Security of Operations on Random Numbers

Abstract

Random numbers are basic building blocks for cryptography. For example, they are heavily utilized in Decentralized Finance (DeFi) and blockchain applications. Cryptographers and practitioners frequently employ bit selection, arithmetic, and logical operations to generate cryptographically secure random numbers (CSPRNs), thereby achieving the desired level of entropy and security. There is a need to analyze the security of such operations on CSPRNs. In this paper, we have studied and analyzed the security properties of arithmetic and some string operations on CSPRNs, and reviewed Boolean logic operations with a focus on the preservation or loss of entropy. We have analyzed and presented several proofs of security or lack of it for such operations. We have implemented and conducted experiments to corroborate these results using the NIST test suite. Our work applies not only to classical random numbers but also to quantum random numbers.