Work

Searching for differential addition chains

Year: 2025

Type: article

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.

Source: Research in Number Theory

DOI: 10.1007/s40993-024-00604-8

Authors: Daniel J. Bernstein, Jolijn Cottaar, Tanja Lange

Institutions: University of Illinois Chicago, Academia Sinica, Eindhoven University of Technology

Language: English

Topic: Cryptography and Residue Arithmetic

Subfield: Information Systems

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,590

Funders: Deutsche Forschungsgemeinschaft, Academia Sinica, Nederlandse Organisatie voor Wetenschappelijk Onderzoek