Selmer-Inspired Elliptic Curve Generation

• URL: http://arxiv.org/abs/2510.02383v1
• Date: Tue, 30 Sep 2025 17:33:36 GMT
• Title: Selmer-Inspired Elliptic Curve Generation
• Authors: Awnon Bhowmik,
• Abstract summary: Elliptic curve cryptography (ECC) is foundational to modern secure communication.<n>Existing standard curves have faced scrutiny for opaque parameter-generation practices.<n>This work introduces a Selmer-inspired framework for constructing elliptic curves that is both transparent and auditable.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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