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

Elliptic Curve

Elliptic curve cryptography (ECC) has become a cornerstone in securing digital communications, thanks to its efficiency and robust security features. Kristin Lauter shares her journey from academia to industry, highlighting the transition from theoretical mathematics to practical cryptographic applications 1. She emphasizes the importance of understanding algorithmic complexity and real-world running times in deploying cryptographic systems. Her work at Microsoft Research played a pivotal role in standardizing ECC, which is now widely used to protect internet connections and digital identities 2.

I went from the math world where the average number of people that read a published math paper is like 0.8 and that includes the reviewer.

--- Kristin Lauter

Lauter also reflects on her teaching experiences, noting how cryptography excited her students more than traditional number theory, which fueled her passion for the field 3.

   

Isogeny-Based

Isogeny-based cryptography represents a promising frontier in the quest for secure cryptographic protocols, particularly in the post-quantum era. Kristin Lauter discusses the development of super singular isogeny graphs, which serve as the foundation for this cryptographic approach 4. These graphs are optimal expander graphs, making them highly resistant to known routing algorithms. Lauter explains the challenge of finding paths between nodes in these graphs, a problem that remains unsolved without additional information 5.

The hard problem is routing, like, given two nodes, how can you find a route?

--- Kristin Lauter

She also recounts the inspiration behind using these graphs for cryptographic hash functions, sparked by the breaking of the MD5 hash function in 2005 6.

   

Quantum Challenges

Quantum-resistant cryptography is a critical area of research as quantum computing threatens traditional cryptographic methods. Kristin Lauter highlights the need for innovative hard problems, such as those involving super singular isogeny graphs, to ensure security against quantum attacks 7. She notes the importance of not providing extra information in cryptographic protocols, as it can simplify attacks. Lauter also discusses the challenges of scaling cryptographic systems, particularly in the context of lattice-based cryptography and homomorphic encryption 8.

When you give extra information, you better be prepared that you're going to help an attacker break the system.

--- Kristin Lauter

Her team's work on attacking the Kyber post-quantum crypto scheme underscores the ongoing efforts to strengthen cryptographic defenses in the face of evolving threats.