Optimization of Tree Modes for Parallel Hash Functions: A Case Study

TL;DR

This paper investigates optimal tree-based structures for parallel hash functions, aiming to minimize running time and processor count through topology optimization, applicable to various inner hash functions.

Contribution

It introduces a scheme for optimizing tree topology in parallel hash functions to reduce running time and processor requirements without compromising efficiency.

Findings

Optimized tree topology reduces hash computation time.

Modified tree structures minimize processor usage.

Applicable to SBL and sponge-based hash functions.

Abstract

This paper focuses on parallel hash functions based on tree modes of operation for an inner Variable-Input-Length function. This inner function can be either a single-block-length (SBL) and prefix-free MD hash function, or a sponge-based hash function. We discuss the various forms of optimality that can be obtained when designing parallel hash functions based on trees where all leaves have the same depth. The first result is a scheme which optimizes the tree topology in order to decrease the running time. Then, without affecting the optimal running time we show that we can slightly change the corresponding tree topology so as to minimize the number of required processors as well. Consequently, the resulting scheme decreases in the first place the running time and in the second place the number of required processors.