The National Science Foundation awarded a $258,576 Project Grant under the Mathematical and Physical Sciences program (CFDA 47.049) to the University of California, Davis for the period of June 1, 2022 to May 31, 2025.
The grant funds research that seeks to apply classical number theory to cryptographic hash functions, which are important for password protection and digital signatures. The principal investigator will construct new algorithms for finding paths in graphs related to certain number theory questions and short cycles in these graphs, with implications for both hash function security and number theory. The multidisciplinary project brings together experts in number theory and cryptography and also aims to involve undergraduate and graduate students. Work will continue on thin groups related to Markoff triples and their application as a cryptographic hash function. The investigator will prove results on average sizes of lifts of modular Markoff triples to integer triples and compare the security of new hash functions to accepted secure functions today.
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