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.
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.
| Original language | English |
|---|---|
| Article number | 45 |
| Number of pages | 23 |
| Journal | Research in Number Theory |
| Volume | 11 |
| Issue number | 2 |
| Early online date | 27 Mar 2025 |
| DOIs | |
| Publication status | Published - Jun 2025 |
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