Linear Secret Sharing from Algebraic-Geometric Codes
| dc.creator | Chen, Hao | |
| dc.date | 2006-03-02 | |
| dc.date | 2006-03-10 | |
| dc.date.accessioned | 2026-07-07T08:16:23Z | |
| dc.date.available | 2026-07-07T08:16:23Z | |
| dc.description | It is well-known that the linear secret-sharing scheme (LSSS) can be constructed from linear error-correcting codes (Brickell [1], R.J. McEliece and D.V.Sarwate [2],Cramer, el.,[3]). The theory of linear codes from algebraic-geometric curves (algebraic-geometric (AG) codes or geometric Goppa code) has been well-developed since the work of V.Goppa and Tsfasman, Vladut, and Zink(see [17], [18] and [19]). In this paper the linear secret-sharing scheme from algebraic-geometric codes, which are non-threshold scheme for curves of genus greater than 0, are presented . We analysis the minimal access structure, $d_{min}$ and $d_{cheat}$([8]), (strongly) multiplicativity and the applications in verifiable secret-sharing (VSS) scheme and secure multi-party computation (MPC) of this construction([3] and [10-11]). Our construction also offers many examples of the self-dually $GF(q)$-representable matroids and many examples of new ideal linear secret-sharing schemes addressing to the problem of the characterization of the access structures for ideal secret-sharing schemes([3] and [9]). The access structures of the linear secret-sharing schemes from the codes on elliptic curves are given explicitly. From the work in this paper we can see that the algebraic-geometric structure of the underlying algebraic curves is an important resource for secret-sharing, matroid theory, verifiable secret-sharing and secure multi-party computation. | |
| dc.description | 11 pages, note added in the new version | |
| dc.identifier | https://arxiv.org/abs/cs/0603008 | |
| dc.identifier | http://arxiv.org/abs/cs/0603008 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/133763 | |
| dc.subject | Cryptography and Security | |
| dc.subject | Information Theory | |
| dc.title | Linear Secret Sharing from Algebraic-Geometric Codes | |
| dc.type | text |