Welcome to the resource topic for 2025/736
Title:
Superglue: Fast formulae for (2,2) gluing isogenies
Authors: Max Duparc
Abstract:We study the structure of theta structure on products of elliptic curves, detailing their construction through the symmetries induced by 4-torsion points. In particular, we show how these symmetries allow the computation of theta structures projectively, thus avoiding the use of modular inversions.
Furthermore, we explore the self-similarity of the matrix representation of theta structures, arising from the action of the canonical 2-torsion point in the Kummer line. Combined with the sparsity of certain 4-torsion points, this structure leads to new formulae for computing gluing (2,2) isogenies that require significantly fewer precomputations and arithmetic operations.
These new equations also naturally support the evaluation of points on the quadratic twist at negligible additional cost, without requiring operations in a field extension.
ePrint: https://eprint.iacr.org/2025/736
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