Abstract:
The paper is devoted to McEliece-type code-based cryptosystems, which can potentially be used as post-quantum ones. Modifications of the McEliece cryptosystem using algebraic geometric codes associated with an elliptic curve are considered; in particular, the ECC2 cryptosystem is examined. A polynomial algorithm is proposed that uses the Schur — Hadamard product operations of linear codes and the calculation of the dual code, which allows one to restore the elliptic curve and the divisor $D$ from the generator matrix of the corresponding elliptic $[n,k]_{q}$-code $\mathcal{C}_{\mathcal{L}}(D,kP_{\infty})$ for $3<k<(n-4)/{2}$. The complexity of this algorithm is calculated as $O((k^{2}+q^{2})n^{2})$ operations in a finite field.
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