Searching for differential addition chains

Abstract The literature sometimes uses slow algorithms to find minimum-length continued-fraction differential addition chains to speed up subsequent computations of multiples of points on elliptic curves. This paper introduces two faster algorithms to find these chains. The first algorithm prunes more effectively than previous algorithms. The second algorithm uses a meet-in-the-middle approach and appears to have a limiting cost exponent below 1.

Authors

Institutions

Publication Details

Journal
Research in Number Theory
Published
2025-03-27
DOI
https://doi.org/10.1007/s40993-024-00604-8
Primary Topic
Cryptography and Residue Arithmetic
Type
article
Field-Weighted Citation Impact
0.00

Funders

Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
article

Searching for differential addition chains

Tanja Lange, Daniel J. Bernstein, Jolijn Cottaar
Research in Number Theory
Cryptography and Residue Arithmetic
article

Searching for differential addition chains

Tanja Lange, Daniel J. Bernstein, Jolijn Cottaar
article en

Abstract

Abstract The literature sometimes uses slow algorithms to find minimum-length continued-fraction differential addition chains to speed up subsequent computations of multiples of points on elliptic curves. This paper introduces two faster algorithms to find these chains. The first algorithm prunes more effectively than previous algorithms. The second algorithm uses a meet-in-the-middle approach and appears to have a limiting cost exponent below 1.

Research in Number TheoryVol. 11(2)
University of Illinois Chicago (US), Eindhoven University of Technology (NL), Academia Sinica (TW)
Deutsche Forschungsgemeinschaft, Academia Sinica, Nederlandse Organisatie voor Wetenschappelijk Onderzoek
Openalex Percentile: Top 93%
Cryptography and Residue Arithmetic
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.