Differential addition chains

@inproceedings{Bernstein2006DifferentialAC,
  title={Differential addition chains},
  author={Daniel J. Bernstein},
  year={2006}
}
Differential addition chains (also known as strong addition chains, Lucas chains, and Chebyshev chains) are addition chains in which every sum is already accompanied by a difference. Low-cost differential addition chains are used to efficiently exponentiate in groups where the operation a, b, a/b 7→ ab is fast: in particular, to perform x-coordinate scalar multiplication P 7→ mP on an elliptic curve y = x + Ax + x. Similarly, low-cost two-dimensional differential addition chains are used to… CONTINUE READING

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