Gröbner bases beat the classical modular-polynomial setup here, for 2^k and 3^k supersingular isogenies.
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01 02 Concrete Bit-Operation Cost of XL: For Solving Multivariate Quadratic Systems Using Wiedemann and Berlekamp-Massey eprint.iacr.orgA bit-operation cost model for XL plus Wiedemann/Berlekamp-Massey, with formulas and experiments for MQ challenge and NIST candidates.03 Heuristic subexponential key recovery for McEliece from rank-2 relations in binary Goppa codes, because algebra bites.