We present quantum circuits to implement an exhaustive key search for the Advanced
Encryption Standard (AES) and analyze the quantum resources required to carry out such …

One of the most cost-critical operations when applying Shor's algorithm to binary elliptic
curves is the underlying field arithmetic. Here, we consider binary fields F _ 2^ n F 2 n in …

In this paper, we mainly discuss the quantum reversible circuits of multiplication over GF (2
8), which has many applications in modern cryptography. The quantum circuits of …

Elliptic curves over finite fields GF (2^ n) play a prominent role in modern cryptography.
Published quantum algorithms dealing with such curves build on a short Weierstrass form in …

Improving over an earlier construction by Kaye and Zalka, Maslov et al. describe an
implementation of Shor's algorithm which can solve the discrete logarithm problem on binary …

Finite fields of the form GF (2^ m) play an important role in coding theory and cryptography.
We show that the choice of how to represent the elements of these fields can have a …

When designing quantum circuits for Shor's algorithm to solve the discrete logarithm
problem, implementing the group arithmetic is a cost-critical task. We introduce a software …

Quantum computers represent a serious threat to the safety of modern encryption standards.
Within symmetric cryptography, Advanced Encryption Standard (AES) is believed to be …

Numerical simulations, optimisation problems, statistical analysis and computer graphics are
only a few examples from the wide range of real-life applications which rely on solving large …

Quantum computers and quantum computing is a reality of the near feature. Companies
such as Google and IBM have already declared they have built a quantum computer and …