Cryptanalysis of Public-key Cryptosystems Based on Algebraic Geometry Codes

Irene Márquez-Corbella, Edgar Martínez-Moro & Ruud Pellikaan
This paper addresses the question of retrieving the triple $(\mathcal{X},\mathcal{P},\mathcal{E})$ from the algebraic geometry code $\mathcal{C}_L(\mathcal{X},\mathcal{P},\mathcal{E})$, where $\mathcal{X}$ is an algebraic curve over the finite field $\mathbb{F}_q, \mathcal{P}$ is an $n$-tuple of $\mathbb{F}_q$-rational points on $\mathcal{X}$ and $E$ is a divisor on $\mathcal{X}$. If deg($E$) $\geq 2g + 1$ where $g$ is the genus of $\mathcal{X}$, then there is an embedding of $\mathcal{X}$ onto $\mathcal{Y}$ in the projective space of the linear series of the...
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