[Resource Topic] 2025/147: Efficient algorithms for the detection of $(N,N)$-splittings and endomorphisms

Welcome to the resource topic for 2025/147

Title:
Efficient algorithms for the detection of (N,N)-splittings and endomorphisms

Authors: Maria Corte-Real Santos, Craig Costello, Sam Frengley

Abstract:

We develop an efficient algorithm to detect whether a superspecial genus 2 Jacobian is optimally (N, N)-split for each integer N \leq 11. Incorporating this algorithm into the best-known attack against the superspecial isogeny problem in dimension 2 (due to Costello and Smith) gives rise to significant cryptanalytic improvements. Our implementation shows that when the underlying prime p is 100 bits, the attack is sped up by a factor of 25; when the underlying prime is 200 bits, the attack is sped up by a factor of 42; and, when the underlying prime is 1000 bits, the attack is sped up by a factor of 160. Furthermore, we describe a more general algorithm to find endomorphisms of superspecial genus 2 Jacobians.

ePrint: https://eprint.iacr.org/2025/147

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