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Quantum computers can execute algorithms that dramatically outperform classical computation. As the best-known example, Shor discovered an efficient quantum algorithm for factoring integers, whereas factoring appears to be difficult for…
The aim of this paper is to elucidate the implications of quantum computing in present cryptography and to introduce the reader to basic post-quantum algorithms. In particular the reader can delve into the following subjects: present…
Simon's problem is one of the most important problems demonstrating the power of quantum algorithms, as it greatly inspired the proposal of Shor's algorithm. The generalized Simon's problem is a natural extension of Simon's problem, and…
This paper describes the work carried out by the Inter-American Development Bank, the IDB Lab, LACChain, Cambridge Quantum Computing (CQC), and Tecnologico de Monterrey to identify and eliminate quantum threats in blockchain networks. The…
Post-quantum cryptography studies the security of classical, i.e. non-quantum cryptographic protocols against quantum attacks. Until recently, the considered adversaries were assumed to use quantum computers and behave like classical…
The impending arrival of cryptographically relevant quantum computers (CRQCs) threatens the security foundations of modern software: Shor's algorithm breaks RSA, ECDSA, ECDH, and Diffie-Hellman, while Grover's algorithm reduces the…
Quantum computers can break the RSA and El Gamal public-key cryptosystems, since they can factor integers and extract discrete logarithms. If we believe that quantum computers will someday become a reality, we would like to have…
In quantum information processing (QIP), the quantum Fourier transform (QFT) has a plethora of applications [1] [2] [3]: Shor's algorithm and phase estimation are just a few well-known examples. Shor's quantum factorization algorithm, one…
The assumed computationally difficulty of factoring large integers forms the basis of security for RSA public-key cryptography, which specifically relies on products of two large primes or semi-primes. The best-known factoring algorithms…
Shor's factorisation algorithm is a combination of classical pre- and post-processing and a quantum period finding (QPF) subroutine which allows an exponential speed up over classical factoring algorithms. We consider the stability of this…
Most quantum algorithms that give an exponential speedup over classical algorithms exploit the Fourier transform in some way. In Shor's algorithm, sampling from the quantum Fourier spectrum is used to discover periodicity of the modular…
We propose a sequential minimal optimization method for quantum-classical hybrid algorithms, which converges faster, is robust against statistical error, and is hyperparameter-free. Specifically, the optimization problem of the…
We investigate the boundary between classical and quantum computational power. This work consists of two parts. First we develop new classical simulation algorithms that are centered on sampling methods. Using these techniques we generate…
We study the amplification of security against quantum attacks provided by iteration of block ciphers. In the classical case, the Meet-in-the-middle attack is a generic attack against those constructions. This attack reduces the time…
Given a function f as an oracle, the collision problem is to find two distinct inputs i and j such that f(i)=f(j), under the promise that such inputs exist. Since the security of many fundamental cryptographic primitives depends on the…
Attempts to separate the power of classical and quantum models of computation have a long history. The ultimate goal is to find exponential separations for computational problems. However, such separations do not come a dime a dozen: while…
Quantum computers have the potential to speed up certain problems that are hard for classical computers. Hybrid systems, such as the nitrogen vacancy (NV) center in diamond, are among the most promising systems to implement quantum…
Modern cryptography relies on keyed symmetric ciphers to ensure the secrecy and authenticity of high bandwidth data transfer. While the advent of quantum computers poses a challenge for public key cryptography, unbroken ciphers are…
Modern cryptographic protocols rely on sophisticated hash functions to generate quasi-unique numbers that serve as signatures for user authentication and other security verifications. The security could be compromised by finding texts…
The goal of this paper is to outline a general-purpose scalable implementation of Shor's period finding algorithm using fundamental quantum gates, and to act as a blueprint for linear optical implementations of Shor's algorithm for both…