Galois Private Set Intersection (PSI) is a cryptographic technique that enables organizations to compute the intersection of their datasets with other parties without revealing additional information beyond the common elements. The technology addresses scenarios where organizations need to compare datasets to identify shared elements while maintaining data confidentiality. PSI maintains data encryption throughout the comparison process, allowing parties to identify common data elements without exposing sensitive information. The technique is designed for use cases such as healthcare data sharing for disease tracking and financial fraud detection through transaction data comparison. The solution addresses privacy concerns in data matching operations by eliminating the traditional trade-off between data utility and confidentiality. Organizations can perform dataset comparisons while maintaining compliance with data privacy regulations by preventing unnecessary exposure of sensitive data during the comparison process. PSI operates as a cryptographic protocol that processes encrypted datasets to determine intersections without decrypting the underlying data or revealing non-matching elements to participating parties.