Beyond Controlled Noise: Achieving Symmetric FHE through Dynamic Position Shifting
For practitioners needing practical FHE, this work offers a potentially efficient alternative to traditional schemes, though security claims require further validation.
The paper proposes a symmetric FHE scheme using plaintext fragmentation and dynamic interposition to overcome noise growth and computational overhead, achieving efficient multiplicative homomorphism without exponential noise accumulation.
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.