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Coding-Based Hybrid Post-Quantum Cryptosystem for Non-Uniform Information

Saar Tarnopolsky, Alejandro Cohen

TL;DR

The paper addresses secure communication of non-uniform messages over a multi-link network in a post-quantum setting, introducing NU-HUNCC, a hybrid scheme that combines polar-based almost-uniform source coding with a sub-linear seed, an information-theoretic secure channel code, and selective post-quantum encryption. It provides a rigorous information-theoretic security guarantee against IT-Eve via $k_s$-IS, and a cryptographic security guarantee against Crypto-Eve via ISS-CCA1, achieving high data rates close to network capacity. A key practical insight is that the seed length $d_J$ can be kept sub-linear with $d_J \in [n^{0.7214}, n^{0.7331}]$, enabling efficient pre-processing and scalable security for non-uniform sources. The results offer a viable path toward PQ-secure, high-rate transmission in distributed settings and secure storage applications, balancing information-theoretic and computational security requirements.

Abstract

We introduce for non-uniform messages a novel hybrid universal network coding cryptosystem (NU-HUNCC) in the finite blocklength regime that provides Post-Quantum (PQ) security at high communication rates. Recently, hybrid cryptosystems offered PQ security by premixing the data using secure coding schemes and encrypting only a small portion of it, assuming the data is uniformly distributed. An assumption that is often challenging to enforce. Standard fixed-length lossless source coding and compression schemes guarantee a uniform output in normalized divergence. Yet, his is not sufficient to guarantee security. We consider an efficient almost uniform compression scheme in non-normalized variational distance for the proposed hybrid cryptosystem, that by utilizing uniform sub-linear shared seed, guarantees PQ security. Specifically, for the proposed PQ cryptosystem, first, we provide an end-to-end coding scheme, NU-HUNCC, for non-uniform messages. Second, we show that NU-HUNCC is information-theoretic individually secured (IS) against an eavesdropper with access to any subset of the links. Third, we introduce a modified security definition, individually semantically secure under a chosen ciphertext attack (ISS-CCA1), and show that against an all-observing eavesdropper, NU-HUNCC satisfies its conditions. Finally, we provide an analysis that shows the high communication rate of NU-HUNCC and the negligibility of the shared seed size.

Coding-Based Hybrid Post-Quantum Cryptosystem for Non-Uniform Information

TL;DR

The paper addresses secure communication of non-uniform messages over a multi-link network in a post-quantum setting, introducing NU-HUNCC, a hybrid scheme that combines polar-based almost-uniform source coding with a sub-linear seed, an information-theoretic secure channel code, and selective post-quantum encryption. It provides a rigorous information-theoretic security guarantee against IT-Eve via -IS, and a cryptographic security guarantee against Crypto-Eve via ISS-CCA1, achieving high data rates close to network capacity. A key practical insight is that the seed length can be kept sub-linear with , enabling efficient pre-processing and scalable security for non-uniform sources. The results offer a viable path toward PQ-secure, high-rate transmission in distributed settings and secure storage applications, balancing information-theoretic and computational security requirements.

Abstract

We introduce for non-uniform messages a novel hybrid universal network coding cryptosystem (NU-HUNCC) in the finite blocklength regime that provides Post-Quantum (PQ) security at high communication rates. Recently, hybrid cryptosystems offered PQ security by premixing the data using secure coding schemes and encrypting only a small portion of it, assuming the data is uniformly distributed. An assumption that is often challenging to enforce. Standard fixed-length lossless source coding and compression schemes guarantee a uniform output in normalized divergence. Yet, his is not sufficient to guarantee security. We consider an efficient almost uniform compression scheme in non-normalized variational distance for the proposed hybrid cryptosystem, that by utilizing uniform sub-linear shared seed, guarantees PQ security. Specifically, for the proposed PQ cryptosystem, first, we provide an end-to-end coding scheme, NU-HUNCC, for non-uniform messages. Second, we show that NU-HUNCC is information-theoretic individually secured (IS) against an eavesdropper with access to any subset of the links. Third, we introduce a modified security definition, individually semantically secure under a chosen ciphertext attack (ISS-CCA1), and show that against an all-observing eavesdropper, NU-HUNCC satisfies its conditions. Finally, we provide an analysis that shows the high communication rate of NU-HUNCC and the negligibility of the shared seed size.
Paper Structure (15 sections, 3 theorems, 42 equations, 2 figures)

This paper contains 15 sections, 3 theorems, 42 equations, 2 figures.

Table of Contents

  1. Introduction
  2. System Model
  3. Security against IT-Eve
  4. Security against Crypto-Eve
  5. Non-Uniform Hybrid Universal Network Coding Cryptosystem (NU-HUNCC)
  6. Secure Individual Random code against IT-Eve (Security Proof Sketch of Theorem \ref{['Direct']})
  7. Partial Encryption against Crypt-Eve (Security Proof Sketch of Theorem \ref{['Individual-SS-CCA1']})
  8. Conclusions And Future Work
  9. Source and IS Channel Coding Schemes
  10. Polar Source Code
  11. IS Random Channel Coding
  12. Reliability
  13. $k_s$-IS Information Leakage against IT-Eve
  14. Individual SS-CCA1 Against Crypto-Eve
  15. Seed Length

Key Result

Theorem 1

Assume a noiseless multipath communication $(\ell,w)$. NU-HUNCC reliably delivers with high probability $\ell$ non-uniform messages from a DMS $(\mathcal{V},p_V)$ to the legitimate receiver, such that $\mathbb{P}(\underline{\hat{V}}_{\mathcal{L}}(\underline{Y}_{\mathcal{L}}) \neq \underline{V}_{\mat

Figures (2)

  • Figure 1: NU-HUNCC cryptosystem with $\ell$ noiseless communication links and two types of Eve's: IT-Eve with access to $w < \ell$ links, and Crypto-Eve with access to all the links. The lossless almost uniform compression is done by the polar codes-based encoder from NegligbleCost.$c$ of the links are encrypted by a PQ public-key SS-CCA1 cryptosystem. The mixing of the messages is done by the individual secure random network coding scheme from SMSMcohen2022partial. The uniform seed is encrypted as well and shared by a separate link. In practice, the encrypted seed is concatenated to the $c$ encrypted messages.
  • Figure 2: Numerical simulation of the seed size for a source $(\mathcal{V},p_V)$ with entropy $H(V) = 0.9$. For messages with a size greater than $2^{18}$ bits, the seed size already decreases to about $2.2\%$ of the compressed message size.

Theorems & Definitions (7)

  • Definition 1
  • Definition 2
  • Definition 3
  • Remark 1
  • Theorem 1
  • Theorem 2
  • Theorem 3