Beyond Controlled Noise: Achieving Symmetric FHE through Dynamic Position Shifting

TL;DR

This paper introduces a symmetric Fully Homomorphic Encryption scheme that employs dynamic position shifting and fragmentation to control noise growth and improve efficiency.

Contribution

It presents a novel encryption framework with position-based fragmentation and regulators to manage noise and enhance security in symmetric FHE.

Findings

Achieves noise management through position shifting and fragmentation.

Provides a security mechanism based on mutual dependence of exponents and coefficients.

Offers a modular encryption scheme with controlled noise growth.

Abstract

Traditional Fully Homomorphic Encryption (FHE) schemes often suffer from prohibitive computational overhead and complex noise management. In this paper, we propose a novel symmetric FHE through a mechanism of plaintext fragmentation and dynamic interposition. Our approach is built upon a modular encryption foundation, c = mk + rp, which is naturally additive but typically limited by exponential noise growth during multiplication. To resolve this, we introduce an interposition framework where the plaintext is partitioned into multiple fragments across distinct logical positions. We introduce a dual-regulator system to govern the multiplication process; exponent regulators (t_i) redirect the product of fragments to a new target position, preventing the accumulation of secret key exponents, while coefficient regulators (d_i) normalize the resulting scalars. Security is established through a binding mechanism where exponents and coefficients are mutually dependent, shielding the secret key k from algebraic manipulation and substitution attacks.