Primitive Vector Cipher(PVC): A Hybrid Encryption Scheme based on the Vector Computational Diffie-Hellman (V-CDH) Problem
Gülçin ÇİVİ BİLİR
TL;DR
PVC presents a novel hybrid encryption scheme that unifies authenticated Diffie–Hellman key exchange with matrix-based submatrix encryption. The core idea uses a DH-derived primitive vector to generate secret matrices and a HKDF-driven CSPRNG mask, paired with per-block column offsets to achieve IND-CPA security under the Vector CDH assumption, with STS integration pushing toward IND-CCA. The approach combines formal security reductions, KPA-resistant design, and diffusion/entropy analyses, demonstrating strong statistical security and parallelizable performance. Practically, PVC offers linear scalability, low memory overhead, and hardware-friendly parallelism, making it suitable for high-throughput, low-latency deployments while relying on standard cryptographic assumptions.
Abstract
This work introduces the Primitive Vector Cipher (PVC), a novel hybrid encryption scheme integrating matrix-based cryptography with advanced Diffie-Hellman key exchange. PVC's security is grounded on the established hardness of the Vector Computational Diffie- Hellman (V-CDH) problem. The two-layered design uses HKDF to mask plaintext via a DH-authenticated shared primitive vector and randomize cipher blocks with a per-block offset. This approach eliminates deterministic repetitions and provides strong resistance against linear and known-plaintext attacks. PVC's block-wise structure allows for massive parallelism and excellent linear scaling. Security is formally analyzed, demonstrating INDCPA security under V-CDH. STS protocol integration elevates security toward IND-CCA guarantees.