### Abstract

Original language | English |
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Place of Publication | Oberwolfach |

Publisher | Mathematisches Forschungsinstitut Oberwolfach |

Number of pages | 17 |

Publication status | Published - 2012 |

### Publication series

Name | Oberwolfach Preprints |
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Volume | OWP 2012-01 |

### Fingerprint

### Cite this

*Cryptanalysis of public-key cryptosystems based on algebraic geometry codes*. (Oberwolfach Preprints; Vol. OWP 2012-01). Oberwolfach: Mathematisches Forschungsinstitut Oberwolfach.

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*Cryptanalysis of public-key cryptosystems based on algebraic geometry codes*. Oberwolfach Preprints, vol. OWP 2012-01, Mathematisches Forschungsinstitut Oberwolfach, Oberwolfach.

**Cryptanalysis of public-key cryptosystems based on algebraic geometry codes.** / Márquez-Corbella, I.; Martínez-Moro, E.; Pellikaan, G.R.

Research output: Book/Report › Report › Academic

TY - BOOK

T1 - Cryptanalysis of public-key cryptosystems based on algebraic geometry codes

AU - Márquez-Corbella, I.

AU - Martínez-Moro, E.

AU - Pellikaan, G.R.

PY - 2012

Y1 - 2012

N2 - This paper addresses the question of retrieving the triple (X ;P; E) from the algebraic geometry code CL(X ;P; E), where X is an algebraic curve over the finite field Fq, P is an n-tuple of Fq-rational points on X and E is a divisor on X . If deg(E) = 2g + 1 where g is the genus of X , then there is an embedding of X onto Y in the projective space of the linear series of the divisor E. Moreover, if deg(E) = 2g + 2, then I(Y), the vanishing ideal of Y, is generated by I2(Y), the homogeneous elements of degree two in I(Y). If n > 2 deg(E), then I2(Y) = I2(Q), where Q is the image of P under the map from X to Y. These two results imply that certain algebraic geometry codes are not secure if used in the McEliece public-key cryptosystem.

AB - This paper addresses the question of retrieving the triple (X ;P; E) from the algebraic geometry code CL(X ;P; E), where X is an algebraic curve over the finite field Fq, P is an n-tuple of Fq-rational points on X and E is a divisor on X . If deg(E) = 2g + 1 where g is the genus of X , then there is an embedding of X onto Y in the projective space of the linear series of the divisor E. Moreover, if deg(E) = 2g + 2, then I(Y), the vanishing ideal of Y, is generated by I2(Y), the homogeneous elements of degree two in I(Y). If n > 2 deg(E), then I2(Y) = I2(Q), where Q is the image of P under the map from X to Y. These two results imply that certain algebraic geometry codes are not secure if used in the McEliece public-key cryptosystem.

M3 - Report

T3 - Oberwolfach Preprints

BT - Cryptanalysis of public-key cryptosystems based on algebraic geometry codes

PB - Mathematisches Forschungsinstitut Oberwolfach

CY - Oberwolfach

ER -