Research Projects

This project attempts to investigate new properties of higher order boolean derivatives to detect non-randomness in cryptographic hash functions. The primary targets are international hash standard SHA3 and NIST Lightweight Cryptography finalist Xoodyak. The basic idea is to improve the limitations of SymSum distinguisher which was proposed in FSE 2017 by Saha et al on SHA3. Two main limitations of SymSum have been identified in contemporary literature. One being the reduction in degrees of freedom buy a factor of 2 owing to the partitioning of variables in computing higher order vectorial derivatives. The second factor is the deterministic nature of the distinguisher. We believe that both these limitations can be overcome. For handling the first issue, the plan is to look at higher order simple derivatives instead of vectorial derivatives. However, the choice of variables to compute the derivative will play a crucial role. This is the research component of this phase. For handling the second issue we will allow some of the input states to admit partial asymmetry (which in classical SymSum required fully symmetric states). This in our opinion should give a partially asymmetric state in the output sum of SHA3. The research component would be the study of the degree of asymmetry and probabilistic nature of this property. Finally, Xoodyak which has a very unique structure but borrows some properties from SHA3 will be analayzed in the light of classical SymSum as well probabilistic SymSum to developed as a part of this project. The project investigator is expecting a couple of good publications and one of the best distinguishers on SHA3/Xoodyak as a basic output of his project.