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Title:
An algorithm for efficient detection of (N,N)-splittings and its application to the isogeny problem in dimension 2
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 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 25{\tt x}; when the underlying prime is 200 bits, the attack is sped up by a factor 42{\tt x}; and, when the underlying prime is 1000 bits, the attack is sped up by a factor 160{\tt x}.
ePrint: https://eprint.iacr.org/2022/1736
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