Forging Montgomery-Sharif quantum money can be attacked with a Grover search whose oracle checks curve cardinalities via division polynomials at rational points and quadratic twists, an O(log^4 p) speedup over point counting at still-exponential total cost.
IET Information Security �� (4), 362–366 (2019)
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Cryptanalysis of Isogeny-Based Quantum Money with Rational Points
Forging Montgomery-Sharif quantum money can be attacked with a Grover search whose oracle checks curve cardinalities via division polynomials at rational points and quadratic twists, an O(log^4 p) speedup over point counting at still-exponential total cost.