**IN MEMORY OF**

**Peter L. Montgomery**

Peter Lawrence Montgomery passed away on February 18, 2020 in Pong, Thailand.

Peter was born in San Francisco, California, on September 25, 1947. He went to UC Berkeley in 1967 and received a BA in Mathematics in 1969 and an MA in 1971. Peter's undergraduate advisor was Derrick H. Lehmer, an excellent match given Peter's research interests since high school: integer factorization.

In 1967, Peter was among the five persons ranking highest in the William Lowell Putnam Mathematical competition and became a Putnam Fellow. In 1972 Peter started working as a junior programmer for System Development Corporation (which later became Unisys) and became the expert on the CDC 7600.

During this time Peter remained active in the mathematical community. When implementing textbook multi-precision multiplication in assembler on a PDP series computer, he noticed there were unused registers and wanted to find a way to exploit them. He managed to do so by interleaving the multiplication with the modular reduction. This led to arguably one of his most widely-used results: Montgomery multiplication.

About twenty years after his time in Berkeley, David G. Cantor supervised Peter's PhD dissertation on his favorite topic in computational number theory. In order to optimize the elliptic curve factorization method, Peter "discovered an alternative parametrization that requires no inversions". This is now known as Montgomery curves and the Montgomery ladder and found applications in high-performance public-key cryptography as well as countermeasures against side-channel attacks.

In 1998 Peter accepted a position with the Security and Cryptography group at Microsoft Research in Redmond, WA. He retired in 2014. During his time at MSR, Peter continued collaborations with researchers world-wide and was a regular long-term guest at various universities and research institutes.

Peter was well known for his great sense of humor, practical jokes and his talent with numbers. With his positive attitude he was an example to visiting students and interns. As a mentor, colleague and friend he was always liked. We will miss him.

**
Joppe Bos, Arjen Lenstra, Dan Shumow
**

Peter was very much interested in our community and attended frequently ARITH symposia. His landmark multiplication algorithm left a significant mark on cryptography.

I knew Peter, first as a (very mature) student in my Arithmetic course at UCLA and later as a member of his PhD committee in Mathematics Department. His mentor David Cantor praised him as a genius. In the arithmetic class his homework solutions were impressive: he would provide elegant proofs and incisive comments.

Whenever I asked him to review papers for the IEEE Transactions on Computers, he would come up with significant improvements. Invariably, the authors wanted to include him as a coauthor - he always laughed off these suggestions.

He showed a great sense of subtle humor and chuckled a lot listening to our presentations at symposia. I never found out what was he really thinking. Nevertheless, he kept coming. He will be missed.

**Milos Ercegovac**