Performance Analysis of Hash Functions: A Comprehensive Study of Average Search Length and Distribution Properties

Abstract

Abstract

This study examines the performance analysis of hash functions, with a basic focus on examining the average search length of keys using different hash functions including division remainder method, universal hashing, and multiplication method. Hashing functions from H1 class of universal hashing defined by Wegman and Carter are used to evaluate the effect of prime numbers. It was found that the choice of prime number influences the effectiveness of universal hashing functions—the smaller the prime number, the better its performance. The study also compares the performance of universal hashing against radix transformation and division remainder method, revealing that universal hashing can excel under specific conditions. The analysis includes comprehensive subsets of the Universe, examining all possible subsets to understand how hash functions distribute data properly. Results indicate that the division-remainder method performs best in terms of distributing subsets with fewer collisions, resulting in smaller average successful search lengths. This method also demonstrated the highest percentage of perfect distributions across all subset sizes. The study concludes with insights into the effect of different parameters on hash performance, providing a valuable resource for understanding the significance of hash functions in cryptographic applications.

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