A key-exchange system based on imaginary quadratic fields
Journal of Cryptology
Quadratic fields and cryptography
Number theory and cryptography
Quantum computation and quantum information
Quantum computation and quantum information
Security of Cryptosystems Based on Class Groups of Imaginary Quadratic Orders
ASIACRYPT '00 Proceedings of the 6th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Algorithms for quantum computation: discrete logarithms and factoring
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
Logical reversibility of computation
IBM Journal of Research and Development
Circuit for Shor's algorithm using 2n+3 qubits
Quantum Information & Computation
Shor's discrete logarithm quantum algorithm for elliptic curves
Quantum Information & Computation
Hi-index | 0.00 |
In this paper, we present a quantum algorithm which solves the discrete logarithm problem in the class group of an imaginary quadratic number field. We give an accurate estimation of the qubit complexity for this algorithm. Based on this result and analog results for the factoring and the discrete logarithm problem in the point group of an elliptic curve, we compare the run-times of cryptosystems which are based on problems above. Assuming that the size of quantum computers will grow slowly, we give proposals which cryptosystem should be used if middle-size quantum computers will be built.