As I write this, I am on my way to the Toronto International Film Festival for the premiere of Werner Herzog’s new documentary “Theater of Thought,” about the brain and emerging neurotechnology — a documentary that includes an interview with me. My interview focuses on the encryption technologies I developed for protecting health and genomic privacy, because they could be relevant tools for protecting brain signal privacy and neurorights.
I have not seen the film yet, but it is an art film about science made for the general public, so how bad could it be? I certainly enjoyed being interviewed for the film and having the opportunity to talk about my love of mathematics.
The Early Days
I loved doing math problems as a child, especially story problems with my dad while driving to our remote summer cabin in northern Wisconsin. I was lucky to have teachers in grade school who let me work through math textbooks on my own; consequently, I ended up several years ahead in math going into high school. This, along with an overload of classes, allowed me to graduate from high school when I was 15.
My father was the Dean of Students at a small Midwestern liberal arts college in Appleton, Wisconsin. We lived in the dean’s house next to campus, so I grew up accompanying my dad to college events, including weekly meetings of the international student club, where I met students from all around the world. My mother was a professor at the University of Wisconsin-Green Bay, where she founded one of the earliest women’s studies programs in the country, along with leading many other interdisciplinary programs, including one on Native American studies.
Before heading to college at the University of Chicago, I took a year off to travel with my family to Kassel, Germany, where my mother was an exchange professor (Austausch Professorin) for a year. I attended the 13th grade at Wilhelm’s Gymnasium, “majoring” in math and French, and studied Italian in the evenings at the local university.
This valuable experience allowed me to make friends, embed in another culture, travel abroad, and work on perfecting my German. I loved learning languages, and success navigating the translation between German and French and Italian gave me confidence which carried me into college at the age of 16.
The math curriculum at the University of Chicago was very theoretical, and in my first quarter there, I tried to drop out of my Honors Calculus class. In a stroke of good fortune, my professor was Jill Pipher, and she wouldn’t sign my drop slip. I was one of the few girls in the class, and she asked me why I wanted to drop out. I told her I didn’t understand all the epsilons and deltas, and she replied, “That’s ok, nobody else does either.”
So she saved me from falling victim to the disparity in confidence between girls and boys, and I continued on to love the class and become a math major. Jill is now vice president of research at Brown University, past president of the American Mathematical Society, and the first woman to direct one of the NSF Math Institutes, the Institute for Computational and Experimental Research in Mathematic (ICERM). She was the only female math teacher or professor I ever had.
Outside of class, I played viola in the symphony and joined the nascent women’s varsity soccer team, becoming co-captain and UAA all-conference in my third year.
I did not know that going to graduate school in math was an option, and I had a rebellious idea to become an airline stewardess (maybe because I loved to travel?). Again, I was lucky, because my third-year Honors Algebra professor, Niels Nygaard, suggested that I apply to PhD programs in math. I spent my fourth year in college on the Paris study-abroad program, and he helped me find advanced courses in number theory at University of Paris XI (Orsay), which later inspired my direction in research.
I was happy to be accepted to the PhD program at Chicago and to return there to a familiar setting. I survived graduate school thanks to four main factors: working together on problem-solving with fellow classmates; finding satisfaction in teaching math courses for undergraduates; discovering fun and community through organizing the women graduate students in physical sciences into intramural soccer and basketball teams; and being supported by my PhD advisor, Niels Nygaard.
Thanks to my positive experience teaching math courses as a graduate student (I won a teaching award), I thought the next stage in my career would be as a college math professor coaching women’s soccer. However, I was not offered a math professor or soccer coach position at the small Midwestern colleges to which I applied. Instead, I was offered a Hildebrandt Research Assistant Professor position at the University of Michigan and a year-long visiting researcher position at the Max Planck Institute (MPI) in Germany. The perfect chance to return to Germany and travel extensively to conferences in my field!
I had met Tom Passananti in my first year of graduate school at Chicago. He was pursuing his PhD in Latin American history, with a focus on Mexico. We were married in 1997, during the year at Max Planck, while living in Bonn, Germany. We enjoyed biking together along the Rhine and Mosel rivers, playing soccer, and exploring Europe, including our honeymoon in Rome.
The research communities in both MPI and Michigan were outstanding and stimulating, and I began to work with Jean-Pierre Serre, 1954 Fields Medalist and noted leader of 20th century mathematics in France, at the College de France in Paris. I published two papers, supported by an Association for Women in Mathematics Mentoring grant, with his letters as appendices.
I was less thrilled with the attitude toward teaching excellence in the academic math research community; it was not considered an essential job requirement, nor apparently, was clear communication. At Michigan, I developed a new course on the mathematics of error-correcting codes and cryptography. It was an exciting time for advances and applications of error-correction, with the emergence of the CDMA (Code Division Multiple Access) technology and the founding of Qualcomm.
I met many engineering PhD students and professors thanks to teaching that course, and became interested in finding out more about how math was used in the real world. That curiosity led me to Microsoft Research, where I was recruited to work on elliptic curve cryptography for secure communication, connection, and commerce.
Cryptography
I like to joke that I am a mathematician masquerading as a computer scientist, which is not really a joke. When I moved to join the cryptography research group at Microsoft Research in 1999, I immersed myself in an industry research lab surrounded by many of the leading researchers in computer science in the world.
Cryptography is the science of keeping secrets, securing communication, and managing identity and access — in other words, an essential piece of the foundation of secure e-commerce and global digital communication worldwide. I knew and had taught about the mathematical foundations of cryptography, based on hard problems in number theory, but I had to ramp up quickly on the computer science and engineering side.
I learned complexity theory and provable security models, and I gradually shifted my mental outlook to that of an “algorithmic” number theorist who cares about running times and storage costs of algorithms at scale and about engineering efficient, stable, and useable deployments of systems and protocols.
Industry research provided a wealth of new research problems and directions, and I loved the opportunity to connect with a wider audience about my research. After filing a patent application on an invention in my first year, I was asked to explain elliptic curve cryptography in detail to patent attorneys and to various (somewhat less enthusiastic) executives.
Friend and mentor Dottie Hanck, vice chair in the Department of Medicine at the University of Chicago, gave me good advice: figure out what is important for the business and pitch your contributions in that context. I found it a refreshing change from the academic community for two reasons: clear communication was an essential and highly valued skill, and it was possible to argue for the importance of your work in terms of its impact on the world, and on the business, not just based on how it fits into the hierarchy of work and theorems by old or dead white men. I felt that this helped to level the playing field somewhat for women, and I embraced the opportunity to advance and excel.
Elliptic Curve Cryptography
During my first five years at Microsoft Research I worked closely with Peter Montgomery on building and shipping elliptic curve cryptography (ECC) at Microsoft (1999-2005). (I wrote about this work in a memorial article for Peter in the Notices of the American Mathematical Society.(1))
We met weekly with engineering teams across the company, and starting with Windows Vista around 2005, ECC was rolled out as part of the Crypto Next Generation suite of algorithms in the operating system, to enable cryptographic agility in Microsoft products.
It was then ported to mobile systems with different computer architectures, where we collaborated with product teams to optimize the elliptic curve operations for those architectures. I also worked on standardization of ECC protocols in the external community and eventually was invited to give a plenary talk on the development and deployment of ECC at the 2012 SIAM Annual meeting.
Introducing … Post-Quantum Cryptography
Throughout this period, I continued to publish in number theory and to collaborate with external academics. I hired and trained many interns and post-docs in both number theory and cryptography and hosted countless summer visitors.
In the summer of 2005, I was working with my summer visitor and long-time collaborator Eyal Goren, professor at McGill University, and my post-doc Denis Charles on a new number-theoretic construction of expander graphs. That summer, a Chinese researcher and her team found an unexpected weakness in MD5, a widely standardized cryptographic hash function.
The buzz around this topic, combined with our ongoing research project on generalizations of supersingular isogeny graphs (SIGs), led me to the idea of proposing path-finding on these SIG graphs as a hard problem on which to base the security of a new cryptographic hash function, now called the CGL hash function.
We presented the new hash function at the 2005 NIST Hash Function competition; in 2008 it was written up in Science magazine. But it was still considered esoteric and obscure at the time. Although I continued to work on finding number-theoretic attacks on the system, our proposal didn’t garner significant attention from the community until around 2011, when a key exchange protocol was proposed based on the same hard problem in SIG graphs.
Progress on realizing the dream of building quantum computers also caused a shift in perspective, because existing public key cryptosystems will be vulnerable to efficient attacks on quantum computers once they are realized at scale. In 2017, NIST launched a five-year post quantum cryptography (PQC) competition, and a key exchange protocol based on SIG was one of the submissions, making it to the fourth round.
Health and Genomic Privacy
In 2008, our lab director, Eric Horvitz, invited me to step into the role of research manager for the cryptography research group at Microsoft Research. I was reluctant to sacrifice research time for the sake of management, but Eric made the case for the potential for broader impact, and was he ever right about that!
Jennifer Chayes, my long-time mentor and former manager, intervened to convince me to accept the opportunity and bigger responsibility, and supported me to grow into the new role. As I worked to build the group and broaden my scope, I included privacy protection in the group’s mission, and renamed it Cryptography and Privacy Research. I became interested in encryption tools for protecting health and genomic privacy. For the first time, I felt that I was working on problems that normal people would actually care about, and I found it highly motivating.
Homomorphic Encryption and Private AI
In 2011, a surprise breakthrough in my team, providing a solution for homomorphic encryption (HE) based on lattices, caused me to pivot sharply toward studying the mathematics of lattice-based cryptography.
HE is a new type of encryption that allows for computation on encrypted data. Computation on sensitive data can be outsourced without compromising privacy, because the data can be encrypted before uploading to the cloud, and all computation performed on the encrypted data. After decryption, the result will be the same as the outcome would have been if the computation had been performed locally. This technology enables long-term storage and processing of sensitive data, protecting privacy. HE is an important tool for protecting privacy of electronic medical records and genomic data.
When I was invited to give a tutorial on HE at Cold Spring Harbor for the Biological Data Science community, a chance meeting with the founders of the NIH-funded Secure Genome Analysis Competition opened up new collaborations and many years of work on encryption tools for protecting genomic privacy. I was determined to advance this technology to protect privacy, with many co-conspirators and a strong sense of purpose.
My team built and open source–released SEAL (Simple Encrypted Arithmetic Library), a software library for HE, known for usability, robust engineering, and efficiency. I worked with our Microsoft Research Outreach team to launch an international standardization community for HE, HomomorphicEncryption.org (2017–2021), which has been a model for other cryptographic standardization efforts. We published the first draft standard for homomorphic encryption in 2018, and it is now widely cited.
The Artificial Intelligence Era
Most importantly, my work on HE led me into the field of AI, where I am today. Artificial intelligence is revolutionizing society before our eyes by providing high-quality services to assist in decision-making of all kinds, including medical diagnoses, driving directions, automatic speech recognition, automatic speech translation between languages, endless playlists of music and movie recommendations, face recognition, bird and flower identification, and, eventually, self-driving cars.
All of these rely on mathematical algorithms to process large amounts of data and learn from the data and train models (machine learning). The models can be used in a second stage to make predictions or take actions.
This whole AI pipeline presents significant privacy challenges, because it requires so much data for both training and prediction. But HE provides a potential solution since the data can be processed in encrypted form. My team coined the term “private AI” and was the first to show that it was possible to process neural net predictions on encrypted data (CryptoNets at ICML 2016). Since then, I have immersed myself in AI algorithms. Consciously deciding that I want to be part of the AI revolution, in 2021 I accepted the role of Director of Research Science for West Coast Labs at Facebook AI Research, now called Meta AI.
Microsoft Research
In hindsight, it is clear how much moving to Microsoft Research in 1999 completely changed my career path and trajectory (in a positive direction). All credit goes to my husband for suggesting this bold move. But at the time it felt a little bit like jumping off a cliff into the unknown.
Most of my academic mentors and colleagues assumed that I had left mathematics research, which was far from true. The full-time research job, interesting new research questions motivated by applications, and the absence of teaching duties ensured a new level of productivity in my research. It was at that stage that I also learned to collaborate with colleagues to make progress faster, including interdisciplinary projects with software engineers. Until that point all my published papers had been single-author.
In my first year at Microsoft Research I found out I was pregnant with twins. We felt very fortunate, totally clueless, and more than a little bit scared. Giving birth to, nursing, and raising identical twin daughters is undoubtedly the hardest thing I have ever done, but also the most rewarding. My husband would say the same, and the only way we survived was by doing it together and enlisting the help of our parents. It was a team effort from the beginning, and throughout their childhood, my husband carried the lion’s share of the load, juggling family with his full-time job as a history professor. To young women hoping to have a family and a satisfying professional life, I say a supportive partner is a tremendous help!
However, becoming a mother put a further dent in my connection to the academic math community. I had to withdraw from giving an invited lecture at the European Congress of Mathematics in July 2000, the month Joyce and Josephine were born. Math conferences are organized primarily through speaking invitations issued by the organizers. I did not receive another invitation to speak at a math conference for several years. This limited my ability to publicize my research and seemed to affect the acceptance rate of my publications.
I had to go back to work after only 12 weeks maternity leave, which was very challenging given that our daughters were barely the weight of newborns at that age. But I returned to research and publishing full-time, while my husband finished his PhD. So it was shocking to me when, several years later, one of my trusted advisors said that it would probably be hard for me to return to research after having twins, despite the fact that I had been sending him preprints of my recent papers throughout the three years since their birth!
I must be a fighter because I would not accept being left out of the research conferences, and I fought back. Resilience and adaptability turn out to be very valuable qualities to develop. But after reintegrating into the number theory conference circuit, and roughly 10 years after my PhD, I was still one of the only women at the conferences, and one of very few women speakers or organizers.
Women in Number Theory and the Association for Women in Mathematics (my proudest achievement)
In 2006, together with fellow women number theorists Rachel Pries and Renate Scheidler, we decided to change that. We sat down for lunch at a conference where I had invited them to speak and made a list of more than 75 women PhDs in number theory who we knew. Why weren’t they being included as speakers in the conferences we were attending? We decided to start our own conference for women in number theory (WIN), and to run it in a collaboration style in order to include graduate students, build community, and strengthen the talent pipeline for women.
More than 15 years later, the WIN model has now become a template for collaboration conferences in mathematics, has spawned more than 25 Research Networks for Women in other areas of mathematics, and has been supported by several million dollars in federal grant funding. Founding WIN and organizing conferences and research communities for women endowed me with a focused sense of purpose.
I felt I was on a mission, and that mission led me to become president of the Association for Women in Mathematics (AWM; 2015–2017) and to serve in the leadership of the mathematics profession (on the Council of the American Mathematical Society and the Executive Committee of the Conference Board of Mathematical Sciences), to continue to fight for change and inclusion in the mathematical sciences. As part of this effort, I founded the AWM book series to publish research volumes by women in mathematics. I still serve as series editor, and in seven years we have already published 35 volumes.
It also felt like a natural consequence to engineer the design and launch of the AWM Fellows program to recognize work to advance women and girls in math. To increase recognition of work by women in mathematics, we started the AWM Presidential Award given at the biannual AWM Research Symposium, launched the AWM Dissertation Prizes, and created awards in four categories for AWM Student Chapters. I set a goal to double the number of AWM Student Chapters in math departments at universities; there are now more than 100.
On the public advocacy front, I led the creation of the AWM Hill Visits program to visit Capitol Hill twice a year to advocate for women in science, helping pass some important bills in Congress and involving student chapters in the process.
I have written extensively about my work on WIN and for AWM.(2-4) I expended a tremendous amount of my professional energy on these programs but have always said that I got back more than I gave: from the energy of other women taking up the cause and from the confidence and community which we built together, to say nothing of the productive research collaborations and fun we had together at conferences.
I soon found that I no longer enjoyed going to normal conferences, as I became addicted to WIN-style conferences. At last count I had more than 60 female co-authors, most of them from WIN.
It was an honor and a privilege to work closely with AWM presidents who came before me (Georgia Benkart, Jill Pipher, and Ruth Charney); with the women of WIN (Rachel, Renate, Michelle Manes, Kate Stange, Alina Bucur, and many others) to grow and spread Research Networks for Women to other areas of math; with my partner in crime AWM Executive Director Magnhild Lien to launch many AWM programs; and current and future AWM Presidents (Kathryn Leonard and Talitha Washington) on the AWM Research Networks and Capitol Hill visits.
Outcomes of My Years as President of American Women in Mathematics
In the five years since I finished my term as AWM president, I have often said that the proudest accomplishment of my career was co-founding WIN and being AWM president (all part of one big effort from my point of view). But my career is not over yet, so we’ll see if that remains true!
For a while I felt that if I never did anything else significant in science, it would be enough, because I had already accomplished so much more than I ever thought I would — founding WIN, the AWM Research Networks for Women program, and the other AWM initiatives. At that time, I didn’t envision leading West Coast Labs for one of the top AI research organizations in the world!
It was a very hard decision to leave Microsoft Research after 22 years, and I consulted my trusted mentors and role models, notably Maria Klawe, Jennifer Chayes, and Jeannette Wing. I was ready for the move and the increase in scope and impact, and was thrilled to be trusted with such a responsibility. It helped me move forward after the devastating loss of my younger brother Nick in 2021, who died suddenly of a pulmonary embolism at the age of 48.
The confidence I gained as a leader in the profession through my experience as AWM president had translated into increased leadership scope at Microsoft Research, where I served on the senior leadership team for four years (2017-2021). My experience and knowledge also empowered me to proactively increase the percentage of women hired as researchers at both Microsoft Research and FAIR (now Meta AI).
Young women professionals in academia often are advised to “say no” to service roles and instead focus on research. While that is likely good advice to an extent early in your career, I question whether it is good advice overall, and it certainly depends on the expected impact from the opportunity. My own experience taught me that the human capital we build through relationships and common experiences has tremendous value.
I also felt pressure to accept speaking invitations at prestigious conferences where there were (still) few women speakers, since I thought it hypocritical to say “no” after advocating for including (more) women in conference programs. I also thought it was important to contribute to increasing the visibility of women in the profession, and to serve as a role model. Little did I envision that it would have a positive impact on my own family.
My daughters travelled with me to conferences such as the International Congress of Mathematics in Korea (2014), where the Fields Medal was awarded to a woman for the first time, presented by the (female) president of Korea. They also volunteered at AWM conferences while in high school, taking photos, creating the conference poster, and selling t-shirts. It must have made a good impression because they both did multiple summer internships at Microsoft, and both are now starting PhDs in computer science after graduating in 2022 from the University of Chicago.
Before leaving Microsoft Research, while speaking with our (then) VP of Research Eric Horvitz, I noted obstacles for senior technical women leaders: trust, access, visibility. Leading West Coast Labs for Meta AI Research, I feel I finally have all three of these: trust and access internally, and visibility externally through opportunities such as talking about privacy preserving technologies to protect neural rights in Werner Herzog’s new film.
I have enjoyed other fun moments in the sun, such as being invited to roundtable discussions at the White House (twice), and being featured in Janice Kaplan’s best-selling book The Genius of Women for our research network’s approach to advancing careers for women in science.
In 2020 I was invited to deliver a TED-style talk at Congreso Futuro to the Chilean public on private AI and privacy-preserving technologies for health data, in preparation for Chile to be the first country to enshrine neural privacy rights into law. I’m 52 years old and, having finally reached a point in my career where I no longer feel as though I am fighting for trust, access, and visibility on a daily basis, I am ready to consider what to do next!
References
Bos JW, Lauter KE. In Memoriam: Peter L. Montgomery (1947–2020). Notices of the American Mathematical Society. 2021;68:538-546. www.ams.org/notices/202104/rnoti-p538.pdf .
Benkart G, Lauter K, Wiegand S. AWM at 50 and beyond. Notices of the American Mathematical Society. 2021;68:387-397.
AWM and the Genius of Women: Reflections by AWM’s 22nd President Kristin Lauter. AWM 50th Anniversary Volume. Springer-Nature, 2022. https://awm-math.org/wp-content/uploads/2022/08/Lauter_Reflections50th.pdf
Bauer K, Chambers E, Johnson B, Lauter K, Leonard K. Research networks for women. European Mathematical Society Magazine, 2022.