702 citations · 789 across the 8 of their papers we have counts for
8 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…
On the success probability of quantum order finding
Martin Ekerå
We prove a lower bound on the probability of Shor's order-finding algorithm successfully recovering the order in a single run. The bound implies that by performing two limited…
On completely factoring any integer efficiently in a single run of an order finding algorithm
Martin Ekerå
We show that given the order of a single element selected uniformly at random from , we can with very high probability, and for any integer , efficiently find the…
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…
Revisiting Shor's quantum algorithm for computing general discrete logarithms
Martin Ekerå
We heuristically show that Shor's algorithm for computing general discrete logarithms achieves an expected success probability of approximately 60% to 82% in a single run when modi…
Quantum algorithms for computing short discrete logarithms and factoring RSA integers
Martin Ekerå, Johan Håstad
In this paper we generalize the quantum algorithm for computing short discrete logarithms previously introduced by Ekerå so as to allow for various tradeoffs between the number of…