ERGODIC TRANSFORMATIONS

Title: ERGODIC TRANSFORMATIONS

Research Question: How can ergodic transformations be used to create pseudorandom number generators with high security and flexibility?

Methodology: The study uses techniques and constructions to compose generators that output uniformly distributed sequences with high linear and 2-adic spans. The paper introduces counter-dependent pseudorandom generators, which modify their state transition and output functions dynamically while working.

Results: The research shows that these generators produce sequences with desirable 'features of randomness', such as period length, distribution of overlapping and non-overlapping k-tuples, linear complexity, and p-adic span. It also demonstrates that with the use of these functions, it is possible to construct a stream cipher with a key-dependent state transition and output functions, making it difficult for cryptanalysts to recover the key.

Implications: The findings of this research have significant implications for the field of cryptography and simulation. The proposed generators provide high security and flexibility, making them suitable for use in various applications. The techniques and constructions introduced in the paper can be used to design and implement secure and efficient pseudorandom number generators.

Link to Article: https://arxiv.org/abs/0401030v1 Authors: arXiv ID: 0401030v1