As all of you are aware the ability to break encryption of sensitive data like financial systems, private correspondence, government systems in a timely fashion is the holy grail of computer espionage. With the current technology it is unfeasible to break the encryption in a reasonable timeframe. If the target is using a 256-bit key an attacker will need to try a max of 2256 possible combinations to brute-force it. This means that even with the fastest supercomputer in the world will take millions of years to try all the combinations (Nohe, 2019). The number of combinations required to crack the encryption key increase exponentially, so a 2048-bit key has 22048 possible combinations and will take correspondingly longer time to crack. However, with the recent advances in Quantum computing the dream of breaking encryption in a timely manner is close to becoming reality in the near future.
Introduction to Quantum Computing
So, what is this Quantum computing and what makes it so special? Quantum computing is an emerging technology field that leverages quantum phenomena to perform computations. It has a great advantage over conventional computing due to the way it stores data and performs computations. In a traditional system information is stored in the form of bits, each of which can be either 0 or 1 at any given time. This makes a ‘bit’ the fundamental using of information in traditional computing. A Quantum computer on the other hand uses a ‘qubit’ as its fundamental unit and unlike the normal bit, a qubit can exist simultaneously as 0 and 1 — a phenomenon called superposition (Freiberger, 2017). This allows a quantum computer to act on all possible states of a qubit simultaneously, enabling it to perform massive operations in parallel using only a single processing unit. In fact, a theoretical projection has postulated that a Quantum Computer could break a 2048-bit RSA encryption in approximately 8 hours (Garisto, 2020).
In 1994 Peter W. Shor of AT&T deduced how to take advantage of entanglement and superposition to find the prime factors of an integer (Shor, 1994). He found that a quantum computer could, in principle, accomplish this task much faster than the best classical calculator ever could. He then proceeded to write an algorithm called Shor’s algorithm that could be used to crack the RSA encryption which prompted computer scientists to begin learning about quantum computing.
Introduction to Current Cryptography
Current security of cryptography relies on certain “hard” problems—calculations which are practically impossible to solve without the correct cryptographic key. Just as it is easy to break a glass jar but difficult to stick it back together there are certain calculations that are easy to perform but difficult to reverse. For example, we can easily multiply two numbers to get the result, however it is very hard to start with the result and work out which two numbers were multiplied to produce it. This becomes even more hard as the numbers get larger and this forms the basis of algorithms like the RSA (Rivest et al., 1978) that would take the best computers available billions of years to solve and all current IT security aspects are built on top of this basic foundation.
There are multiple ways of classifying cryptographic algorithms but in this paper, they will be classified based on the keys required for encryption and decryption. The main types of cryptographic algorithms are symmetric cryptography and asymmetric cryptography.
Symmetric Cryptography
Symmetric cryptography is a type of encryption that uses the same key for both encryption and decryption. This requires the sender and receiver to exchange the encryption key securely before encrypted data can be exchanged. This type of encryption is one of the oldest in the world and was used by Julius Caesar to protect his communications in Roman times (Singh, 2000). Caesar’s cipher, as it is known is a basic substitution cypher where a number is used to offset each alphabet in the message. For example, if the secret key is ‘4’ then each alphabet would be replaced with the 4th letter down from it, i.e. A would be replaced with E, B with F and so on. Once the sender and receiver agree on the encryption key to be used, they can start communicating. The receiver would take each character of the message and then go back 4 letters to arrive at the plain-text message. This is a very simple example, but modern cryptography is built on top of this principle.
Another example is from world war II during which the Germans were encrypting their transmissions using the Enigma device to prevent the Allies from decrypting their messages as they had in the first World War (Rijmenants, 2004). Each day both the receiver and sender would configure the gears and specific settings to a new value as defined by secret keys distributed in advance. This allowed them to transmit information in an encrypted format that was almost impossible for the allied forces to decrypt. Examples of symmetric encryption algorithms include Advanced Encryption Standard (AES), Data Encryption Standard (DES), and International Data Encryption Algorithm (IDEA).
Symmetric encryption algorithms are more efficient than asymmetric algorithms and are typically used for bulk encryption of data.
Asymmetric Cryptography
Unlike symmetric cryptography asymmetric cryptography uses two keys, one for encryption and a second key for decryption (Rouse et al., 2020). Asymmetric cryptography was created to address the problems of key distribution in symmetric encryption and is also known as public key cryptography. Modern public key cryptography was first described in 1976 by Stanford University professor Martin Hellman and graduate student Whitfield Diffie. (Diffie & Hellman, 1976)
Asymmetric encryption works with public and private keys where the public key is used to encrypt the data and the private key is used to decrypt the data (Rouse et al., 2020). Before sharing data, a user would generate a public-private keypair and they would then publish their public key on their website or in key management portals. Now, whoever wants to send private data to them would use their public key to encrypt the data before sending it. Once they receive the cipher-text they would use their private key to decrypt the data. If we want to add another layer of authentication to the communication, the sender would encrypt the data with their private key first and then do a second layer of encryption using the recipient’s public key. The recipient would first decrypt the message using their private key, then decrypt the result using the senders public key. This validates that the message was sent by the sender without being tampered. Public key cryptography algorithms in use today include RSA, Diffie-Hellman and Digital Signature Algorithm (DSA).
Quantum Computing vs Classical Computing
Current state of Quantum Computing
Since the early days of quantum computing we have been told that a functional quantum computer is just around the corner and the existing encryption systems will be broken soon. There has been significant investment in the field of Quantum computers in the past few years, with organizations like Google, IBM, Amazon, Intel and Microsoft dedicating a significant amount of their R&D budget to create a quantum computer. In addition, the European Union has launched a Quantum Technologies Flagship program to fund research on quantum technologies (Quantum Flagship Coordination and Support Action, 2018).
As of September 2020, the largest quantum computer is comprised of 65 qubits and IBM has published a roadmap promising a 1000 qbit quantum computer by 2023 (Cho, 2020). While this is an impressive milestone, we are still far away from a fully functional general use quantum computer. To give an idea of how far we still have to go Shor’s algorithm requires 72k3 quantum gates to be able to factor a k bits long number (Shor, 1994). This means in order to factor a 2048-bit number we would need a 72 * 20483 = 618,475,290,624 qubit computer which is still a long way off in the future.
Challenges in Quantum Computing
There are multiple challenges in creating a quantum computer with a large number of qubits as listed below (Clarke, 2019):
- Qubit quality or loss of coherence: The qubits being generated currently are useful only on a small scale, after a particular no of operations they start producing invalid results.
- Error Correction at scale: Since the qubits generate errors at scale, we need algorithms that will compensate for the errors generated. This research is still in the nascent stage and requires significant effort before it will be ready for production use.
- Qubit Control: We currently do not have the technical capability to control multiple qubits in a nanosecond time scale.
- Temperature: The current hardware for quantum computers needs to be kept at extremely cold temperatures making commercial deployments difficult.
- External interference: Quantum computes are extremely sensitive to interference. Research at MIT has found that ionizing radiation from environmental radioactive materials and cosmic rays can and does interfere with the integrity of quantum computers.
Cryptographic algorithms vulnerable to Quantum Computing
Symmetric encryption schemes impacted
According to NIST, most of the current symmetric cryptographic algorithms will be relatively safe against attacks by quantum computer provided a large key is used (Chen et al., 2016). However, this might change as more research is done and quantum computers come closer to reality.
Asymmetric encryption schemes impacted
Unlike symmetric encryption schemes most of the current public key encryption algorithms are highly vulnerable to quantum computers because they are based on the previously mentioned factorization problem and calculation of discrete logarithms and both of these problems can be solved by implementing Shor’s algorithm on a quantum computer with enough qubits. We do not currently have the capability to create a computer with the required number of qubits due to challenges such as loss of qubit coherence due to ionizing radiation (Vepsäläinen et al., 2020), but they are a solvable problem looking at the ongoing advances in the field and the significant effort being put in the field by companies such as IBM and others (Gambetta et al., 2020).
Post Quantum Cryptography
The goal of post-quantum cryptography is to develop cryptographic algorithms that are secure against quantum computers and can be easily integrated into existing protocols and networks.
Quantum proof algorithms
Due to the risk posed by quantum computers, the National Institute of Standards and Technology (NIST) has been examining new approaches to encryption and out of the initial 69 submissions received three years ago, the group has narrowed the field down to 15 finalists and has now begun the third round of public review of the algorithms (Moody et al., 2020) to help decide the core of the first post-quantum cryptography standard. They are expecting to end the round with one or two algorithms for encryption and key establishment, and one or two others for digital signatures (Moody et al., 2020).
Quantum Key Distribution
Quantum Key Distribution (QKD) uses the characteristics of quantum computing to implement a secure communication channel allowing users to exchange a random secret key that can then be used for symmetrical encryption (IDQ, 2020). QKD solves the problem of secure key exchange for symmetrical encryption algorithms and it has the capability to detect the presence of any third party attempting to eavesdrop on the key exchange. If there is an attempt by a third-party to eavesdrop on the exchange, they will create anomalies in the quantum superpositions and quantum entanglement which will alert the parties to the presence of an eavesdropper, at which point the key generation will be aborted (IDQ, 2020). The QKD is used to only produce and distribute an encryption key securely, not to transmit any data. Once the key is exchanged it can be used with any symmetric encryption algorithm to transmit data securely.
Conclusion
Development of a quantum computer may be 100 years off or may be invented in the next decade, but we can be sure that once they are invented, they will change the face of computing forever including the field of cryptography. However, we should not panic as this is not the end of the world as the work on quantum resistant algorithms is going much faster than the work on creating a quantum computer. The world’s top cryptographic experts have been working on Quantum safe encryption for the past three years and we are nearing the completion of the world’s first post-quantum cryptography standard (Moody et al., 2020). Even if the worst happens and it is not possible to create a quantum safe algorithm immediately, we still have the ability to encrypt and decrypt data using one-time pads until a safer alternative or a new technology is developed.
References
Chen, L., Jordan, S., Liu, Y.-K., Moody, D., Peralta, R., Perlner, R., & Smith-Tone, D. (2016). Report on Post-Quantum Cryptography. https://doi.org/10.6028/nist.ir.8105
Cho, A. (2020, September 15). IBM promises 1000-qubit quantum computer-a milestone-by 2023. Science. https://www.sciencemag.org/news/2020/09/ibm-promises-1000-qubit-quantum-computer-milestone-2023.
Clarke, J. (2019, March). An Optimist’s View of the Challenges to Quantum Computing. IEEE Spectrum: Technology, Engineering, and Science News. https://spectrum.ieee.org/tech-talk/computing/hardware/an-optimists-view-of-the-4-challenges-to-quantum-computing.
Diffie, W., & Hellman, M. (1976). New directions in cryptography. IEEE Transactions on Information Theory, 22(6), 644–654. https://doi.org/10.1109/tit.1976.1055638
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Gambetta, J., Nazario, Z., & Chow, J. (2020, October 21). Charting the Course for the Future of Quantum Computing. IBM Research Blog. https://www.ibm.com/blogs/research/2020/08/quantum-research-centers/.
Garisto, D. (2020, May 4). Quantum computers won’t break encryption just yet. https://www.protocol.com/manuals/quantum-computing/quantum-computers-wont-break-encryption-yet.
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Rouse, M., Brush, K., Rosencrance, L., & Cobb, M. (2020, March 20). What is Asymmetric Cryptography and How Does it Work? SearchSecurity. https://searchsecurity.techtarget.com/definition/asymmetric-cryptography.
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Vepsäläinen, A. P., Karamlou, A. H., Orrell, J. L., Dogra, A. S., Loer, B., Vasconcelos, F., David, K. K., Melville A. J., Niedzielski B. M., Yoder J. L., Gustavsson, S., Formaggio J. A., VanDevender B. A., & Oliver, W. D. (2020). Impact of ionizing radiation on superconducting qubit coherence. Nature, 584(7822), 551–556. https://doi.org/10.1038/s41586-020-2619-8
Note: This was originally written as a paper for one of my classes at EC-Council University in Q4 2020, which is why the tone is a lot more formal than my regular posts.
– Suramya
