Quantum Computational Cryptography

Akinori Kawachi, Takeshi Koshiba

Abstract: Shor’s algorithms for the integer factorization and the discrete logarithm problems can be regarded as a negative effect of the quantum mechanism on publickey cryptography. From the computational point of view, his algorithms illustrate that quantum computation could be more powerful. It is natural to consider that the power of quantum computation could be exploited to withstand even quantum adversaries. Over the last decade, quantum cryptography has been discussed and developed even from the computational complexity-theoretic point of view. In this paper, we will survey what has been studied in quantum computational cryptography. Key Words: computational cryptography, quantum computing, quantum cryptography Category: E.3, F.1.1

Manuel Calixto

Romain Alléaume

Seema Kute, Chitra G. Desai

Background/Objectives: The preferment from conventional computing to quantum computing has created new ­challenges in the field of cryptography. The cryptographic algorithms which ensured intractability in conventional computing surfaces serious challenge in quantum computing. Methods/Statistical Analysis: By applying the quantum mechanics quantum cryptography can be used to unrestrictedly for reliable data communications. Findings: The cryptography currently in use, known as conventional cryptography, depends absolutely on the hardness of the mathematical concepts. Elliptical curve cryptography today known as modern cryptography is used extensively for securing financial transactions. Advances in quantum computing, can easily break this security by reverse computing keys faster than the conventional ­computers. Application/Improvements: This paper is an attempt to review fundamentals of quantum cryptography to as to ­represent it in easiest possible way for a novice demonstrating quantum onetime pad. Keywords: Conventional Cryptography, Density Matrix, Quantum Cryptography, Quantum One Time Pad

David Salomon

Ye.V. Ostrianska, Maryna V. Yesina, І.Д. Горбенко

Virtually all asymmetric cryptographic schemes currently in use are threatened by the potential development of powerful quantum computers. Although there is currently no definite answer and it is very unclear when or even if CRQC will ever be built and the gap between modern quantum computers and the envisioned CRQC is huge, the risk of creating CRQC means that currently deployed public key cryptography must be replaced by quantum-resistant ones alternatives. For example, information encrypted using modern public key cryptography can be recorded by cryptanalysts and then attacked if a QRQC can be created. The potential harm that CRQC could cause is the basis of the motivation to seek countermeasures, even though we have uncertainties about when and if these computers can be built. Deployed systems that use public key cryptography can also take years to update. Post-quantum cryptography is one way to combat quantum computer threats. Its security is based on the complexity of mathematical problems that are currently considered unsolvable efficiently – even with the help of quantum computers. Post-quantum cryptography deals with the development and research of asymmetric cryptosystems, which, according to current knowledge, cannot be broken even by powerful quantum computers. These methods are based on mathematical problems for the solution of which neither efficient classical algorithms nor efficient quantum algorithms are known today. Various approaches to the implementation of post-quantum cryptography are used in modern research, including: code-based cryptography, lattice-based cryptography, hashing-based cryptography, isogeny-based cryptography, and multidimensional cryptography. The purpose of this work is to review the computational model of quantum computers; quantum algorithms, which have the greatest impact on modern cryptography; the risk of creating cryptographically relevant quantum computers (CRQC); security of symmetric cryptography and public key cryptography in the presence of CRQC; NIST PQC standardization efforts; transition to quantum-resistant public-key cryptography; relevance, views and current state of development of quantum-resistant cryptography in the European Union. It also highlights the progress of the most important effort in the field: NIST's standardization of post-quantum cryptography.