Cryptography is based on mathematical problems that are extremely difficult for conventional computers to solve or avoid. However, the quantum machines of the future will be able to do so more easily, making our protection systems obsolete. For now, quantum computers are not powerful or advanced enough to defeat today’s cryptographic protocols, but it is important to prepare for them.

In recent years, there has been a substantial amount of research on quantum computers – machines that exploit quantum mechanical phenomena to solve mathematical problems that are difficult or intractable for conventional computers. Google In March 2018, unveiled the world’s largest quantum computer processor to date. Dubbed Bristlecone, it’s a 72-qubit gate-based superconducting system, beating IBM which had developed 50-qubit processor. The Mountain View company’s Research at Google team created the 72-qubit processor by scaling its previous 9-qubit system. It’s estimated that a single 50-qubit quantum computer would outperform today’s most powerful mainframes.

If large-scale quantum computers are ever built, they will be able to break many of the public-key cryptosystems currently in use. Experts like Michele Mosca, co-founder of the Institute of Quantum Computing at the University of Waterloo (Canada), sees a chance of 50% that by 2031 quantum computers will be able of breaking RSA-2048 encryption—a scheme today regarded as secure. “

An attacker needs about the same time to break the system as it takes the user to run it,” says Dr Tanja Lange, chair of the Coding Theory and Cryptology group at Technische Universiteit Eindhoven. This would seriously compromise the confidentiality and integrity of our global communication digital infrastructure including securing our internet payments, banking transactions, emails and even phone conversations.

Considering the fact that data needs to be kept confidential for 10 to 50 years, organizations should start planning to switch now. Therefore, regardless of whether we can estimate the exact time of the arrival of the quantum computing era, we must begin now to prepare our information security systems to be able to resist quantum computing.

On the other hand, NSA and other spy agencies are also providing thrust to development of quantum computers to be able to break the encryption of their adversaries and terrorists. Former CIA Deputy Director Michael Morell said in an interview on CBS’, “I think what we’re going to learn is that these guys are communicating via these encrypted apps, this commercial encryption which is very difficult or nearly impossible for governments to break, and the producers of which don’t produce the keys necessary for law enforcement to read the encrypted messages.”

The argument is that the role of law enforcement is to protect society – they have always had warrants to get access to information, and technology should not change this. “This means they want to be able to intercept voice calls even if it is voice-over-IP, they want to read all your messages and collect all the metadata including location, they want access to stored data including the cloud, and they want access to confiscated devices as well as remote access to suspects’ devices,” said Preneel.

### Vulnerability of Asymmetric cryptography or public-key cryptography

There are two approaches for encrypting data, private-key encryption and public-key encryption. In private-key encryption, users share a key. This approach is more secure and less vulnerable to quantum technology, but it is also less practical to use in many cases.

The public-key encryption system is based on two keys, one that is kept secret, and another that is available to all. While the public key is widely distributed, private keys are computed using mathematical algorithms. Therefore everyone can send encrypted emails to a recipient, who is the only one able to read them. Because data is encrypted with the public key but decrypted with the private key, it is a form of “asymmetric cryptography”.

Many of our most crucial communication protocols rely principally on three core cryptographic functionalities: public-key encryption, digital signatures, and key exchange. Currently, these functionalities are primarily implemented using Diffie-Hellman key exchange, the RSA (RivestShamir-Adleman) cryptosystem, and elliptic curve cryptosystems. The security of these depends on the difficulty of certain numbers theoretic problems such as Integer Factorization or the Discrete Log Problem over various groups.

Breaking this encryption without the private key would mean finding the “prime factors” used to create the public key. These are two prime numbers that are multiplied together as part of the encryption process to form part of the public key. For sufficiently large prime numbers this is considered an impossible task for today’s computers.

“The algorithms are designed in a way that acquiring the private keys from the public keys is nearly impossible,” he said. “For traditional computers, for example, it would take thousands—to millions—of years, depending on how many bits there are in the keys, says Bikash Koley, CTO for Juniper Networks,

In theory, however, quantum computers should be good at prime factorisation and therefore able to decrypt messages using only the public, and not the private, key. Mathematics that would take thousands of years on today’s technology could be reduced to hours on a quantum machine – and much of today’s security would be obsolete.

Factorization involves decomposing a number into a product of two prime numbers, which is much more tricky than it seems when dealing with very large numbers. Similarly, for the time being, no algorithm can effectively calculate a discrete logarithm.

By harnessing quantum super-positioning to represent multiple states simultaneously, quantum-based computers promise exponential leaps in performance over today’s traditional computers. Quantum computers shall bring the power of massively parallel computing i.e. equivalent of a supercomputer to a single chip. They shall also be invaluable in cryptology and rapid searches of unstructured databases. Quantum algorithms can break current security by reverse computing private keys may only take days or hours.

A quantum computer of sufficient size and complexity will be capable of executing Shor’s Algorithm, a proven algorithm that can break factorization-based encryption that would take a classical computer billions of years of computing time to complete. This advance puts all systems running public key, or asymmetric, cryptography at risk.

In 1994, Peter Shor of Bell Laboratories showed that quantum computers, a new technology leveraging the physical properties of matter and energy to perform calculations, can efficiently solve each of these problems, thereby rendering all public-key cryptosystems based on such assumptions impotent.

In the twenty years since Shor’s discovery, the theory of quantum algorithms has developed significantly. Quantum algorithms achieving exponential speedup have been discovered for several problems relating to physics simulation, number theory, and topology. Quantum computing is also believed to be capable of tackling other mathematical problems classical computers can’t solve quickly, including computing discrete logarithm mod primes and discrete logs over elliptic curves.

Some experts even predict that within the next 20 or so years, sufficiently large quantum computers will be built to break essentially all public-key schemes currently in use. Researchers working on building a quantum computer have estimated that it is likely that a quantum computer capable of breaking 2000-bit RSA in a matter of hours could be built by 2030 for a budget of about a billion dollars.

“To factor [crack] a 1,024-bit number [encryption key], you need only 2,048 ideal qubits,” said Bart Preneel, professor of cryptography at KU Leuven University in Belgium. “So you would think we are getting close, but the qubits announced are physical qubits and there are errors, so they need about 1,000 physical qubits to make one logical [ideal] qubit. Qubits’ delicate quantum state can be disrupted by things like tiny changes in temperature or very slight vibrations, so it can require thousands of linked qubits to produce a single logical one that can be reliably used for computation. So to scale this up, you need 1.5 million physical qubits. This means quantum computers will not be a threat to cryptography any time soon.

### Security Risk

While quantum computing promises unprecedented speed and power in computing, it also poses new risks. As this technology advances over the next decade, it is expected to break some encryption methods that are widely used to protect customer data, complete business transactions, and secure communications. Thus a sufficiently powerful quantum computer will put many forms of modern communication—from key exchange to encryption to digital authentication—in peril.

NSA, whose mission is to protect vital US national security information and systems from theft or damage, is also advising US agencies and businesses to prepare for a time in the not-too-distant future when the cryptography protecting virtually all e-mail, medical and financial records, and online transactions is rendered obsolete by quantum computing.

### Post-quantum Cryptography

Organizations are now working on post-quantum cryptography (also called quantum-resistant cryptography), whose aim is to develop cryptographic systems that are secure against both quantum and classical computers, and can interoperate with existing communications protocols and networks.

There is also need to speed up preparations for the time when super-powerful quantum computers can crack conventional cryptographic defenses. The widespread adoption of quantum-resistant cryptography will be a long and difficult process that could probably take 20 years to complete. The first step is to create these new algorithms, then standardize them , integrate them into protocols, then integrate the protocols into products, said Bill Becker, vice president of product management at SafeNet AT, a provider of information assurance to government customers.

### NIST launched an international competition in 2017

Historically, it has taken almost two decades to deploy our modern public key cryptography infrastructure. It’s possible that highly capable quantum machines will appear before then, and if hackers get their hands on them, the result could be a security and privacy nightmare.

“Therefore, regardless of whether we can estimate the exact time of the arrival of the quantum computing era, we must begin now to prepare our information security systems to be able to resist quantum computing,” says NIST. Consequently, the search for algorithms believed to be resistant to attacks from both classical and quantum computers has focused on public key algorithms.

US National Institute of Standards and Technology (NIST) will play a leading role in the effort to develop a widely accepted, standardized set of quantum-resistant algorithms. The NIST competition is not just limited to encryption. Other algorithms will have to analyze the signature, in other words, authenticate the source of a message without being susceptible to falsification. In both cases, the criteria clearly include security, but also the system’s speed and fluidity.

The NIST, which is in charge of establishing various technological and measurement standards in the United States, launched an international competition in 2017 to build scientific consensus regarding post-quantum cryptography. This process has entered its third and final phase, with both academic and industrial researchers contributing to the effort. Among the sixty-nine initial submissions, the NIST selected those that would make it to the following stage of the competition based on criteria such as security, performance, and the characteristics of the implementation. It also took into consideration studies published by the scientific community, in addition to possible attacks against each scheme.

The plan is to select the final algorithms in the next couple of years and to make them available in draft form by 2024. So, while organizations can start preparing for post-quantum cryptography now, they will have to wait at least four years to know which algorithm to adopt once Nist has chosen the best submissions for incorporation into a standard.

### Symmetric cryptography and Post Quantum Cryptography

In traditional cryptography, there are two forms of encryption: symmetric and asymmetric. Most of today’s computer systems and services such as digital identities, the Internet, cellular networks, and cryptocurrencies use a mixture of symmetric algorithms like AES and SHA-2 and asymmetric algorithms like RSA (Rivest-Shamir-Adleman) and elliptic curve cryptography. The asymmetric parts of such systems would very likely be exposed to significant risk if we experience a breakthrough in quantum computing in the coming decades.

In contrast to the threat quantum computing poses to current public key algorithms, most current symmetric cryptographic algorithms (symmetric ciphers and hash functions) are considered to be relatively secure from attacks by quantum computers. While the quantum Grover’s algorithm does speed up attacks against symmetric ciphers, doubling the key size can effectively block these attacks. Thus post-quantum symmetric cryptography does not need to differ significantly from current symmetric cryptography

In fact, even a quantum computer capable of breaking RSA-2048 would pose no practical threat to AES-128 whatsoever. Grover’s algorithm applied to AES-128 requires a serial computation of roughly 265 AES evaluations that cannot be efficiently parallelized. As quantum computers are also very slow (operations per second), very expensive, and quantum states are hard to transfer from a malfunctioning quantum computer, it seems highly unlikely that even clusters of quantum computers will ever be a practical threat to symmetric algorithms. AES-128 and SHA-256 are both quantum resistant according to the evaluation criteria in the NIST PQC (post quantum cryptography) standardization project

The good news here, said Preneel, is that the impact for symmetric cryptography is not so bad. “You just have larger encryption keys and then you are done,” he said. The goal of post-quantum cryptography (also called quantum-resistant cryptography) is to develop cryptographic systems that are secure against both quantum and classical computers, and can interoperate with existing communications protocols and networks. NIST has initiated a process to solicit, evaluate, and standardize one or more quantum-resistant public-key cryptographic algorithms.

### Quantum Resistant Algorithms

Various avenues are being pursued. NIST has identified main families for which post-quantum primitives have been proposed include those based on lattices, codes, and multivariate polynomials, as well as a handful of others.

One of them, cryptographic lattices, involves finding the shortest vectors between two points on a mesh, in a space with hundreds of dimensions. Each vector, therefore, has a huge number of coordinates, and the problem becomes extremely arduous to solve.

**Lattice-based cryptography** – Cryptosystems based on lattice problems have received renewed interest, for a few reasons. Exciting new applications (such as fully homomorphic encryption, code obfuscation, and attribute-based encryption) have been made possible using lattice-based cryptography. Most lattice-based key establishment algorithms are relatively simple, efficient, and highly parallelizable. Also, the security of some lattice-based systems are provably secure under a worst-case hardness assumption, rather than on the average case. On the other hand, it has proven difficult to give precise estimates of the security of lattice schemes against even known cryptanalysis techniques.

Another approach relies on error-correcting codes, which are used to improve degraded communications, for instance restoring the appearance of a video burned on a DVD that has been damaged. Some of these codes provide a very effective framework for encryption but function quite poorly when it comes to verifying a signature.

**Code-based cryptography** – In 1978, the McEliece cryptosystem was first proposed, and has not been broken since. Since that time, other systems based on error-correcting codes have been proposed. While quite fast, most code-based primitives suffer from having very large key sizes. Newer variants have introduced more structure into the codes in an attempt to reduce the key sizes, however the added structure has also led to successful attacks on some proposals. While there have been some proposals for code-based signatures, code-based cryptography has seen more success with encryption schemes.

Another solution, multivariate cryptography, is based on a somewhat similar principle by proposing to solve polynomials with so many variables that it is no longer possible to calculate within a reasonable time frame.

**Multivariate polynomial cryptography** – These schemes are based on the difficulty of solving systems of multivariate polynomials over finite fields. Several multivariate cryptosystems have been proposed over the past few decades, with many having been broken. While there have been some proposals for multivariate encryption schemes, multivariate cryptography has historically been more successful as an approach to signatures.

The construction of lattices is quite present among the finalists, as it works equally well for encryption and signatures. However, everyone in the community does not agree that they should be the focus of attention. The NIST prefers exploring a broad spectrum of approaches for establishing its standards. This way, if a particular solution is attacked, the others will remain secure.

For example, the SPHINCS+ algorithm from the Eindhoven University of Technology in the Netherlands, is based on hash functions. A digital fingerprint is ascribed to data, an operation that is extremely difficult to perform in the opposite direction, even using a quantum algorithm. Still, signatures obtained in this way are resource-intensive.

**Hash-based signatures** – Hash-based signatures are digital signatures constructed using hash functions. Their security, even against quantum attacks, is well understood. Many of the more efficient hash-based signature schemes have the drawback that the signer must keep a record of the exact number of previously signed messages, and any error in this record will result in insecurity. Another drawback is that they can produce only a limited number of signatures. The number of signatures can be increased, even to the point of being effectively unlimited, but this also increases the signature size.

**Other –** A variety of systems have been proposed which do not fall into the above families. One such proposal is based on evaluating isogenies on supersingular elliptic curves. While the discrete log problem on elliptic curves can be efficiently solved by Shor’s algorithm on a quantum computer, the isogeny problem on supersingular curves has no similar quantum attack known. Like some other proposals, for example those based on the conjugacy search problem and related problems in braid groups, there has not been enough analysis to have much confidence in their security

There are seven algorithms involving researchers based in France. With regard to encryption, Crystals-Kyber, NTRU, and Saber are based on lattices, while Classic McEliece rely on error-correcting codes. Damien Stehlé, a professor at ENS Lyon and a member of the LIP Computer Science Laboratory,2 and Nicolas Sendrier, from the INRIA research centre in Paris, are taking part in the competition. In the signature category, the Crystals-Dilithium and Falcon algorithms use lattices, and Rainbow opts for multivariate systems. Stehlé is once again part of the team, as are Pierre-Alain Fouque, a professor at Rennes 1 and member of the IRISA laboratory, as well as Jacques Patarin, a professor at the UVSQ (Université de Versailles-Saint-Quentin-en-Yvelines), writes researcher Adeline Roux-Langlois.

I focus on lattice-based cryptography, in which I provide theoretical proof that the security of cryptographic constructions is based on problems that are hard enough to be reliable. Encryption and signature are the first applications that come to mind, but it could also be used to ensure the very particular confidentiality of electronic voting, for which the authenticity of votes must be verified before counting, while not revealing who voted for whom. I am also working on anonymous authentication, which for example enables individuals to prove that they belong to a group without disclosing other information, or that they are adults without giving their age or date of birth, writes Adeline.

### Quantum key distribution (QKD) as the alternative

In addition to post-quantum cryptography running on classical computers, researchers in quantum networking are looking at quantum key distribution (QKD), which would theoretically be a provably secure way to do unauthenticated key exchange. QKD is however not useful for any other use cases such as encryption, integrity protection, or authentication where cryptography is used today as it requires new hardware and is also very expensive compared to software-based algorithms running on classical computers.

In a well-written white paper, the UK government is discouraging use of QKD stating that it seems to be introducing new potential avenues for attack, that the hardware dependency is not cost-efficient, that QKD’s limited scope makes it unsuitable for future challenges, and that post-quantum cryptography is a better alternative. QKD will likely remain a niche product until quantum networks are needed for non-security reasons.

### Standardizing post-quantum cryptographic algorithms

The US National Institute of Standards and Technology (NIST) is currently standardizing stateless quantum-resistant signatures, public-key encryption, and key-establishment algorithms and is expected to release the first draft publications between 2022–2024. After this point, the new standardized algorithms will likely be added to security protocols like X.509, IKEv2, TLS and JOSE and deployed in various industries. The IETF crypto forum research group has finished standardizing two stateful hash-based signature algorithms, XMSS and LMS which are also expected to be standardized by NIST. XMSS and LMS are the only post-quantum cryptographic algorithms that could currently be considered for production systems e.g. for firmware updates.

The US government is currently using the Commercial National Security Algorithm Suite for protection of information up to ‘top secret’. They have already announced that they will begin a transition to post-quantum cryptographic algorithms following the completion of standardization in 2024. Why should the industry be taking note of this decision? ‘Top secret’ information is often protected for 50 to 75 years, so the fact that the US government is not planning to finalize the transition to post-quantum cryptography until perhaps 2030 seems to indicate that they are quite certain that quantum computers capable of breaking P-384 and RSA-3072 will not be available for many decades.

### NSA Guidance

NSA guidance advises using the same regimen of algorithms and key sizes that have been recommended for years. Those include 256-bit keys with the Advanced Encryption Standard, Curve P-384 with Elliptic Curve Diffie-Hellman key exchange and Elliptic Curve Digital Signature Algorithm, and 3072-bit keys with RSA encryption. But for those who have not yet incorporated one of the NSA’s publicly recommended cryptographic algorithms—known as Suite B in NSA parlance—last week’s advisory recommends holding off while officials plot a new move to crypto algorithms that will survive a postquantum world.

“Our ultimate goal is to provide cost effective security against a potential quantum computer,” officials wrote in a statement posted online. “We are working with partners across the USG, vendors, and standards bodies to ensure there is a clear plan for getting a new suite of algorithms that are developed in an open and transparent manner that will form the foundation of our next Suite of cryptographic algorithms.”

### Challenges of post-quantum transition

The replacement of current cryptographic standards with new post-quantum standards presents significant technical challenges due to worldwide interconnectedness and established protocols. Although purchasing post-quantum encryption solutions available on the market today could prove tempting as a way to reduce quantum computing risks, doing so may create a more challenging transition to the NIST-approved standard in 2024 at a significant cost.

It’s going to be a huge amount of effort to develop, standardize, and deploy entirely new classes of algorithms. Previous transitions from weaker to stronger cryptography have been based on the bits-of security paradigm, which measures the security of an algorithm based on the time-complexity of attacking it with a classical computer (e.g. an algorithm is said to have 128 bits of security if the difficulty of attacking it with a classical computer is comparable to the time and resources required to brute-force search for a 128-bit cryptographic key.)

“The transition to post-quantum encryption algorithms is as much dependent on the development of such algorithms as it is on their adoption. While the former is already ongoing, planning for the latter remains in its infancy. We must prepare for it now to protect the confidentiality of data that already exists today and remains sensitive in the future.” – U.S. Secretary of Homeland Security, Alejandro Mayorkas, March 31, 2021

### DHS Transition to Post-Quantum Cryptography

The Department of Homeland Security (DHS), in partnership with the Department of Commerce’s National Institute of Standards and Technology (NIST), has released a roadmap to help organizations protect their data and systems and to reduce risks related to the advancement of quantum computing technology.

DHS’s Cybersecurity and Infrastructure Security Agency (CISA) is conducting a macro-level assessment of priority National Critical Functions to determine where post-quantum cryptography transition work is underway, where the greatest risk resides, and what sectors of National Critical Functions may require Federal support.

DHS’s new guidance will help organizations prepare for the transition to post-quantum cryptography by identifying, prioritizing, and protecting potentially vulnerable data, algorithms, protocols, and systems.

“Unfortunately, the bits-of-security paradigm does not take into account the security of algorithms against quantum cryptanalysis, so it is inadequate to guide our transition to quantum-resistant cryptography. There is not yet a consensus view on what key lengths will provide acceptable levels of security against quantum attacks,” “At the same time, this recommendation does not take into account the possibility of more sophisticated quantum attacks, our understanding of quantum cryptanalysis remains rather limited, and more research in this area is urgently needed, says NIST.”

Recent reports from academia and industry now says that large-scale cryptography-breaking quantum computers are highly unlikely during the next decade. There has also been general agreement that quantum computers do not pose a large threat to symmetrical algorithms. Standardization organizations like IETF and 3GPP and various industries are now calmly awaiting the outcome of the NIST PQC standardization.

Quantum computers will likely be highly disruptive for certain industries, but probably not pose a practical threat to asymmetric cryptography for many decades and will likely never be a practical threat to symmetric cryptography. Companies that need to protect information or access for a very long time should start thinking about post-quantum cryptography. But as long as US government protects ‘top secret’ information with elliptic curve cryptography and RSA, they are very likely good enough for basically any other non-military use case.

### References and Resources also include:

http://csrc.nist.gov/publications/drafts/nistir-8105/nistir_8105_draft.pdf

http://csrc.nist.gov/groups/ST/post-quantum-crypto/

https://news.cnrs.fr/articles/towards-a-post-quantum-cryptography

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