Decomposition formula of the Jacobian group of plane curve

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Paper 2013/548

Decomposition formula of the Jacobian group of plane curve

Koh-ichi Nagao

Abstract

We give an algorithm for decomposing given element of Jacobian gruop into the sum of the decomposed factor, which consists of certain subset of the points of curve.

Note: Using proposed method, decomposition attack (or index calculus) to the algebraic curve cryptosystem including hyperelliptic curve cryptosystem, can work.

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Preprint. MINOR revision.
Keywords: Decomposition Attack ECDLP
Contact author(s): nagao @ kanto-gakuin ac jp
History: 2013-12-13: last of 3 revisions; 2013-09-04: received; See all versions
Short URL: https://ia.cr/2013/548
License: CC BY