Searching for differential addition chains

ePrint Report: Searching for differential addition chains

Daniel J. Bernstein, Jolijn Cottaar, Tanja Lange

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.

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