SIAMCOMP
2010
13 years 2 months ago
2010
We provide algorithms to count and enumerate representatives of the (right) ideal classes of an Eichler order in a quaternion algebra defined over a number field. We analyze the ...
MOC
2000
13 years 4 months ago
2000
Abstract. The distribution of ideal class groups of Fq(T, M(T)) is examined for degree-four monic polynomials M Fq[T] when Fq is a finite field of characteristic greater than 3 wi...
EUROCRYPT
2000
Springer
13 years 8 months ago
2000
Springer
We present a chosen-ciphertext attack against both NICE cryptosystems. These two cryptosystems are based on computations in the class group of non-maximal imaginary orders. More pr...
EUROCRYPT
1998
Springer
13 years 8 months ago
1998
Springer
We introduce a new cryptosystem with trapdoor decryption based on the di culty of computing discrete logarithms in the class group of the non-maximal imaginary quadratic order O q ...
ANTS
1998
Springer
13 years 8 months ago
1998
Springer
d Abstract) Michael J. Jacobson, Jr. Technische Universit
ANTS
2004
Springer
13 years 9 months ago
2004
Springer
We present a technique to recover f ∈ Q(ζp) where ζp is a primitive pth root of unity for a prime p, given its norm g = f ∗ ¯f in the totally real field Q(ζp + ζ−1 p )....
STOC
2005
ACM
14 years 4 months ago
2005
ACM
Computing the unit group and class group of a number field are two of the main tasks in computational algebraic number theory. Factoring integers reduces to solving Pell's eq...