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

• URL: http://arxiv.org/abs/2402.08407v1
• Date: Tue, 13 Feb 2024 12:12:39 GMT
• Title: Coding-Based Hybrid Post-Quantum Cryptosystem for Non-Uniform Information
• Authors: Saar Tarnopolsky, Alejandro Cohen,
• Abstract summary: We introduce for non-uniform messages a novel hybrid universal network coding cryptosystem (NU-HUNCC) We show that NU-HUNCC is information-theoretic individually secured against an eavesdropper with access to any subset of the links.
• Score: 53.85237314348328
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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