Gram Schmidt Cryptohack Jun 2026

for vector operations, but a "solid" implementation from scratch using standard Python lists or the library looks like this: gram_schmidt = [np.array(v, dtype=float) range(len(basis)): = basis[i].copy() # Calculate projection coefficient mu_ij = np.dot(basis[i], u[j]) / np.dot(u[j], u[j]) # Subtract the projection ui -= mu_ij * u[j] u.append(ui) # Example input from CryptoHack challenge orthogonal_basis = gram_schmidt(v)

Crucially, the LLL algorithm calculates the of the basis vectors at gram schmidt cryptohack

Without Gram–Schmidt, LLL would have no measure of “almost orthogonality” and no way to ensure a basis is reduced in a useful sense. for vector operations, but a "solid" implementation from