Sur les courbes elliptiques et application à la cryptographie
| dc.contributor.author | Bilel Selikh | |
| dc.date.accessioned | 2022-07-17T09:42:18Z | |
| dc.date.available | 2022-07-17T09:42:18Z | |
| dc.date.issued | 2022 | |
| dc.description.abstract | This thesis deals with the study of the elliptic curves over finite rings and their cryptographic applications. Firstly, we defined the elliptic curves Ea,b(Fq["]) and Ea,b(F3d ["]) over the rings Fq["] and F3d ["] respectively, with "4 = "3 by its projective equations, then we studied the classification of elements in these elliptic curves. Moreover, using the elliptic curve Ea,b(Fq["]), we introduced new non-commutative cryptography schemes on a special rings so that these cryptosystems are based on the two hard problems, the conjugal classical problem and the discrete logarithm problem, and they have strong security and very difficult to solve for decryption. At the end of the thesis we have given a numerical example of cryptography (encryption and decryption) on the elliptic curve E4 a,b over the ring F3d ["] where "4 = 0 by using two methods (with a secret key and a password). | en_US |
| dc.identifier.uri | http://dspace.univ-msila.dz:8080//xmlui/handle/123456789/30476 | |
| dc.publisher | Université de M'sila | en_US |
| dc.subject | Elliptic curve; Finite ring; Local ring; Elliptic curve cryptography; Noncommutative cryptography; Fully homomorphic encryption. | en_US |
| dc.title | Sur les courbes elliptiques et application à la cryptographie | en_US |
| dc.type | Thesis | en_US |