Quantum-Resistant One-Way Puzzles from Program Obfuscation and Kolmogorov Complexity: A Minimal-Assumption Framework

Quantum-Resistant One-Way Puzzles from Program Obfuscation and Kolmogorov Complexity: A Minimal-Assumption Framework | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 26 August 2025 V1 Latest version Share on Quantum-Resistant One-Way Puzzles from Program Obfuscation and Kolmogorov Complexity: A Minimal-Assumption Framework Authors : Maher Asaad Baker 0000-0001-8013-6044 [email protected] and Fuad Al-Qrize Authors Info & Affiliations https://doi.org/10.22541/au.175624416.69459338/v1 169 views 124 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract We introduce a novel construction of quantum-resistant one-way puzzles based on the uncomputability of Kolmogorov complexity and the obfuscation of pseudorandom generators. The security of our scheme relies on the minimal assumption that quantum polynomial-time (QPT) adversaries cannot efficiently approximate the Kolmogorov complexity 𝑲(𝒔) of strings sampled from specific distributions. We define a new cryptographic primitive-Kolmogorov puzzles-and formally prove that inversion implies a nontrivial compression of random strings, contradicting the Incompressibility Lemma. To support this, we provide a theoretical security reduction and simulation-based evidence. Compression algorithms (e.g., gzip) serve as heuristic estimators of 𝑲(𝒔), and Grover-based quantum circuits implemented in Qiskit validate the infeasibility of brute-force inversion. While our obfuscation uses lightweight heuristics, the reduction remains valid under any black-box obfuscator. This work offers a complexity-theoretic approach to post-quantum cryptography without algebraic assumptions, aligning with NIST's call for diverse post-quantum primitives. Supplementary Material File (quantum-resistant one-way puzzles from program obfuscation and kolmogorov complexity.pdf) Download 498.93 KB Information & Authors Information Version history V1 Version 1 26 August 2025 Copyright This work is licensed under a Creative Commons Attribution 4.0 International License Keywords incompressibility kolmogorov complexity meta-complexity non-algebraic assumptions one-way puzzles post-quantum cryptography program obfuscation quantum resistance theoretical cryptography Authors Affiliations Maher Asaad Baker 0000-0001-8013-6044 [email protected] SOLAV View all articles by this author Fuad Al-Qrize SOLAV View all articles by this author Metrics & Citations Metrics Article Usage 169 views 124 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Maher Asaad Baker, Fuad Al-Qrize. Quantum-Resistant One-Way Puzzles from Program Obfuscation and Kolmogorov Complexity: A Minimal-Assumption Framework. Authorea . 26 August 2025. 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