### A Tutorial Introduction to Lattice-based Cryptography and Homomorphic Encryption

A few of us have been working with homomorphic encryption for a number of years now, but we never found a paper / book that covers all the foundational mathematical material in one place. So we decided to write one — well my postdoc Kelvin Yang Li decided to write one and Mike Purcell and I assisted … More A Tutorial Introduction to Lattice-based Cryptography and Homomorphic Encryption

### Notes on Cyclotomic Polynomials and Their Galois Groups

Cyclotomic polynomials are widely used in the construction of lattice cryptography and homomorphic encryption schemes based on the Ring Learning With Error problem. In this short note, Kelvin Li and I attempt a self-contained introduction to the cyclotomic polynomials and the Galois groups of cyclotomic extensions.

### Linking Integer Records: The Simplest Case of PPRL

Privacy-Preserving Record Linkage (PPRL) is one of those problems that still doesn’t have a solid and widely accepted mathematical definition, perhaps because the problem of Record Linkage itself, especially the kind that doesn’t reduce to supervised learning through an abundance of labelled matches, still doesn’t have a solid mathematical definition despite thousands of papers published … More Linking Integer Records: The Simplest Case of PPRL

### Useful Technical Tutorials on Fully Homomorphic Encryption

I have gone through quite a few articles over the last 12 months in my attempt to get a proper understanding of fully homomorphic encryption (FHE) schemes. The process was somewhat frustrating because most of the articles are either too basic, giving just very high-level intuitions, or too deep, assuming too much background on the … More Useful Technical Tutorials on Fully Homomorphic Encryption

### How to Quickly and Meaningfully Improve the Financial System’s Collective Ability to Detect Crimes

Complex financial crimes are hard to detect primarily because data related to different pieces of the overall puzzle are usually distributed across a network of financial institutions, regulators, and law-enforcement agencies. The problem is also rapidly increasing in complexity because new platforms are emerging all the time that facilitate the transfer of value across a … More How to Quickly and Meaningfully Improve the Financial System’s Collective Ability to Detect Crimes

### Extending the Paillier Cryptosystem to Handle Floating Point Numbers

The Paillier Cryptosystem is a partial homomorphic encryption scheme that supports two important operations: addition of two encrypted integers and the multiplication of an encrypted integer by an unencrypted integer. In practice, many applications of Paillier require an extension of the underlying scheme beyond integers to handle floating-point numbers. For example, just about every popular machine learning … More Extending the Paillier Cryptosystem to Handle Floating Point Numbers