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zooqueen
ac61e71667
Scrub residual Ring-LWE mislabels of the Corona/Pulsar threshold
signature family per canonical decision-b (source: ringtail/sign/config.go
M=8,N=7, q=0x1000000004A01).
- Corona = Module-LWE (Ringtail-derived parameter set, A in R_q^{8x7}),
not Ring-LWE / not "Module-LWE at rank 1".
- Pulsar = Module-LWE (ML-DSA-65, FIPS-204 byte-equal).
- Corona+Pulsar differ by parameter regime/codebase, NOT hardness family:
intra-lattice parameter/implementation diversity, NOT family-disjoint.
- True family-disjoint defense = Magnetar (hash, SLH-DSA) / HQC (codes).
Reframed the false Corona(R-LWE)-vs-Pulsar(M-LWE) family-independence
across lp-219/lp-220/lp-222/lp-223 (P3Q kinds), lux-quasar-composition
(profile hardness table + composition corollary/proof), lux-magnetar-pq,
and the superseded triple-proof/quasar drafts (anonymous lattice
threshold lane = Corona). Legitimate FHE/TFHE Ring-LWE, NTT citations,
and neutral "rank-1" lattice facts left intact. PDFs rebuilt.
38 lines
1.8 KiB
TeX
38 lines
1.8 KiB
TeX
\section{Security Analysis}
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\subsection{Defense in Depth}
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The triple-proof design rests on three independent mathematical assumptions:
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\begin{enumerate}[leftmargin=2em]
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\item \textbf{Discrete logarithm} (BLS): Hardness of the elliptic curve discrete logarithm problem on BLS12-381.
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\item \textbf{Lattice problems} (ML-DSA + Corona): Hardness of Module-LWE (both legs are Module-LWE, at distinct parameter sets).
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\item \textbf{Hash functions} (STARK): Collision resistance of the hash function used in the STARK proof system.
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\end{enumerate}
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Any two of these three assumptions suffice for full security:
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\begin{center}
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\begin{tabular}{lccc}
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\toprule
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\textbf{Scenario} & \textbf{BLS} & \textbf{ML-DSA/RT} & \textbf{STARK} \\
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\midrule
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Classical adversary & \checkmark & \checkmark & \checkmark \\
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Quantum breaks DL & $\times$ & \checkmark & \checkmark \\
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Lattice weakness found & \checkmark & $\times$ & \checkmark \\
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STARK hash broken & \checkmark & \checkmark (individual sigs) & $\times$ \\
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Quantum + lattice & $\times$ & $\times$ & \checkmark$^*$ \\
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\bottomrule
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\end{tabular}
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\end{center}
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$^*$If both discrete log and lattice problems are broken, only the STARK proof (hash-based) remains. This provides integrity but not authenticity --- a scenario considered extremely unlikely given current understanding of quantum computing and lattice cryptography.
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\subsection{Quantum Attack Window}
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A quantum adversary attempting to forge a BLS signature must do so within the epoch window (1 second). Current estimates for breaking BLS12-381 with a CRQC require $>10^6$ logical qubits operating for minutes to hours. The 1-second epoch window is physically impossible to exploit with foreseeable quantum technology.
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Even if the epoch window were exploitable, the ML-DSA + Corona proofs would detect the forgery at the next epoch boundary.
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