We can view the hashing process as mapping the free abelian group generated by to a finite group 4. The Role of Group Actions
Group Actions and Hashing Unordered Multisets: An Algebraic Approach to Data Integrity 1. Introduction
The paper should conclude with the "Birthday Paradox" implications for multiset hashing and how choosing a large enough prime
Traditional hash functions (like SHA-256) are designed for sequences. If you change the order of items in a list, the hash changes. However, in many applications—such as database query optimization, chemical informatics, or distributed state verification—we need to treat {A, A, B} the same as {B, A, A} . This paper explores how provide a formal framework for designing such "order-invariant" hash functions. 2. Mathematical Preliminaries
Zobrist, A. L. (1970). "A New Hashing Method with Applications for Game Playing."