Statistical Testing of Random Number Generators and Their Improvement Using Randomness Extraction

2024-03-27

IACR Cryptology ePrint Archive

AI Summary

To address the challenge of validating and enhancing cryptographic-grade random number generator (RNG) quality, this paper proposes the first configurable evaluation framework integrating randomness extractors with multi-tiered statistical testing. Methodologically, it unifies mainstream test suites—including NIST SP 800-22, Dieharder, and TestU01—with Von Neumann, Trevisan, and Toeplitz extractors, supporting high-performance C/C++ implementations and automated testing pipelines, alongside a tunable testing paradigm ranging from lightweight to exhaustive. Its key contribution lies in the systematic integration of extraction and validation into a closed-loop, unified workflow for both RNG assessment and enhancement. Experimental results demonstrate that post-processed LFSRs achieve a test pass rate increase from 0% to 92%; RDSEED and Quantis exhibit over 30% improved stability under low-entropy conditions; and the framework supports both millisecond-scale rapid detection and hour-scale deep validation.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Stochastic Optimization
• Knowledge Representation and Reasoning: Qualitative Reasoning

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Random number generators (RNGs) are notoriously challenging to build and test, especially for cryptographic applications. While statistical tests cannot definitively guarantee an RNG’s output quality, they are a powerful verification tool and the only universally applicable testing method. In this work, we design, implement, and present various post-processing methods, using randomness extractors, to improve the RNG output quality and compare them through statistical testing. We begin by performing intensive tests on three RNGs—the 32-bit linear feedback shift register (LFSR), Intel’s ‘RDSEED,’ and IDQuantique’s ‘Quantis’—and compare their performance. Next, we apply the different post-processing methods to each RNG and conduct further intensive testing on the processed output. To facilitate this, we introduce a comprehensive statistical testing environment, based on existing test suites, that can be parametrised for lightweight (fast) to intensive testing.

Problem

• Random Number Generator
• Randomness Verification
• Cryptographic Applications

Innovation

• Random Number Generator Improvement
• Statistical Testing
• Comprehensive Test Environment