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This project investigates the foundational computational underpinnings of secure systems. Cryptographic constructions such as encryption, signatures, and more rely for their security on the conjectured computational difficulty of certain problems. For example, many public key encryption currently in use would be broken if someone discovered an efficient algorithm to factor large integers. Unfortunately, the current state of art is that we are unable to prove that these problems are truly hard, and so need to rely on unproven conjectures. Moreover, a handful of these conjectures serve as the foundations of many if not most of current cryptographic schemes, and so each such conjecture is a single point of failure whose refutation could have severe consequences for a large fraction of our systems. In particular, progress in quantum computing threatens some of these conjectures, and motivates reevaluation of the right basis for cryptography.
The goal of this project is better understand and remedy these issues. Concretely, this project investigates cryptographic schemes, and particularly public key encryption, that are based on assumptions that are qualitatively different from current ones, and hence more likely to survive technological or algorithmic advances that would break current schemes. The project obtains new forms of evidence for computational assumptions, thus deriving some assurances that current schemes are secure. The project also explores assumptions for new cryptographic primitives such as software obfuscation that are more well founded by computational complexity considerations
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TWC: Small: Complexity Assumptions for Cryptographic Schemes