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.
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
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
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
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