NP-completeness of the Goppa parameterised random binary quasi-dyadic syndrome decoding problem
by Pierre-Louis Cayrel; Mbouye Khady Diagne; Cheikh Thiécoumba Gueye
International Journal of Information and Coding Theory (IJICOT), Vol. 4, No. 4, 2017

Abstract: In 1978, the syndrome decoding problem (SDP) was proven to be NP-complete for random binary codes. Since then, the security of several cryptographic applications relies on its hardness. In 2009, Finiasz extended this result by demonstrating the NP-completeness of certain subclasses of SDP. In this paper, we prove the NP-completeness of the Goppa parameterised quasi-dyadic syndrome decoding problem. We use a reduction to the four-dimensional matching problem (proven NP-complete).

Online publication date: Mon, 02-Oct-2017

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