While modern research in cryptography has transformed a significant portion of computer security from an art into a science, ultimately the security guarantees for all current cryptographic protocols (encryption, digital signatures, etc.) rely on conjectures, such as the intractability of factoring large integers is intractable or of finding collisions in certain "hash functions". The possibility that these conjectures are false (as was recently discovered for some popular hash functions) is a genuine threat to cybersecurity. This project aims to reduce this threat by minimizing the assumptions needed for specific cryptographic primitives (such as commitment schemes, which can be viewed as "digital safes"), and attempting to base cryptography on the hardness of an entire class of problems. More generally, the project aims to strengthen the foundations of cryptography and cybersecurity using techniques from computational complexity theory. Society benefits from this project because of the enabling role that cryptography plays in electronic commerce. Stronger foundations for cryptography help prevent electronic commerce from becoming vulnerable to unforeseen attack. Further impact of this project comes through the training of graduate and undergraduate students, both through their attendance in courses taught by the PI and through their direct involvement in the research.
CT-ISG: The Assumptions for Cryptography