Picard Groups and Refined Discrete Logarithms
2005 ◽
Vol 8
◽
pp. 1-16
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Keyword(s):
AbstractLet K denote a number field, and G a finite abelian group. The ring of algebraic integers in K is denoted in this paper by $/cal{O}_K$, and $/cal{A}$ denotes any $/cal{O}_K$-order in K[G]. The paper describes an algorithm that explicitly computes the Picard group Pic($/cal{A}$), and solves the corresponding (refined) discrete logarithm problem. A tamely ramified extension L/K of prime degree l of an imaginary quadratic number field K is used as an example; the class of $/cal{O}_L$ in Pic($/cal{O}_K[G]$) can be numerically determined.
2006 ◽
Vol 02
(04)
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pp. 569-590
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Keyword(s):
1977 ◽
Vol 31
(2)
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pp. 165-171
Keyword(s):
1980 ◽
Vol 79
◽
pp. 123-129
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2010 ◽
Vol 2010
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pp. 1-14
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1987 ◽
Vol 101
(3)
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pp. 417-417
1995 ◽
Vol 1995
(462)
◽
pp. 19-30
Keyword(s):
2016 ◽
Vol 12
(06)
◽
pp. 1625-1639