4 papers
A high-level comparison of state-of-the-art quantum algorithms for breaking asymmetric cryptography
Martin Ekerå, Joel Gärtner
We provide a high-level cost comparison between Regev's quantum algorithm with Ekerå-Gärtner's extensions on the one hand, and existing state-of-the-art quantum algorithms for fact…
Extending Regev's factoring algorithm to compute discrete logarithms
Martin Ekerå, Joel Gärtner
Regev recently introduced a quantum factoring algorithm that may be perceived as a -dimensional variation of Shor's factoring algorithm. In this work, we extend Regev's factorin…
On the success probability of the quantum algorithm for the short DLP
Martin Ekerå
Ekerå and Håstad have introduced a variation of Shor's algorithm for the discrete logarithm problem (DLP). Unlike Shor's original algorithm, Ekerå-Håstad's algorithm solves the sho…
How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits
Craig Gidney, Martin Ekerå
We significantly reduce the cost of factoring integers and computing discrete logarithms in finite fields on a quantum computer by combining techniques from Shor 1994, Griffiths-Ni…