Amortized Σ-Protocol for MLWE Problem

MLWE is a fundamental hard problem in post-quantum lattice cryptography. Standard Σ-protocols perform poorly for multiple MLWE statements due to high communication and computation costs. This paper presents an amortized Σ-protocol for MLWE using a lightweight fold-split-fold technique that decomposes norm-bounded error vectors without relying on NTT, MLE, or sum-check protocols. The protocol achieves completeness, special soundness, and non-abort SHVZK with constant-round interaction and lightweight verification. The construction avoids complex tools and provides an efficient batch proof mechanism, offering a simple and practical solution for post-quantum cryptographic applications.