# Mathematical Digest

### Short Summaries of Articles about Mathematics

in the Popular Press

"Hiding in lattices: An improved mathematical strategy for encrypting data,"by Ivars Peterson. *Science News*, 5 July 1997, pages 12-13.

Data encryption schemes are widely used to insure the security of informationtransmissions. For example, companies routinely use such schemes to protectcommunications with customers over the World Wide Web. As computers becomefaster and more powerful, and therefore more capable of cracking the encryptiondevices in use today, computer scientists and mathematicians continue todevelop new schemes that are more difficult to breach. This article describesa possible basis for a new encryption scheme, developed by IBM researchersMiklos Atjai and Cynthia Dwork. Rather than using factorization of largenumbers, as is common in encryption schemes, this method uses lattices (equallyspaced sets of points) in a high-dimensional space. The new encryption methodwould be based on the fact that, in high dimensions, it is extremely difficultto locate the point in the lattice that is the closest to a given point.

*--- Allyn Jackson*