A course in computational algebraic number theory
A course in computational algebraic number theory
On the Power of Quantum Computation
SIAM Journal on Computing
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
Quantum Fourier sampling simplified
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Polynomial-time quantum algorithms for Pell's equation and the principal ideal problem
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Complexity of Lattice Problems
Complexity of Lattice Problems
Computing a lattice basis from a system of generating vectors
EUROCAL '87 Proceedings of the European Conference on Computer Algebra
ANTS-I Proceedings of the First International Symposium on Algorithmic Number Theory
Polynomial time quantum algorithm for the computation of the unit group of a number field
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Limitations of quantum coset states for graph isomorphism
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Lattices that admit logarithmic worst-case to average-case connection factors
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
On the impossibility of a quantum sieve algorithm for graph isomorphism
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Weak Fourier-Schur sampling, the hidden subgroup problem, and the quantum collision problem
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Limitations of quantum coset states for graph isomorphism
Journal of the ACM (JACM)
Algorithms for ray class groups and Hilbert class fields
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
On the Impossibility of a Quantum Sieve Algorithm for Graph Isomorphism
SIAM Journal on Computing
Quantum measurements for hidden subgroup problems with optimal sample complexity
Quantum Information & Computation
Efficient quantum algorithm for identifying hidden polynomials
Quantum Information & Computation
Fully homomorphic encryption with relatively small key and ciphertext sizes
PKC'10 Proceedings of the 13th international conference on Practice and Theory in Public Key Cryptography
On the probability of generating a lattice
Journal of Symbolic Computation
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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 equation, which is a special case of computing the unit group, but a reduction in the other direction is not known and appears more difficult. We give polynomial-time quantum algorithms for computing the unit group and class group when the number field has constant degree.