GENERALIZED JACOBIAN AND DISCRETE LOGARITHM PROBLEM ON ELLIPTIC CURVES

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DAGHIGH H.; BAHRAMIAN M.

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ISSN: 2588-4824

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Journal: Iranian Journal of Mathematical Sciences and Informatics Year:2009 | Volume:4 | Issue:2 Page(s): 55-64

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Title

GENERALIZED JACOBIAN AND DISCRETE LOGARITHM PROBLEM ON ELLIPTIC CURVES

Author(s)

DAGHIGH H. | BAHRAMIAN M. | Issue Writer Certificate

Keywords

ELLIPTIC CURVE

DISCRETE LOGARITHM PROBLEM

GENERALIZED JACOBIAN

Abstract

Let E be an ELLIPTIC CURVE over the finite field Fq, P a point in E(Fq) of order n, and Q a point in the group generated by P. The DISCRETE LOGARITHM PROBLEM on E is to find the number k such that Q = kP. In this paper we reduce the DISCRETE LOGARITHM PROBLEM on E[n] to the discrete logarithm on the group F*q , the multiplicative group of nonzero elements of Fq, in the case where n ï q - 1, using GENERALIZED JACOBIAN of E.

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APA: Copy

DAGHIGH, H., & BAHRAMIAN, M.. (2009). GENERALIZED JACOBIAN AND DISCRETE LOGARITHM PROBLEM ON ELLIPTIC CURVES. IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS (IJMSI), 4(2), 55-64. SID. https://sid.ir/paper/310298/en

Vancouver: Copy

DAGHIGH H., BAHRAMIAN M.. GENERALIZED JACOBIAN AND DISCRETE LOGARITHM PROBLEM ON ELLIPTIC CURVES. IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS (IJMSI)[Internet]. 2009;4(2):55-64. Available from: https://sid.ir/paper/310298/en

IEEE: Copy

H. DAGHIGH, and M. BAHRAMIAN, “GENERALIZED JACOBIAN AND DISCRETE LOGARITHM PROBLEM ON ELLIPTIC CURVES,” IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS (IJMSI), vol. 4, no. 2, pp. 55–64, 2009, [Online]. Available: https://sid.ir/paper/310298/en

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