Cryptography represents one of the most amazing unanticipated applications of pure mathematics to the real world. Without it, internet commerce would be unthinkable. Mathematical tools, in combination with theoretical computer science, have become a critical cornerstone for many Internet-based and wireless applications. Indeed, security, privacy and fault-tolerance have become key requirements for many emerging applications.
As remarkable as the first generation of insights into cryptography and computer security were, they have not in fact brought us bullet-proof security, as new challenges and attacks has arisen. The setting of the Internet-based applications has become far more complex; the potential attacks more numerous and sophisticated. Initial “stand-alone” requirements for security were replaced by a need for security in far more complex environments, where complicated interactions with multiple participants and with multiple and often diverse goals must nevertheless be made resilient against sophisticated attack models. As our society becomes ever more “paperless” in areas that include medical applications, taxation, information exchange, and even household electronics and appliances, the issues of security and privacy become ever more important. Examples include electronic voting and election protocols, zero-knowledge proofs, on-line shopping, electronic cash, stronger notions of encryption and of electronic bidding protocols, data mining and more general multi-party computations with strong security and composability notions. Often, deep mathematical results are used from diverse areas to analyze security and robustness of these protocols, including algebra, combinatorics, number theory, arithmetic algebraic geometry, probability theory, and coding theory. The purpose of this program is to crystallize fundamental problems that are posed by cryptographic applications and stimulate cross-disciplinary exchanges which will accelerate research-both on mathematical foundations needed by cryptographers and on cryptographic applications.
This program is being coordinated with the Fields Institute’s Fall 2006 Thematic Program in Cryptography.
Dan Boneh (Stanford University)
Shafi Goldwasser (Massachusetts Institute of Technology)
Eyal Kushilevitz (Technion - Israel Institute of Technology)
Arjen Lenstra (Lucent Technologies Bell Laboratories)
Rafail Ostrovsky, Chair (UCLA)
Joseph Silverman (Brown University)