کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4595135 1335799 2008 15 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A Weil pairing on the p-torsion of ordinary elliptic curves over K[ϵ]
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
A Weil pairing on the p-torsion of ordinary elliptic curves over K[ϵ]
چکیده انگلیسی

For an elliptic curve E over any field K, the Weil pairing en is a bilinear map on n-torsion. In this paper, we consider E over the dual numbers K[ϵ] and define a non-degenerate “Weil pairing on p-torsion” which shares many of the same properties of the Weil pairing. We also show that the discrete logarithm attacks on p-torsion subgroups of Semaev and Rück may be viewed as Weil-pairing-based attacks, just like the MOV attack. Finally, we describe an attack on the discrete logarithm problem on anomalous curves, analogous to that of Smart, using a lift of E over Fp[ϵ].

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Number Theory - Volume 128, Issue 6, June 2008, Pages 1874-1888