Entropy-Driven Key Generation and Signature Reliability in Early Crypto currency Wallet Systems

Abstract

This study examines the role of entropy quality in private key and signature generation within early cryptocurrency wallet systems, focusing on the conditions under which weak randomness led to nonce repetition and subsequent exposure of ECDSA private keys. Through a reconstructed signing environment reflecting historical low-entropy states, we demonstrate how deterministic and non-deterministic key workflows became vulnerable when seeded with insufficient randomness. A reliability heatmap illustrates the threshold behavior at which entropy degradation leads to predictable signatures and key recovery feasibility. The results underscore that the cryptographic robustness of elliptic curve schemes depends critically on secure entropy acquisition, particularly in constrained or headless deployments, and highlight the necessity of incorporating high-quality hardware-based randomness sources in modern wallet architectures.