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Diffie-Hellman
Le premier algorithme à clés asymétriques
vendredi 8 mars 2002
Généralités :
Inventé en 1976 par Whitfield Diffie et Martin Hellman c’est le plus ancien cryptosytème à clé publique, et il est encore largement en usage.
Il peut être utilisé pour la signature électronique ou pour établir des clés symétriques entre deux ou plusieurs protagonistes sans qu’ils aient à échanger auparavant de secret partagé par un canal sûr, comme dans IPSec ou SSL.
Dans ce cas, il est toujours utilisé en conjonction avec un algorithme symétrique.
Sa sécurité repose sur la difficulté de calculer des logarithmes discrets par rapport à la "facilité" de calculer les exponentielles.
Principe :
Soient Dédé-la-malice et Julie-la-furie deux protagonistes désirant établir une clé secrète alors qu’ils ne disposent ni de secret partagé ni de canal sûr.
Dédé et Julie se mettent d’accord sur deux grands entiers premiers entre eux, n et g.
Dédé choisit un grand nombre entier aléatoire x, calcule : X=(g^x)mod(n) et l’envoie à Julie.
Julie choisit un grand nombre entier aléatoire y, calcule : Y=(g^y)mod(n) et l’envoie à Dédé.
Dédé calcule k=(Y^x)mod(n)
Julie calcule k’=(X^y)mod(n)
On a k=k’=(g^xy)mod(n)
Dédé et Julie sont donc parvenus à établir une clé secrète commune (qui pourra par exemple servir de clé DES pour s’échanger des données confidentielles).
Remarques :
Un attaquant qui espionne le canal de communication entre Dédé et Julie connaîtra n, g, X et Y. Pour retrouver x ou y il faudra qu’il calcule un logarithme discret modulo n, ce qui est très coûteux.
Les choix de n et de g peuvent poser des problèmes des sécurité :
n doit être "grand"
(n-1)/2 doit être premier
D-H peut être étendu à 3 participants ou plus.
D-H peut-être étendu aux courbes elliptiques.
D-H peut-être vulnérable à " l’attaque du milieu " : un attaquant se place entre les deux protagonistes et substitue systématiquement toutes les valeurs échangées par de nouvelles valeurs qu’il a lui même générées. Les protagonistes croiraient ainsi avoir échangé une clé secrète alors qu’ils l’auraient en fait échangée avec l’attaquant. Ce dernier est alors en mesure de déchiffrer les communications qui l’utiliseraient.
La parade est de signer toutes les transactions à l’aide de clés asymétriques certifiées par une autorité reconnue par les protagonistes.
El-Gamal, un autre algorithme à clés publiques dérive directement de D-H.
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Deprecated: Function eregi_replace() is deprecated in /var/alternc/html/c/cryptosec/ecrire/inc/filtres.php on line 377
Deprecated: Function eregi_replace() is deprecated in /var/alternc/html/c/cryptosec/ecrire/inc/filtres.php on line 378
Deprecated: Function ereg_replace() is deprecated in /var/alternc/html/c/cryptosec/ecrire/inc/filtres.php on line 379
Deprecated: Function eregi_replace() is deprecated in /var/alternc/html/c/cryptosec/ecrire/inc/texte.php on line 334
Deprecated: Function ereg_replace() is deprecated in /var/alternc/html/c/cryptosec/ecrire/inc/texte.php on line 277
Deprecated: Function ereg_replace() is deprecated in /var/alternc/html/c/cryptosec/ecrire/inc/texte.php on line 278
Deprecated: Function ereg_replace() is deprecated in /var/alternc/html/c/cryptosec/ecrire/inc/texte.php on line 281
Deprecated: Function ereg_replace() is deprecated in /var/alternc/html/c/cryptosec/ecrire/inc/texte.php on line 305
Deprecated: Function ereg_replace() is deprecated in /var/alternc/html/c/cryptosec/ecrire/inc/texte.php on line 323
Deprecated: Function ereg() is deprecated in /var/alternc/html/c/cryptosec/ecrire/inc/texte.php on line 1419
Deprecated: Function eregi_replace() is deprecated in /var/alternc/html/c/cryptosec/ecrire/inc/filtres.php on line 377
Deprecated: Function eregi_replace() is deprecated in /var/alternc/html/c/cryptosec/ecrire/inc/filtres.php on line 378
Deprecated: Function ereg_replace() is deprecated in /var/alternc/html/c/cryptosec/ecrire/inc/filtres.php on line 379
Deprecated: Function eregi_replace() is deprecated in /var/alternc/html/c/cryptosec/ecrire/inc/texte.php on line 334
Deprecated: Function ereg_replace() is deprecated in /var/alternc/html/c/cryptosec/ecrire/inc/texte.php on line 277
Deprecated: Function ereg_replace() is deprecated in /var/alternc/html/c/cryptosec/ecrire/inc/texte.php on line 278
Deprecated: Function ereg_replace() is deprecated in /var/alternc/html/c/cryptosec/ecrire/inc/texte.php on line 281
Deprecated: Function ereg_replace() is deprecated in /var/alternc/html/c/cryptosec/ecrire/inc/texte.php on line 305
Deprecated: Function ereg_replace() is deprecated in /var/alternc/html/c/cryptosec/ecrire/inc/texte.php on line 323
Deprecated: Function ereg() is deprecated in /var/alternc/html/c/cryptosec/ecrire/inc/texte.php on line 1419
Deprecated: Function eregi_replace() is deprecated in /var/alternc/html/c/cryptosec/ecrire/inc/filtres.php on line 377
Deprecated: Function eregi_replace() is deprecated in /var/alternc/html/c/cryptosec/ecrire/inc/filtres.php on line 378
Deprecated: Function ereg_replace() is deprecated in /var/alternc/html/c/cryptosec/ecrire/inc/filtres.php on line 379
Deprecated: Function eregi_replace() is deprecated in /var/alternc/html/c/cryptosec/ecrire/inc/texte.php on line 334
Deprecated: Function ereg_replace() is deprecated in /var/alternc/html/c/cryptosec/ecrire/inc/texte.php on line 277
Deprecated: Function ereg_replace() is deprecated in /var/alternc/html/c/cryptosec/ecrire/inc/texte.php on line 278
Deprecated: Function ereg_replace() is deprecated in /var/alternc/html/c/cryptosec/ecrire/inc/texte.php on line 281
Deprecated: Function ereg_replace() is deprecated in /var/alternc/html/c/cryptosec/ecrire/inc/texte.php on line 305
Deprecated: Function ereg_replace() is deprecated in /var/alternc/html/c/cryptosec/ecrire/inc/texte.php on line 323
Deprecated: Function ereg() is deprecated in /var/alternc/html/c/cryptosec/ecrire/inc/texte.php on line 1419
Deprecated: Function eregi_replace() is deprecated in /var/alternc/html/c/cryptosec/ecrire/inc/filtres.php on line 377
Deprecated: Function eregi_replace() is deprecated in /var/alternc/html/c/cryptosec/ecrire/inc/filtres.php on line 378
Deprecated: Function ereg_replace() is deprecated in /var/alternc/html/c/cryptosec/ecrire/inc/filtres.php on line 379
Deprecated: Function eregi_replace() is deprecated in /var/alternc/html/c/cryptosec/ecrire/inc/texte.php on line 334
Deprecated: Function ereg_replace() is deprecated in /var/alternc/html/c/cryptosec/ecrire/inc/texte.php on line 277
Deprecated: Function ereg_replace() is deprecated in /var/alternc/html/c/cryptosec/ecrire/inc/texte.php on line 278
Deprecated: Function ereg_replace() is deprecated in /var/alternc/html/c/cryptosec/ecrire/inc/texte.php on line 281
Deprecated: Function ereg_replace() is deprecated in /var/alternc/html/c/cryptosec/ecrire/inc/texte.php on line 305
Deprecated: Function ereg_replace() is deprecated in /var/alternc/html/c/cryptosec/ecrire/inc/texte.php on line 323
Deprecated: Function ereg() is deprecated in /var/alternc/html/c/cryptosec/ecrire/inc/texte.php on line 1419
Deprecated: Function eregi_replace() is deprecated in /var/alternc/html/c/cryptosec/ecrire/inc/filtres.php on line 377
Deprecated: Function eregi_replace() is deprecated in /var/alternc/html/c/cryptosec/ecrire/inc/filtres.php on line 378
Deprecated: Function ereg_replace() is deprecated in /var/alternc/html/c/cryptosec/ecrire/inc/filtres.php on line 379
Deprecated: Function ereg() is deprecated in /var/alternc/html/c/cryptosec/ecrire/inc/flock.php on line 60