Cryptography

Abstract

The science of cryptography lies at the very foundations of trust in current and future systems and devices for communication and computation. For example, secure communications over the internet today are possible thanks to mathematical work in cryptography in the 1970s and 80s. Security and efficiency of cryptographic schemes rely heavily on mathematics: mathematical models describe what security means, hard algorithmic problems are the basis of constructions that achieve the desired security which is established by mathematical proofs, and algorithmic optimizations make the schemes applicable in practice. Dramatic changes in computational technologies raise new challenges, and therefore new opportunities, for cryptography. These challenges include the near-ubiquitous use of remote storage and computation including cloud computing, which bring to fore new concerns of privacy, security and integrity; the advances in quantum computation which necessitate the development of more robust mathematical foundations of the field; and a revolution in machine learning and artificial intelligence that is poised to affect our lives in fundamental ways and which once again bring up an entirely new suite of problems for cryptography, ones related to trust, security, integrity and fairness of these systems. In the last half decade, there have been spectacular advances in cryptography, in the areas of program obfuscation, verifiable computation, elliptic curves and isogenies, lattice-based cryptography, quantum cryptography, cryptographic techniques in machine learning, and more. This workshop brought together experts from mathematics and computer science such as algorithmic number theory and algebra, quantum computation and complexity theory, in order to discuss recent advances and make progress in constructing the new generation of cryptographic systems that protect the future of information and computation.