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» Isomorphisms of Algebraic Number Fields
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MOC
2002
113views more  MOC 2002»
13 years 5 months ago
Computation of several cyclotomic Swan subgroups
Let Cl(OK [G]) denote the locally free class group, that is the group of stable isomorphism classes of locally free OK [G]-modules, where OK is the ring of algebraic integers in th...
Timothy Kohl, Daniel R. Replogle
AAECC
2007
Springer
143views Algorithms» more  AAECC 2007»
13 years 12 months ago
Constructions of Orthonormal Lattices and Quaternion Division Algebras for Totally Real Number Fields
Abstract. We describe some constructions of orthonormal lattices in totally real subfields of cyclotomic fields, obtained by endowing their ring of integers with a trace form. We...
B. A. Sethuraman, Frédérique E. Oggi...
TC
1998
13 years 5 months ago
A New Representation of Elements of Finite Fields GF(2m) Yielding Small Complexity Arithmetic Circuits
—Let F2 denote the binary field and F 2 m an algebraic extension of degree m > 1 over F2 . Traditionally, elements of F 2 m are either represented as powers of a primitive ele...
Germain Drolet
ITCC
2005
IEEE
13 years 11 months ago
Improved Routing-Based Linear Algebra for the Number Field Sieve
Recently, efficient custom-hardware designs were proposed for the linear algebra step of the Number Field Sieve integer factoring algorithm. These designs make use of a heuristic ...
Willi Geiselmann, Hubert Köpfer, Rainer Stein...
CRYPTO
2005
Springer
127views Cryptology» more  CRYPTO 2005»
13 years 11 months ago
Black-Box Secret Sharing from Primitive Sets in Algebraic Number Fields
A black-box secret sharing scheme (BBSSS) for a given access structure works in exactly the same way over any finite Abelian group, as it only requires black-box access to group o...
Ronald Cramer, Serge Fehr, Martijn Stam