Nous introduisons une variante du protocole de signature et d'identification de Fiat-Shamir, basée sur la difficulté pratique qu'il y a à calculer des générateurs des idéaux principaux dans les corps de nombres. Nous montrons en outre comment utiliser les heuristiques de Cohen-Lenstra-Martinet pour les groupes de classes dans le but de construire des corps de nombres dans lesquels le calcul de générateurs des idéaux principaux est encore hors d'atteinte.
We explain a variant of the Fiat-Shamir identification and signature protocol that is based on the intractability of computing generators of principal ideals in algebraic number fields. We also show how to use the Cohen-Lenstra-Martinet heuristics for class groups to construct number fields in which computing generators of principal ideals is intractable.
@article{JTNB_2000__12_2_293_0, author = {Buchmann, Johannes and Maurer, Markus and M\"oller, Bodo}, title = {Cryptography based on number fields with large regulator}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {293--307}, publisher = {Universit\'e Bordeaux I}, volume = {12}, number = {2}, year = {2000}, mrnumber = {1823187}, zbl = {0999.94029}, language = {en}, url = {http://archive.numdam.org/item/JTNB_2000__12_2_293_0/} }
TY - JOUR AU - Buchmann, Johannes AU - Maurer, Markus AU - Möller, Bodo TI - Cryptography based on number fields with large regulator JO - Journal de théorie des nombres de Bordeaux PY - 2000 SP - 293 EP - 307 VL - 12 IS - 2 PB - Université Bordeaux I UR - http://archive.numdam.org/item/JTNB_2000__12_2_293_0/ LA - en ID - JTNB_2000__12_2_293_0 ER -
%0 Journal Article %A Buchmann, Johannes %A Maurer, Markus %A Möller, Bodo %T Cryptography based on number fields with large regulator %J Journal de théorie des nombres de Bordeaux %D 2000 %P 293-307 %V 12 %N 2 %I Université Bordeaux I %U http://archive.numdam.org/item/JTNB_2000__12_2_293_0/ %G en %F JTNB_2000__12_2_293_0
Buchmann, Johannes; Maurer, Markus; Möller, Bodo. Cryptography based on number fields with large regulator. Journal de théorie des nombres de Bordeaux, Tome 12 (2000) no. 2, pp. 293-307. http://archive.numdam.org/item/JTNB_2000__12_2_293_0/
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