The DOI matches its Crossref record.
A Remark Concerning m-Divisibility and the Discrete Logarithm in the Divisor Class Group of Curves
Abstract
The aim of this paper is to show that the computation of the discrete logarithm in the m-torsion part of the divisor class group of a curve X over a finite field ko (with char(ko) prime to m), or over a local field k with residue field ko, can be reduced to the computation of the discrete logarithm in k0(4m)* . For this purpose we use a variant of the (tame) Tate pairing for Abelian varieties over local fields. In the same way the problem to determine all linear combinations of a finite set of elements in the divisor class group of a curve over k or ko which are divisible by m is reduced to the computation of the discrete logarithm in ko(Cm)* -
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cited by
Handbook of applied cryptography
(1997) · Choice Reviews Online · doi:10.5860/choice.34-4512 · Cited by 10,357
A One Round Protocol for Tripartite Diffie–Hellman
Joux, A. (2000) · Lecture Notes in Computer Science · doi:10.1007/10722028_23 · Cited by 1,039
The State of Elliptic Curve Cryptography
Koblitz, N., Menezes, A., & Vanstone, S. (2000) · Designs, Codes and Cryptography · doi:10.1023/a:1008354106356 · Cited by 685
SNARKs for C: Verifying Program Executions Succinctly and in Zero Knowledge
Ben-Sasson, E., Chiesa, A., Genkin, D., Tromer, E., & Virza, M. (2013) · Lecture Notes in Computer Science · doi:10.1007/978-3-642-40084-1_6 · Cited by 598
The Weil Pairing, and Its Efficient Calculation
Miller, V. S. (2004) · Journal of Cryptology · doi:10.1007/s00145-004-0315-8 · Cited by 578
Metadata
- Authors
- Frey, G., & Ruck, H.-G.
- Venue
- Mathematics of Computation
- Publisher
- JSTOR
- Published
- 1994-04
- Volume
- 62
- Issue
- 206
- Pages
- 865
- ISSN
- 0025-5718 (ISSN-L)
- OpenAlex
- W2094556471
- Cited by
- 551
- References
- 0
- FWCI
- 1.18
- Type
- journal article
- Language
- en
- Open access
- closed
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: A Remark Concerning m-Divisibility and the Discrete Logarithm in the Divisor Class Group of Curves. https://app.cochat.ai/papers/10.2307/2153546
- The paper
- Frey, G., & Ruck, H.-G. (1994). A Remark Concerning m-Divisibility and the Discrete Logarithm in the Divisor Class Group of Curves. Mathematics of Computation. https://doi.org/10.2307/2153546
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
