A new cryptographic algorithm based on decomposition problem in elliptic curve cryptography / Hilyati Hanina Zazali
This study describes three algorithms for efficient implementations in Elliptic Curve Cryptography (ECC). The first algorithm determines an approach of performing key exchanges between two subgroups for Decomposition Problem and three subgroups for Triple Decomposition Problem. The algorithms wor...
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| Format: | Thesis |
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2012
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| Online Access: | http://studentsrepo.um.edu.my/6167/ http://studentsrepo.um.edu.my/6167/1/00%2DCOVER_DEPAN.pdf http://studentsrepo.um.edu.my/6167/2/01%2DCOVER_DEPAN.pdf http://studentsrepo.um.edu.my/6167/3/02%2DDeclaration.pdf http://studentsrepo.um.edu.my/6167/4/FULL_CHAPTER_THESIS.pdf |
| _version_ | 1848773090150973440 |
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| author | Hilyati Hanina, Zazali |
| author_facet | Hilyati Hanina, Zazali |
| author_sort | Hilyati Hanina, Zazali |
| building | UM Research Repository |
| collection | Online Access |
| description | This study describes three algorithms for efficient implementations in Elliptic
Curve Cryptography (ECC). The first algorithm determines an approach of performing
key exchanges between two subgroups for Decomposition Problem and three
subgroups for Triple Decomposition Problem. The algorithms work by arranging
parameters using finite field group in elliptic curve E. It is a new approach which
performs core operation using multiplication of points based in ECC. The algorithm
explores computational advantages of computing cofactor number of points on E
and it is computationally infeasible to obtain if the cofactor are large enough. This
approach presents better platform in finite field E as compared to the original works
using the braid groups. The second algorithm deals with the use of Decomposition
Problem in encryption scheme for ECC. We introduce two concepts of splitting messages
using the scheme in El-Gamal and Massey-Omura algorithms. The messages
can be split either before or after the user sends the messages to the receiver. The
third algorithm describes the application of Decomposition Problem to the signing
and verifying digital messages in ECC. Since subexponential-time algorithm is
known for ordinary discrete logarithm problem and integer factorization problem
and not for elliptic curve discrete logarithm problem, the algorithm presented for
the digital signature in this study has substantially greater strength per key bit than
in other digital signature algorithm |
| first_indexed | 2025-11-14T13:36:52Z |
| format | Thesis |
| id | um-6167 |
| institution | University Malaya |
| institution_category | Local University |
| last_indexed | 2025-11-14T13:36:52Z |
| publishDate | 2012 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | um-61672016-03-04T02:36:06Z A new cryptographic algorithm based on decomposition problem in elliptic curve cryptography / Hilyati Hanina Zazali Hilyati Hanina, Zazali Q Science (General) This study describes three algorithms for efficient implementations in Elliptic Curve Cryptography (ECC). The first algorithm determines an approach of performing key exchanges between two subgroups for Decomposition Problem and three subgroups for Triple Decomposition Problem. The algorithms work by arranging parameters using finite field group in elliptic curve E. It is a new approach which performs core operation using multiplication of points based in ECC. The algorithm explores computational advantages of computing cofactor number of points on E and it is computationally infeasible to obtain if the cofactor are large enough. This approach presents better platform in finite field E as compared to the original works using the braid groups. The second algorithm deals with the use of Decomposition Problem in encryption scheme for ECC. We introduce two concepts of splitting messages using the scheme in El-Gamal and Massey-Omura algorithms. The messages can be split either before or after the user sends the messages to the receiver. The third algorithm describes the application of Decomposition Problem to the signing and verifying digital messages in ECC. Since subexponential-time algorithm is known for ordinary discrete logarithm problem and integer factorization problem and not for elliptic curve discrete logarithm problem, the algorithm presented for the digital signature in this study has substantially greater strength per key bit than in other digital signature algorithm 2012 Thesis NonPeerReviewed application/pdf http://studentsrepo.um.edu.my/6167/1/00%2DCOVER_DEPAN.pdf application/pdf http://studentsrepo.um.edu.my/6167/2/01%2DCOVER_DEPAN.pdf application/pdf http://studentsrepo.um.edu.my/6167/3/02%2DDeclaration.pdf application/pdf http://studentsrepo.um.edu.my/6167/4/FULL_CHAPTER_THESIS.pdf Hilyati Hanina, Zazali (2012) A new cryptographic algorithm based on decomposition problem in elliptic curve cryptography / Hilyati Hanina Zazali. Masters thesis, University of Malaya. http://studentsrepo.um.edu.my/6167/ |
| spellingShingle | Q Science (General) Hilyati Hanina, Zazali A new cryptographic algorithm based on decomposition problem in elliptic curve cryptography / Hilyati Hanina Zazali |
| title | A new cryptographic algorithm based on decomposition problem in elliptic curve cryptography / Hilyati Hanina Zazali
|
| title_full | A new cryptographic algorithm based on decomposition problem in elliptic curve cryptography / Hilyati Hanina Zazali
|
| title_fullStr | A new cryptographic algorithm based on decomposition problem in elliptic curve cryptography / Hilyati Hanina Zazali
|
| title_full_unstemmed | A new cryptographic algorithm based on decomposition problem in elliptic curve cryptography / Hilyati Hanina Zazali
|
| title_short | A new cryptographic algorithm based on decomposition problem in elliptic curve cryptography / Hilyati Hanina Zazali
|
| title_sort | new cryptographic algorithm based on decomposition problem in elliptic curve cryptography / hilyati hanina zazali |
| topic | Q Science (General) |
| url | http://studentsrepo.um.edu.my/6167/ http://studentsrepo.um.edu.my/6167/1/00%2DCOVER_DEPAN.pdf http://studentsrepo.um.edu.my/6167/2/01%2DCOVER_DEPAN.pdf http://studentsrepo.um.edu.my/6167/3/02%2DDeclaration.pdf http://studentsrepo.um.edu.my/6167/4/FULL_CHAPTER_THESIS.pdf |