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Title: :  P-adic numbers applied on an elliptic curve cryptography
PaperId: :  9579
Published in:   International Journal Of Advance Research And Innovative Ideas In Education
Publisher:   IJARIIE
e-ISSN:   2395-4396
Volume/Issue:    Volume 5 Issue 2 2019
DUI:    16.0415/IJARIIE-9579
Licence: :   IJARIIE is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Author NameAuthor Institute
Maherindrainibelahasa Ratsimamitaka Edouard University of Antananarivo in STII
Randimbindrainibe FalimananaUniversity of Antananarivo in ESPA
Ravaliminoarimalalason Toky BasilideUniversity of Antananarivo in ESPA

Abstract

cryptography
p-adic integers- p-adic numbers- p-adic valuation- p-adic absolute values- elliptic curve- rational point of elliptic curve- trace of elliptic curve- recductuin modulo p- cryptosystem- public key.
This paper use the group of -rational points of elliptic curve over p-adic numbers field in cryptography. Since this group is an abelian group and can be made cyclic, « addition » on this group have also important geometrical interpretation We introduice some notations in section 1 and review some properties of a p-adic numbers. In section 2, we review group structure of elliptic curves over the field of p-adic numbers.In section 3 we show one possibility to apply the group of -rational points on an elliptic curve in cryptography.In sectio 4, we give an example of cryptosystem based on the key exchange of Diffie-HellmanThe section 5 is reserved for the conclusion.

Citations

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IJARIIE Maherindrainibelahasa Ratsimamitaka Edouard , Randimbindrainibe Falimanana, and Ravaliminoarimalalason Toky Basilide. "P-adic numbers applied on an elliptic curve cryptography" International Journal Of Advance Research And Innovative Ideas In Education Volume 5 Issue 2 2019 Page 213-229
MLA Maherindrainibelahasa Ratsimamitaka Edouard , Randimbindrainibe Falimanana, and Ravaliminoarimalalason Toky Basilide. "P-adic numbers applied on an elliptic curve cryptography." International Journal Of Advance Research And Innovative Ideas In Education 5.2(2019) : 213-229.
APA Maherindrainibelahasa Ratsimamitaka Edouard , Randimbindrainibe Falimanana, & Ravaliminoarimalalason Toky Basilide. (2019). P-adic numbers applied on an elliptic curve cryptography. International Journal Of Advance Research And Innovative Ideas In Education, 5(2), 213-229.
Chicago Maherindrainibelahasa Ratsimamitaka Edouard , Randimbindrainibe Falimanana, and Ravaliminoarimalalason Toky Basilide. "P-adic numbers applied on an elliptic curve cryptography." International Journal Of Advance Research And Innovative Ideas In Education 5, no. 2 (2019) : 213-229.
Oxford Maherindrainibelahasa Ratsimamitaka Edouard , Randimbindrainibe Falimanana, and Ravaliminoarimalalason Toky Basilide. 'P-adic numbers applied on an elliptic curve cryptography', International Journal Of Advance Research And Innovative Ideas In Education, vol. 5, no. 2, 2019, p. 213-229. Available from IJARIIE, https://ijariie.com/AdminUploadPdf/P_adic_numbers_applied_on_an_elliptic_curve_cryptography_ijariie9579.pdf (Accessed : 27 August 2024).
Harvard Maherindrainibelahasa Ratsimamitaka Edouard , Randimbindrainibe Falimanana, and Ravaliminoarimalalason Toky Basilide. (2019) 'P-adic numbers applied on an elliptic curve cryptography', International Journal Of Advance Research And Innovative Ideas In Education, 5(2), pp. 213-229IJARIIE [Online]. Available at: https://ijariie.com/AdminUploadPdf/P_adic_numbers_applied_on_an_elliptic_curve_cryptography_ijariie9579.pdf (Accessed : 27 August 2024)
IEEE Maherindrainibelahasa Ratsimamitaka Edouard , Randimbindrainibe Falimanana, and Ravaliminoarimalalason Toky Basilide, "P-adic numbers applied on an elliptic curve cryptography," International Journal Of Advance Research And Innovative Ideas In Education, vol. 5, no. 2, pp. 213-229, Mar-App 2019. [Online]. Available: https://ijariie.com/AdminUploadPdf/P_adic_numbers_applied_on_an_elliptic_curve_cryptography_ijariie9579.pdf [Accessed : 27 August 2024].
Turabian Maherindrainibelahasa Ratsimamitaka Edouard , Randimbindrainibe Falimanana, and Ravaliminoarimalalason Toky Basilide. "P-adic numbers applied on an elliptic curve cryptography." International Journal Of Advance Research And Innovative Ideas In Education [Online]. volume 5 number 2 (27 August 2024).
Vancouver Maherindrainibelahasa Ratsimamitaka Edouard , Randimbindrainibe Falimanana, and Ravaliminoarimalalason Toky Basilide. P-adic numbers applied on an elliptic curve cryptography. International Journal Of Advance Research And Innovative Ideas In Education [Internet]. 2019 [Cited : 27 August 2024]; 5(2) : 213-229. Available from: https://ijariie.com/AdminUploadPdf/P_adic_numbers_applied_on_an_elliptic_curve_cryptography_ijariie9579.pdf
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