Efficient Accessing and Searching in a Sequence of Numbers

TLDR: This paper presents a practical indexing method for a monotonically increasing static sequence of numbers where the access and search queries can be addressed efficiently in terms of both time and space complexity.

Abstract: Accessing and searching in a sequence of numbers are fundamental operations in computing that are encountered in a wide range of applications. One of the applications of the problem is cryptanalytic time-memory tradeoff which is aimed at a one-way function. A rainbow table, which is a common method for the time-memory tradeoff, contains elements from an input domain of a hash function that are normally sorted integers. In this paper, we present a practical indexing method for a monotonically increasing static sequence of numbers where the access and search queries can be addressed efficiently in terms of both time and space complexity. For a sequence of n numbers from a universe U = {0, ..., m ? 1}, our data structure requires n lg(m/n) + O(n) bits with constant average running time for both access and search queries. We also give an analysis of the time and space complexities of the data structure, supported by experiments with rainbow tables.