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Theoretical advances in practical quantum cryptography

Jérémy Ribeiro

Published Feb 27, 2020• 0 citations
Publisher

Abstract

Most of themainstream cryptographic protocols that are used today rely on the assumption that the adversary has limited computational power, and that a given set of mathematical problems is hard to solve (on average), i.e. that there is no polynomial time algorithm that solves these problems. While these assumptions are reasonable for now they might not be as relevant for long termsecurity. Indeed, all the communication that happens today can be recorded by an adversary who can later – when the technology allows it – break security. There are good reasons to think that technological progress may lead to break the assumptions made today. For example the rapidly increasing computational power of our computer already allows one to break anything that has been encrypted using DES in the 70s and 80s in few days using regular desktop type devices. There is also the constant improvement of the efficiency of the known algorithms that solve a class of problems. Note that, even though the discovery of a polynomial algorithm for a problem we believe to be hard is still possible, much weaker improvements on current algorithms that solve these hard problems, can already be a threat for security.

DOI
10.4233/uuid:8f5106ab-9059-4fd6-9448-e4c642362739

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Most of themainstream cryptographic protocols that are used today rely on the assumption that the adversary has limited computational power, and that a given set of mathematical problems is hard to solve (on average), i.e. that there is no polynomial time algorithm that solves these problems. While these assumptions are reasonable for now they might not be as relevant for long termsecurity. Indeed, all the communication that happens today can be recorded by an adversary who can later – when the technology allows it – break security. There are good reasons to think that technological progress may lead to break the assumptions made today. For example the rapidly increasing computational power of our computer already allows one to break anything that has been encrypted using DES in the 70s and 80s in few days using regular desktop type devices. There is also the constant improvement of the efficiency of the known algorithms that solve a class of problems. Note that, even though the discovery of a polynomial algorithm for a problem we believe to be hard is still possible, much weaker improvements on current algorithms that solve these hard problems, can already be a threat for security.
Motivation The ability to guarantee security and privacy in communication are critical factors in encouraging people to accept and trust new tools and methods for today's information-based society (e.g. in eCommerce or eHealth) and for future services (e.g. eGovernment, eVoting). Cybercrime already hinders these new possibilities by creating widespread mistrust in these new services. Another problem is that a (perhaps unpublicized) break-through in mathematics or computer science could completely compromise current state-of-the-art encryption methods overnight, even those which are the basis of all existing internet banking transactions. This is because the security of cutting-edge public-key cryptography (conventional cryptography) relies on the computational difficulty of certain mathematical tasks, meaning that conventional cryptography alone can neither provide any evidence of eavesdropping nor guarantee strong security. The trend towards faster electronics provides the ability to handle longer keys, thus providing better security, but also increases the possibility to break keys. This also has another worrying effect: even using today's most advanced available security technology to protect data during communication with best practice and without making any mistakes, the ongoing improvements in technology (which hence require longer key lengths to ensure security) mean that today's transmitted data will not be secure for more than a few years. Thus, while encrypted data might be safe today, it can still be stored by the adversary now and then broken later on once the future technology has caught up with today's encryption. Alternatively, modern quantum cryptography has created a new paradigm for cryptographic communication, which provides strong, long-term security and incontrovertible evidence of any attempted eavesdropping which is based on theoretically and experimentally proven laws of nature.
The advent of a full-scale quantum computer will severely impact most currently-used cryptographic systems. The most well-known aspect of this impact lies in the computational-hardness assumptions that underpin the security of most current public-key cryptographic systems: a quantum computer can factor integers and compute discrete logarithms in polynomial time, thereby breaking systems based on these problems. However, simply replacing these problems by other which are (believed to be) impervious even to a quantum computer does not completely solve the issue. Indeed, many security proofs of cryptographic systems are no longer valid in the presence of a quantum-capable attacker; while this does not automatically implies that the affected systems would be broken by a quantum computer, it does raises questions on the exact security guarantees that they can provide. This overview document aims to analyze all aspects of the impact of quantum computers on cryptographic, by providing an overview of current quantum-hard computational problems (and cryptographic systems based on them), and by presenting the security proofs that are affected by quantum-attackers, detailing what is the current status of research on the topic and what the expected effects on security are.
Abstract With the recent advancements in quantum computing, there is a threat that today’s widely used digital encryption schemes will become vulnerable to cryptography-breaking quantum algorithms. In particular, today’s most widely used asymmetric encryption schemes will be the most vulnerable. On the other hand, it is likely that symmetric encryption and hashing schemes will remain robust even with the advent of powerful quantum computers of the future. In addition, today’s quantum computers are not powerful enough to implement the asymmetric cryptography-breaking algorithms; however, as quantum computers become more powerful and more research is put into these quantum algorithms, it is only a matter of years before the most widely used asymmetric encryption schemes of today are no longer secure. Therefore, a global effort being led by the National Institute of Standards and Technology (NIST) is underway to tackle this issue. As long as these efforts continue to progress at the current pace the potential adverse effects of these cryptography-breaking quantum algorithms are likely to be largely mitigated.
The advent of a full-scale quantum computer will severely impact most currently-used cryptographic systems.The most well-known aspect of this impact lies in the computational-hardness assumptions that underpin the security of most current public-key cryptographic systems: a quantum computer can factor integers and compute discrete logarithms in polynomial time, thereby breaking systems based on these problems.However, simply replacing these problems by other which are (believed to be) impervious even to a quantum computer does not completely solve the issue.Indeed, many security proofs of cryptographic systems are no longer valid in the presence of a quantum-capable attacker; while this does not automatically implies that the affected systems would be broken by a quantum computer, it does raises questions on the exact security guarantees that they can provide.This overview document aims to analyze all aspects of the impact of quantum computers on cryptographic, by providing an overview of current quantum-hard computational problems (and cryptographic systems based on them), and by presenting the security proofs that are affected by quantum-attackers, detailing what is the current status of research on the topic and what the expected effects on security are.
Ever since its inception, cryptography has been caught in a vicious circle: Cryptographers keep inventing methods to hide information, and cryptanalysts break them, prompting cryptographers to invent even more sophisticated encryption schemes, and so on. But could it be that quantum information technology breaks this circle? At first sight, it looks as if it just lifts the competition between cryptographers and cryptanalysts to the next level. Indeed, quantum computers will render most of today’s public key cryptosystems insecure. Nonetheless, there are good reasons to believe that cryptographers will ultimately prevail over cryptanalysts. Quantum cryptography allows us to build communication schemes whose secrecy relies only on the laws of physics and some minimum assumptions about the cryptographic hardware—leaving basically no room for an attack. While we are not yet there, this paper provides an overview of the principles and state-of-the-art of quantum cryptography, as well as an assessment of current challenges and prospects for overcoming them.
The development in this digital era is fast pacing up to the future where machines will be able to perform tasks more efficiently and rapidly than even today’s supercomputers aren’t able to perform. Increasing technology and exponential development in the domain of Quantum Computing are leading humanity to the future where Computers will be able to solve unsolvable or exponential time-consuming problems in a span of short time. This will be proved advantageous in numerous ways but as every state of development has other aspects, this development will also be able to break down every possible cryptographic algorithm implemented in the classical computing era as they all are based on complex mathematical equations and calculations. A perfectly implemented Quantum Computer will be able to compute the mathematical calculations in parallel due to the phenomenon of Superposition and entanglement. All possible progress in Quantum Algorithms is discussed in the context of digital security in this paper which can be a possible threat to every executed cryptographic algorithm and securities instigated through them.