We will discuss the question of minimizing different complexity measures of cryptographic primitives, some known results and remaining challenges, and how the study of this question can have impact beyond cryptography

Yuval Ishai

Cryptology ePrint Archive

How Low Can We Go?Invited PKC 2020 TalkYuval Ishai?Computer Science Department, TechnionAbstract. We will discuss the question of minimizing different com-plexity measures of cryptographic primitives, some known results andremaining challenges, and how the study of this question can have im-pact beyond cryptography.Given a cryptographic task, such as encrypting a message or securely computinga given function, a natural question is to find the “minimal cost” of carryingout this task. The question can take a variety of forms, depending on the costmeasure. For instance, one can try to minimize computation, communication,rounds, or randomness. In the case of computational cost, one can consider differ-ent computation models, such as circuits or branching programs, and differentcost metrics, such as size or depth. The answer to the question may furtherdepend on the type of computational assumptions one is willing to make.The study of this question, for different cryptographic tasks and clean asymp-totic cost measures, has led to a rich body of work with useful and often un-expected results. The talk will survey some results along this line, highlightingconnections between different research areas in cryptography and relevance be-yond cryptography.In addition to the direct interest in minimizing well-motivated complexitymeasures, there are cases in which “high-end” cryptographic tasks, such as se-cure multiparty computation or program obfuscation, call for minimizing dif-ferent cost measures of lower-end primitives that would otherwise seem poorlymotivated. I will give some examples of this kind.Finally, I will make the case that despite the progress already made, thereis much more to be explored. Research in this area can greatly benefit frommore cooperation between theoretical and applied cryptographers, as well asbetween cryptographers and researchers from other fields, including computa-tional complexity, algorithms, computational learning theory, coding theory, andinformation theory.? yuvali@cs.technion.il. Supported by ERC Project NTSC (742754), NSF-BSFgrant 2015782, BSF grant 2018393, and a grant from the Ministry of Science andTechnology, Israel and Department of Science and Technology, Government of India.

How Low Can We Go?

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