Integer Sub-Decomposition (Isd) Method For Elliptic Curve Scalar Multiplication
Dalam kajian ini, kaedah baru yang dipanggil sub-peleraian integer (ISD) berdasarkan prinsip Gallant, Lambert dan Vanstone (GLV) bagi mengira perkalian skalar kP berbentuk lengkung elips E melebihi kawasan terbatas utama Fp yang mempunyai pengiraan endomorphisms ψj yang efisyen bagi j = 1; 2, men...
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my-usm-ep.323172019-04-12T05:25:46Z Integer Sub-Decomposition (Isd) Method For Elliptic Curve Scalar Multiplication 2015-03 Ajeena, Ruma Kareem K. QA1 Mathematics (General) Dalam kajian ini, kaedah baru yang dipanggil sub-peleraian integer (ISD) berdasarkan prinsip Gallant, Lambert dan Vanstone (GLV) bagi mengira perkalian skalar kP berbentuk lengkung elips E melebihi kawasan terbatas utama Fp yang mempunyai pengiraan endomorphisms ψj yang efisyen bagi j = 1; 2, menghasilkan nilai yang dihitung sebelum ini untuk λ jP, di mana λ j ∈ [1;n−1] telah dicadangkan. Jurang utama dalam kaedah GLV telah ditangani dengan menggunakan kaedah ISD. Skalar k dalam kaedah ISD telah dibahagikan dengan menggunakan rumusan k ≡ k11+k12λ1+k21+k22λ2 (mod n); dengan max{|k11|; |k12|} ≤ √ n dan max{|k21|; |k22|} ≤ √ n. Oleh yang demikian formula perkalian kP scalar ISD boleh dinyatakan seperti berikut: kP = k11P+k12ψ1(P)+k21P+k22ψ2(P): In this study, a new method called integer sub-decomposition (ISD) based on the Gallant, Lambert, and Vanstone (GLV) method to compute the scalar multiplication kP of the elliptic curve E over prime finite field Fp that have efficient computable endomorphisms ψj for j = 1; 2, resulting in pre-computed values of λ jP, where λ j ∈ [1;n−1] has been proposed. The major gaps in the GLV method are addressed using the ISD method. The scalar k, on the ISD method is decomposed using the formulation k ≡ k11+k12λ1+k21+k22λ2 (mod n); with max{|k11|; |k12|} ≤ √ n and max{|k21|; |k22|} ≤ √n. Thus, the ISD scalar multiplication kP formula can be expressed as follows: kP = k11P+k12ψ1(P)+k21P+k22ψ2(P): 2015-03 Thesis http://eprints.usm.my/32317/ http://eprints.usm.my/32317/1/RUMA_KAREEM_K._AJEENA.pdf application/pdf en public phd doctoral Universiti Sains Malaysia Pusat Pengajian Sains Matematik |
| institution |
Universiti Sains Malaysia |
| collection |
USM Institutional Repository |
| language |
English |
| topic |
QA1 Mathematics (General) |
| spellingShingle |
QA1 Mathematics (General) Ajeena, Ruma Kareem K. Integer Sub-Decomposition (Isd) Method For Elliptic Curve Scalar Multiplication |
| description |
Dalam kajian ini, kaedah baru yang dipanggil sub-peleraian integer (ISD) berdasarkan
prinsip Gallant, Lambert dan Vanstone (GLV) bagi mengira perkalian skalar kP
berbentuk lengkung elips E melebihi kawasan terbatas utama Fp yang mempunyai
pengiraan endomorphisms ψj yang efisyen bagi j = 1; 2, menghasilkan nilai yang
dihitung sebelum ini untuk λ jP, di mana λ j ∈ [1;n−1] telah dicadangkan. Jurang
utama dalam kaedah GLV telah ditangani dengan menggunakan kaedah ISD. Skalar k
dalam kaedah ISD telah dibahagikan dengan menggunakan rumusan
k ≡ k11+k12λ1+k21+k22λ2 (mod n);
dengan max{|k11|; |k12|} ≤ √ n dan max{|k21|; |k22|} ≤ √ n.
Oleh yang demikian formula perkalian kP scalar ISD boleh dinyatakan seperti berikut:
kP = k11P+k12ψ1(P)+k21P+k22ψ2(P):
In this study, a new method called integer sub-decomposition (ISD) based on the
Gallant, Lambert, and Vanstone (GLV) method to compute the scalar multiplication
kP of the elliptic curve E over prime finite field Fp that have efficient computable
endomorphisms ψj for j = 1; 2, resulting in pre-computed values of λ jP, where
λ j ∈ [1;n−1] has been proposed. The major gaps in the GLV method are addressed
using the ISD method. The scalar k, on the ISD method is decomposed using the
formulation
k ≡ k11+k12λ1+k21+k22λ2 (mod n); with max{|k11|; |k12|} ≤
√ n and max{|k21|; |k22|} ≤ √n.
Thus, the ISD scalar multiplication kP formula can be expressed as follows:
kP = k11P+k12ψ1(P)+k21P+k22ψ2(P): |
| format |
Thesis |
| qualification_name |
Doctor of Philosophy (PhD.) |
| qualification_level |
Doctorate |
| author |
Ajeena, Ruma Kareem K. |
| author_facet |
Ajeena, Ruma Kareem K. |
| author_sort |
Ajeena, Ruma Kareem K. |
| title |
Integer Sub-Decomposition (Isd)
Method For Elliptic Curve
Scalar Multiplication
|
| title_short |
Integer Sub-Decomposition (Isd)
Method For Elliptic Curve
Scalar Multiplication
|
| title_full |
Integer Sub-Decomposition (Isd)
Method For Elliptic Curve
Scalar Multiplication
|
| title_fullStr |
Integer Sub-Decomposition (Isd)
Method For Elliptic Curve
Scalar Multiplication
|
| title_full_unstemmed |
Integer Sub-Decomposition (Isd)
Method For Elliptic Curve
Scalar Multiplication
|
| title_sort |
integer sub-decomposition (isd)
method for elliptic curve
scalar multiplication |
| granting_institution |
Universiti Sains Malaysia |
| granting_department |
Pusat Pengajian Sains Matematik |
| publishDate |
2015 |
| url |
http://eprints.usm.my/32317/1/RUMA_KAREEM_K._AJEENA.pdf |
| _version_ |
1747820565011365888 |