How can quantum computing be used today?

Quantum computers - an acute threat to encryption?

What influence do quantum computers and the use of quantum informatics have on current encryption methods? What are the benefits of developing such computers? And how will the methods used today develop? Fabian Hauser, who has been part of our tech team since March 2021, dealt with these questions in his bachelor thesis. In the following we present an excerpt from his work.

Quantum computers and their potential effects on current encryption methods

Nowadays there is a wide variety of encryption methods for a wide variety of areas of application. These procedures often use their own methods to disguise the message. For example, in the public key encryption process, finding a pair of keys is based on mathematical problems (1), which even the most powerful supercomputers cannot solve in practice. However, what happens if the problems on which these methods are based can suddenly be solved by another type of computer? As early as 1997, Peter Shor showed that it is theoretically possible to use quantum mechanics to solve two of these problems, prime factorization and finding discrete logarithms (2).

There are still several different mathematical problems today that cannot be calculated efficiently on universal calculators, including factoring whole numbers and finding discrete logarithms. Because of this lack of efficient computation, several encryption schemes have resulted from these two problems, e.g. B. the elliptic curve method (ECC) (3) and RSA (4). For example, should the average computer attempt an RSA using the National Institute of Standards and Technology (NIST) recommended key length 2048-bit to crack and thus solve its prime factorization, it would take a time of need over 14 billion years (6).

In 1997, however, Peter Shor published a paper in which he presented methods that can theoretically solve these problems on a quantum computer (2). Since then, it has been clear that current encryption methods are in acute danger due to the completion of powerful quantum computers.

Encryption of files using Boxcryptor as an example

But let's first take a look at the encryption methods currently used in practice using the example of Boxcryptor encryption software at. At Boxcryptor, files are encrypted as follows: First of all, a random and secure one is created for each file File key generated. This key is a AES key and in the next step is also responsible for the encryption and decryption of the plain text of the file. In addition to these File keys each user has their own RSA key pair (User key) with a public and a private key, which comes into action in the next step. The previously generated File key encrypted with the public key of the RSA. Finally, this is encrypted File key saved with the previously encrypted data in the encrypted file.

When decrypting the file at a later point in time, this procedure is reversed and when the file is decrypted again, the procedure is reversed. At first the File key using the private User key decrypted and then the encrypted content of this file is decrypted again with it. An AES algorithm "with a key length of 256 bits, CBC (Cipher Block Chaining) and PKCS7 padding" is used for the file key, while an RSA algorithm "with a key length of 4096 bits and OAEP padding" is used for the user key.

When looking at the file encryption chain described above, however, it is noticeable that this sequence depends on the secrecy of the private RSA key is. Should attackers get at this, the file key can be decrypted, and thus also the content of the file.

For this very reason, Secomba GmbH, as the operator of Boxcryptor, is also interested in the progress in encryption technology. If, in a few years, quantum computers are powerful enough to crack RSA encryption with 4096 bits, the security of all customer data would no longer be guaranteed. In order to protect the sensitive documents of the users against attacks such as B. to secure industrial espionage, the encryption solution Boxcryptor must also be able to guarantee the security of the data in a post-quantum time.

Status quo and current challenges when using quantum computers

23 years after Peter Shor was able to show in theory that it is possible with the use of quantum mechanics to solve the prime factorization and the finding of discrete logarithms, the research is at a very advanced level. The first quantum computers now create a faster calculation of such math problems as the best supercomputers in the world (7). However, current quantum computers require a long computation time for smaller combinatorial problems. This is particularly due to the high Susceptibility to errors, the by external influences such as vibrations, temperature fluctuations or electromagnetic waves is reinforced (8).

Therefore, algorithms on this type of computer have to go through a certain number of iterations in order to get a realistic result. The disadvantage is that this repeated execution in most cases loses the previously gained computing time, since otherwise the error rate would be too high.

Experts assume that the development of universal quantum computers will take around 20 years (9 & 10), but nevertheless the development of the last 20 years has to be considered. Only a few scientists could have imagined that the first quantum computers with 54 qubits (Google's Sycamore) are already available today and that the algorithms developed in theory at the time, such as e.g. B. Shor can already be applied in practice in some cases. Accordingly, it is difficult to predict the extent to which this research area will develop further, as even single breakthroughs can mean great advances.

But there are still some issues that need to be resolved, such as: B. effective cooling of the system so that the qubits are protected from external temperature effects. If one of these turns out to be particularly complex and the solution takes several years, progress can quickly stagnate. According to the current state of research, however, there are still no such powerful quantum computers that endanger the methods currently used, and probably also those of the next decade.

Excursus: Quantum computers and simulation platforms: IBM Quantum Composer and Microsoft Q

So far, a few companies have managed to build quantum computers with just a few qubits. For example Paris 53 qubit from IBM (11) or Sycamore 54 qubit from Google (12). However, these are mainly intended for research. Private individuals have no way of experimenting with it. Due to the increasing interest of the general public, it is only logical that more and more people turn to this topic in order to gain initial experience in this area. To meet this demand, several companies have already started trials, so-called Simulation platforms of quantum computers to develop which are freely accessible and enable the handling of quantum bits.

Since simulation platforms are run on classic computers, they obviously have no access to qubits due to the physical conditions. For the simulation of n Qubits, however, the machine needs a storage capacity and calculation time of 22N (13, p. 1073). If you should now calculate with numbers that need a few bits to represent, the computing effort for the platforms increases enormously, which is ultimately reflected in a very long calculation time.

IBM Quantum Composer and Microsoft Q # are two well-known platforms through which private individuals who are interested in the development of quantum algorithms can carry out smaller experiments and thus set foot in the world of quantum computing.

IBM Quantum Composer

The Quantum Composer offers a very easy introduction to quantum computing, as it is a graphical interface with which entire quantum circuits can be clicked together with a simple drag and drop. The advantage here is that no programming language has to be learned and individual algorithms can easily be recreated in order to understand how quantum algorithms and qubits work. In addition, there is the possibility of executing the built circuits either on simulations or real quantum computers without major detours.

Microsoft Q

In 2017, Microsoft announced its own programming language specifically for quantum computers at the annual Ignite conference. This open-source programming language is part of the Quantum Development Kit (QDK) from Microsoft, which includes Q # libraries, a simulator and extensions for other programming environments. The syntax of Q # has strong influences from Python, C # and F # and, in addition to new quantum technical operations and data structures, also includes common programming components such as: B. Loops or If-Else branches. Here all common quantum gates are implemented and syntactically quite similarly executable.

Conclusion

Quantum computing is a very exciting topic and, compared to previous years, it is no longer a completely theoretical one. With the help of simulation platforms, interested private individuals can now work with qubits and thus recreate the first quantum algorithms. This is an important step as it increases general interest in the topic and more and more recognizes the importance of this research area. Even if a universal quantum computer were to be developed in the long term, it will never replace the digital computer we are familiar with, but it will be used as a certain supplement for individual problems.

With regard to encryption methods in particular, it is an interesting aspect that, with the development of such a computer, previous methods can be regarded as unsafe, but at the same time a rethinking is taking place, since new paths are also opened up for other methods. “Quantum cryptography” deals with these new possible methods. Nevertheless, neither the quantum computers nor the post-quantum methods are at a level that can be used in practice today.

However, we will keep an eye on the subject of quantum computing. Should the progress of science in this area progress faster than previously assumed, we, the Secomba GmbH team, will react, and our new colleague Fabian Hauser will respond Implementation of a post-quantum encryption process accept. Until then, however, you can be sure that your sensitive data will remain your secret.

(1) Martin E. Hellman. "The Mathematics of Public-Key Cryptography". en. In: Scientific American 241.2 (Aug. 1979), pp. 146-157. ISSN: 0036-8733. DOI: 10.1038 / scientificamerican0879-146.

(2) Peter W. Shor. "Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer". In: SIAM Journal on Computing 26.5 (Oct. 1997), pp. 1484-1509. ISSN: 0097-5397, 1095-7111. DOI: 10. 1137 / S0097539795293172. arXiv: quant - ph / 9508027.

(3) Sheetal Kalra and Sandeep K. Sood. "Elliptic Curve Cryptography: Current Status and Research Challenges". In: High Performance Architecture and Grid Computing. Edited by Archana Mantri et al. Communications in Computer and Information Science. Berlin, Heidelberg: Springer, 2011, pp. 455-460. ISBN: 978-3-642-22577-2. DOI: 10.1007 / 978-3-642-22577-2_62.

(4) R. L. Rivest, A. Shamir, and L. Adleman. "A Method for Obtaining Digital Signatures and Public-Key Cryptosystems". In: Communications of the ACM 21.2 (Feb. 1978), pp. 120-126. ISSN: 0001-0782. DOI: 10.1145 / 359340.359342.

(5) Elaine B. Barker and Quynh H. Dang. Recommendation for Key Management Part 3: Application-Specific Key Management Guidance. en. Techn. Ber. NIST SP 800-57Pt3r1. National Institute of Standards and Technology, Jan. 2015, NIST SP 800-57Pt3r1. DOI: 10.6028 / NIST.SP. 800-57Pt3r1.

(6) All about SSL Cryptography. URL: https://www.digicert.com/faq/ssl-cryptography.htm.

(7) Rafi last. China Claims It’s Achieved ’Quantum Supremacy’ With The World’s Fastest Quantum Computer. Aug. 2020. URL: https://www.sciencealert.com/china-has-developed-the-fastestand-most-powerful-quantum-computer-yet

(8) Maximilian Schlosshauer. "Quantum Decoherence". In: Physics Reports 831 (Oct. 2019), 1? 57. ISSN: 0370-1573. DOI: 10.1016 / j.physrep. 2019.10.001.

(9) Wolfgang Marquardt. "In the next 20 years the quantum computer will become a reality". June 2020.

(10) Wolfgang Wernsdorfer. Quantum computers only in 20 years? May 2017.

(11) Edwin Pednault and John Gunnels. On "Quantum Supremacy". Oct. 2019. URL: https://www.ibm.com/blogs/research/2019/10/onquantum-supremacy/.

(12) Elizabeth Gibney. "Hello Quantum World! Google Publishes Landmark Quantum Supremacy Claim ". In: Nature 574.7779 (Oct. 2019), pp. 461-462. DOI: 10.1038 / d41586-019-03213-z.

(13) Seth Lloyd. "Universal Quantum Simulator". In: American Association for the Advancement of Science. New Series 273 (Aug 1996), pp. 1073-1078.

(14) Wolfgang Wernsdorfer. Quantum computers only in 20 years? May 2017.

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