Lattices and Cryptography: A Match Made in Heaven

Integer lattices play a central role in mathematics and computer science, with applications ranging from number theory and coding theory to combinatorial optimization. Over the past three decades, they have also become a cornerstone of modern cryptography.

In this talk, I will describe the evolution of lattices in cryptography: from the early use of lattices to break classical cryptosystems; to their application in designing new encryption and digital signature schemes with (conjectured) post-quantum security; and to their role in achieving long-standing cryptographic goals such as fully homomorphic encryption that allow us to compute directly on encrypted data.

The talk will not assume any prior background in cryptography.