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  "id": "oai:papers.qnfo.org:decryption-capable-analog-machines-bounded-state-conditions-under-which-key-sear",
  "slug": "decryption-capable-analog-machines-bounded-state-conditions-under-which-key-sear",
  "title": "Decryption-Capable Analog Machines: Bounded-State Conditions under Which Key Search Implies Universal Computation",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "Analog and hybrid physical machines — oscillator networks, photonic solvers, and resonant parametron arrays — increasingly demonstrate search and optimization behavior that resembles the dynamics of codebreaking machines. A standing folk conjecture holds that any machine able to decrypt messages is necessarily a general-purpose computer, because decryption requires the same search dynamics as universal computation. The gap this paper addresses is that the conjecture has never been stated with explicit resource conditions, so it cannot be confirmed or refuted for realistic analog hardware. We formalize a decryption machine as a programmable physical dynamical system that locates a key in a keyspace \\0,1\\^n, and we analyze its computational class using universal resource budgets and bounded-state arguments. We derive that exhaustive 128-bit key search at 10⁹ operations per second requires 3.40× 10²9 s sequentially, that the critical key length against a universal operation budget of 5.24× 10⁹0 is n^*=301 bits, and that a bounded machine with m bits of readable state cannot decide any function requiring more than m bits of working memory, so no bounded analog machine is Turing-complete regardless of its search power. We prove conditionally that unbounded-keyspace, programmable decryption capability implies NP-hard search, and we exhibit a counterexample to the strong conjecture: a fixed oscillator Ising machine with 4-bit phase readout is a finite-state system and decrypts only fixed-width keys. The result separates accelerator-class analog machines from universal ones and gives hardware designers a concrete state-count criterion.",
  "abstract_markdown": "Analog and hybrid physical machines — oscillator networks, photonic solvers, and resonant parametron arrays — increasingly demonstrate search and optimization behavior that resembles the dynamics of codebreaking machines. A standing folk conjecture holds that any machine able to decrypt messages is necessarily a general-purpose computer, because decryption requires the same search dynamics as universal computation. The gap this paper addresses is that the conjecture has never been stated with explicit resource conditions, so it cannot be confirmed or refuted for realistic analog hardware. We formalize a decryption machine as a programmable physical dynamical system that locates a key in a keyspace $\\{0,1\\}^n$, and we analyze its computational class using universal resource budgets and bounded-state arguments. We derive that exhaustive 128-bit key search at $10^9$ operations per second requires $3.40\\times 10^{29}$ s sequentially, that the critical key length against a universal operation budget of $5.24\\times 10^{90}$ is $n^{*}=301$ bits, and that a bounded machine with $m$ bits of readable state cannot decide any function requiring more than $m$ bits of working memory, so no bounded analog machine is Turing-complete regardless of its search power. We prove conditionally that unbounded-keyspace, programmable decryption capability implies NP-hard search, and we exhibit a counterexample to the strong conjecture: a fixed oscillator Ising machine with 4-bit phase readout is a finite-state system and decrypts only fixed-width keys. The result separates accelerator-class analog machines from universal ones and gives hardware designers a concrete state-count criterion.",
  "date": "2026-11-02",
  "first_published": "2026-11-02",
  "last_revised": "2026-11-02T00:00:00Z",
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  "url": "https://papers.qnfo.org/papers/decryption-capable-analog-machines-bounded-state-conditions-under-which-key-sear",
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        "name": "Rowan Brad Quni-Gudzinas",
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    "titles": [
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        "title": "Decryption-Capable Analog Machines: Bounded-State Conditions under Which Key Search Implies Universal Computation"
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        "description": "Analog and hybrid physical machines — oscillator networks, photonic solvers, and resonant parametron arrays — increasingly demonstrate search and optimization behavior that resembles the dynamics of codebreaking machines. A standing folk conjecture holds that any machine able to decrypt messages is necessarily a general-purpose computer, because decryption requires the same search dynamics as universal computation. The gap this paper addresses is that the conjecture has never been stated with explicit resource conditions, so it cannot be confirmed or refuted for realistic analog hardware. We formalize a decryption machine as a programmable physical dynamical system that locates a key in a keyspace \\0,1\\^n, and we analyze its computational class using universal resource budgets and bounded-state arguments. We derive that exhaustive 128-bit key search at 10⁹ operations per second requires 3.40× 10²9 s sequentially, that the critical key length against a universal operation budget of 5.24× 10⁹0 is n^*=301 bits, and that a bounded machine with m bits of readable state cannot decide any function requiring more than m bits of working memory, so no bounded analog machine is Turing-complete regardless of its search power. We prove conditionally that unbounded-keyspace, programmable decryption capability implies NP-hard search, and we exhibit a counterexample to the strong conjecture: a fixed oscillator Ising machine with 4-bit phase readout is a finite-state system and decrypts only fixed-width keys. The result separates accelerator-class analog machines from universal ones and gives hardware designers a concrete state-count criterion.",
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