Tight Quantum-Security Bounds and Parameter Optimization for SPHINCS+ and NTRU

Abstract

The imminent threat of quantum computing necessitates quantum-resistant cryptosystems. This paper establishes tight security bounds for two NIST PQC finalists: SPHINCS+ (hash-based) and NTRU (lattice-based). Our key contributions include: (1) A quantum attack model incorporating decoherence effects ($\tau_d$) and parallelization limits; (2) Improved entropy concentration inequalities reducing SPHINCS+ parameters by 15-20\%; (3) Optimized NTRU lattice parameters via quantum lattice entropy $H_Q(\Lambda)$; (4) Tightened NTRU-to-LWE reduction with polynomial-factor improvement. Theoretical results demonstrate significant security enhancement over existing constructions, providing implementable parameters for standardization.