Subexponential class group and unit group computation in large degree number fields
نویسندگان
چکیده
منابع مشابه
Subexponential Class Group Computation in Quadratic Orders (abstract)
In 1989, the first subexponential algorithm for computing the class group of an imaginary quadratic order was introduced by Hafner and McCurley. Their algorithm is based on an integer factorization algorithm due to Seysen, and is conditional on the truth of the Extended Riemann Hypothesis. Not long after, their result was generalized to arbitrary algebraic number fields by Buchmann. Efficient v...
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We analyse the complexity of the computation of the class group structure, regulator, and a system of fundamental units of a certain class of number fields. Our approach differs from Buchmann’s, who proved a complexity bound of L(1/2, O(1)) when the discriminant tends to infinity with fixed degree. We achieve a subexponential complexity in O(L(1/3, O(1))) when both the discriminant and the degr...
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Number fields and global function fields have many similar properties. Both have many applications to cryptography and coding theory, and the main computational problems for number fields, such as computing the ring of integers and computing the class group and the unit group, have analogues over function fields. The complexity of the number field problems has been studied extensively and these...
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ژورنال
عنوان ژورنال: LMS Journal of Computation and Mathematics
سال: 2014
ISSN: 1461-1570
DOI: 10.1112/s1461157014000345