{"ID":2862962,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.02383","arxiv_id":"2510.02383","title":"Selmer-Inspired Elliptic Curve Generation","abstract":"Elliptic curve cryptography (ECC) is foundational to modern secure communication, yet existing standard curves have faced scrutiny for opaque parameter-generation practices. This work introduces a Selmer-inspired framework for constructing elliptic curves that is both transparent and auditable. Drawing from $2$- and $3$-descent methods, we derive binary quartics and ternary cubics whose classical invariants deterministically yield candidate $(c_4,c_6)$ parameters. Local solubility checks, modeled on Selmer admissibility, filter candidates prior to reconciliation into short-Weierstrass form over prime fields. We then apply established cryptographic validations, including group-order factorization, cofactor bounds, twist security, and embedding-degree heuristics. A proof-of-concept implementation demonstrates that the pipeline functions as a retry-until-success Las Vegas algorithm, with complete transcripts enabling independent verification. Unlike seed-based or purely efficiency-driven designs, our approach embeds arithmetic structure into parameter selection while remaining compatible with constant-time, side-channel resistant implementations. This work broadens the design space for elliptic curves, showing that descent techniques from arithmetic geometry can underpin trust-enhancing, standardization-ready constructions.","short_abstract":"Elliptic curve cryptography (ECC) is foundational to modern secure communication, yet existing standard curves have faced scrutiny for opaque parameter-generation practices. This work introduces a Selmer-inspired framework for constructing elliptic curves that is both transparent and auditable. Drawing from $2$- and $3...","url_abs":"https://arxiv.org/abs/2510.02383","url_pdf":"https://arxiv.org/pdf/2510.02383v1","authors":"[\"Awnon Bhowmik\"]","published":"2025-09-30T17:33:36Z","proceeding":"cs.CR","tasks":"[\"cs.CR\",\"math.NT\"]","methods":"[]","has_code":false}