From Cramer Rule to Lagrange Interpolation

Zhengjun Cao; Lihua Liu

Paper 2026/1362

From Cramer Rule to Lagrange Interpolation

Zhengjun Cao, Department of Mathematics, Shanghai University, Shanghai, 200444, China

Lihua Liu, Department of Mathematics, Shanghai Maritime University, Shanghai, 201306, China

Abstract

Multivariate interpolation arises in a wide range, including computer graphics, multi-secret sharing and secure multiparty computation. But its general representation is rarely discussed. In this note, a general representation for univariate interpolation and multivariate interpolation is formulated, which is helpful for multi-secret sharing illustrations and security arguments. The finding offers a new glimpse into the relation between Cramer rule and Lagrange interpolation formula.

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Preprint.
Keywords: Cramer rule Lagrange interpolation multivariate interpolation multi-secret sharing
Contact author(s): liulh @ shmtu edu cn
History: 2026-07-06: approved; 2026-07-02: received; See all versions
Short URL: https://ia.cr/2026/1362
License: CC0

BibTeX

@misc{cryptoeprint:2026/1362,
      author = {Zhengjun Cao and Lihua Liu},
      title = {From Cramer Rule to Lagrange Interpolation},
      howpublished = {Cryptology {ePrint} Archive, Paper 2026/1362},
      year = {2026},
      url = {https://eprint.iacr.org/2026/1362}
}