arXiv subjects

José Luis Delgado

Publications and source records attributed to José Luis Delgado.

3 recordsLinked to original sources

arXiv2026

The Supersingular Isogeny Problem in Time and Memory $p^{1/3+o(1)}$, Unconditionally

Given a supersingular elliptic curve $E/\mathbb{F}_{p^2}$, the $\mathsf{OneEnd}$ problem asks for a non-scalar endomorphism of $E$. By known reductions, solving this problem also solves the supersingular endomorphism ring and isogeny problems. Wesolowski obtained exponent $1/3$ under an assumption on the factorization of a small degree, whereas the previous unconditional exponent was $2/5$. We give a Las Vegas algorithm, analyzed without a smoothness heuristic, with expected time and memory \[ p^{1/3}\exp\bigl(O(\sqrt{\log p\,\log\log p})\bigr) = p^{1/3+o(1)}. \] The algorithm fixes in advance a family of degrees that are products of small primes. Known counting results provide many isogenies of these degrees from curves to their Frobenius conjugates, and a collision estimate shows that the isogenies occur on sufficiently many distinct curves for a random walk to reach one of them. From such a curve, the algorithm splits a degree into two parts, enumerates two lists of shorter isogenies, and matches their targets to obtain an isogeny to the conjugate, whose composition with Frobenius gives the required endomorphism.

cs.CR↗

arXiv2026

Full-Key Recovery and Forgery from One MQOM v2.1 Signature

We give a full-key-recovery attack on MQOM v2.1, a Round-3 candidate in the NIST additional-signature process, that recovers the complete signing key from one accepted signature and uses it to sign a fresh message. If $δ=\operatorname{FirstBits}_λ(x)$ is the prefix of the witness $x$, the sibling path determines a public value $A$ such that tree parity gives $s=δ\oplus A$. Substitution into the hidden-leaf commitment yields $$\mathsf{Enc}_K(δ\oplus A)=T\oplus\mathsf{LinOrtho}(δ)$$ with public values $K$ and $T$. The correction in the same signature expands a solution into a complete witness, while the public MQ relation identifies those yielding valid signing keys; serializing such a witness gives the secret key, enabling a fresh-message signature accepted by the reference verifier. We evaluate this equation over the specified AES/Rijndael circuits using retained circuit state along a Gray traversal. Complete-domain scans for Categories I and V cost $2^{142.335112}$ and $2^{271.794162}$ Boolean gates. Category-III scans cover $1/2+2^{-20}$ and $0.580004770183$ of the domain at costs of $2^{206.774558}$ and $2^{206.988685}$ gates. All four totals are below the NIST security benchmarks. Reduced-domain runs against the reference implementation recover the byte-exact witness and key in all three categories and produce a fresh-message forgery accepted by the reference verifier. Independently generated source-syntax circuits evaluate the fixed ciphers over the stated domains and translated L3 prefixes, while an exact ideal-cipher factorial-moment bound controls additional equation preimages passed to public-key validation. Every value in the equation is fixed by the accepted transcript, so salt-bound global-root expansion changes its public constants without removing the one-signature recovery channel.

cs.CR↗

arXiv2026

Observability for Post-Quantum TLS Readiness: A Multi-Surface Evidence Framework

Post-quantum migration in Transport Layer Security (TLS) requires evidence-aware measurements that distinguish session negotiation, endpoint capability, certificate-chain evidence, and the provenance of missing observations. This distinction is essential under TLS 1.3 encryption, resumption, mutual TLS, trace truncation, fragmentation, coalescing, active certificate retrieval, and temporal drift. We present a multi-surface framework for post-quantum TLS observability. The framework separates passive session evidence, active probing, certificate-chain evidence, and registry knowledge, and maps them onto measurement planes for session behavior, key establishment, endpoint capability, authentication, lifecycle, observability, and policy. We instantiate it as a reproducible artifact with schema-enforced observations and results, versioned registries, auditable inference rules, stress contracts, and baseline adapters. We evaluate the framework on 29 controlled scenarios spanning TLS 1.2 and TLS 1.3, classical and hybrid key establishment, mutual TLS, resumption, HelloRetryRequest, truncation, fragmentation and coalescing, temporal drift, IPv6, and chain-depth variation. Passive evidence closes session-level planes, active probing establishes capability lower bounds, and multi-surface evidence closes the full measurement object while preserving uncertainty and contradiction when required. Against an inherited TLS quantum-vulnerability analyzer, the baseline detects 2 of 29 runs and 0 of 23 TLS 1.3 runs. In a stratified public campaign over 1000 targets and 2000 fresh probes, the framework completes 1971 handshakes, collects 1368 chain artifacts, confirms hybrid capability for 310 targets, and identifies 310 cases where endpoint capability exceeds what any single classical session view reveals.

cs.CR↗