:10) Polynomial approximations, activation functions, and expressivity

    • (44:32) Scaling up, Llama 2 inference on encrypted data

  • (46:10) Transitioning between MSR and FAIR, industry research

  • (52:45) An efficient algorithm for integer lattice reduction (AI4Crypto)

    • (56:23) Local minima, convergence and limit guarantees, scaling

  • (58:27) SALSA: Attacking Lattice Cryptography with Transformers

    • (58:38) Learning With Errors (LWE) vs. standard ML assumptions

    • (1:02:25) Powers of small primes and faster learning

    • (1:04:35) LWE and linear regression on a torus

    • (1:07:30) Secret recovery algorithms and transformer accuracy

    • (1:09:10) Interpretability / encoding information about secrets

    • (1:09:45) Future work / scaling up

  • (1:12:08) Reflections on working as a mathematician among technologists


The Gradient
The Gradient: Perspectives on AI
Deeply researched, technical interviews with experts thinking about AI and technology. Hosted, recorded, researched, and produced by Daniel Bashir.